www.happycoders.eu Open in urlscan Pro
2606:4700:20::681a:de0  Public Scan

URL: https://www.happycoders.eu/algorithms/big-o-notation-time-complexity/
Submission: On October 09 via api from US — Scanned from DE

Form analysis 5 forms found in the DOM

POST https://app.convertkit.com/forms/2803778/subscriptions

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        <h2>Free Bonus:</h2>
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        <h2>Big O Cheat Sheet</h2>
        <h3>[7 Time Complexity Classes on 1 Page] </h3>
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        </h2>
        <p>Use this 1-page PDF cheat sheet as a reference to quickly look up the seven most important time complexity classes (with descriptions and examples). </p>
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          </div><span class="">Send Me the Cheat Sheet Now!</span>
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        <p style="text-align:center">You get access to this PDF by signing up for my newsletter. I won’t send any spam, and you can opt-out at any time. </p>
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    .formkit-form[data-uid="44f1fea9fb"] blockquote {
      padding: 10px 20px;
      margin: 0 0 20px;
      border-left: 5px solid #e1e1e1;
    }

    .formkit-form[data-uid="44f1fea9fb"] .seva-custom-content {
      padding: 15px;
      font-size: 16px;
      color: #fff;
      mix-blend-mode: difference;
    }

    .formkit-form[data-uid="44f1fea9fb"] {
      box-shadow: 0px 4px 8px rgba(105, 113, 119, 0.2);
      max-width: 740px !important;
      overflow: hidden;
    }

    .formkit-form[data-uid="44f1fea9fb"] [data-style="full"] {
      width: 100%;
      display: -webkit-box;
      display: -webkit-flex;
      display: -ms-flexbox;
      display: flex;
      -webkit-flex-direction: column;
      -ms-flex-direction: column;
      flex-direction: column;
    }

    .formkit-form[data-uid="44f1fea9fb"] .formkit-background {
      background-position: center center;
      background-size: cover;
      height: 280px;
      margin: 20px;
      border-radius: var(--bg-border-radius) !important;
    }

    .formkit-form[data-uid="44f1fea9fb"] .formkit-column {
      padding: 20px;
      position: relative;
      -webkit-order: 2;
      -ms-flex-order: 2;
      order: 2;
    }

    .formkit-form[data-uid="44f1fea9fb"] .formkit-header {
      margin-top: 0;
      margin-bottom: 24px;
      font-weight: 700;
      font-size: calc(30px + (36 - 30) * ((100vw - 400px) / (600 - 400)));
    }

    @media all and (min-width:800px) {
      .formkit-form[data-uid="44f1fea9fb"] .formkit-header {
        font-size: 36px;
      }
    }

    .formkit-form[data-uid="44f1fea9fb"] .formkit-header h2 {
      line-height: 1.2;
      margin-top: 0;
    }

    .formkit-form[data-uid="44f1fea9fb"] .formkit-content {
      margin-bottom: 45px;
      font-size: 16px;
    }

    .formkit-form[data-uid="44f1fea9fb"] .formkit-fields {
      display: -webkit-box;
      display: -webkit-flex;
      display: -ms-flexbox;
      display: flex;
      -webkit-flex-wrap: wrap;
      -ms-flex-wrap: wrap;
      flex-wrap: wrap;
    }

    .formkit-form[data-uid="44f1fea9fb"] .formkit-field {
      margin: 0 0 10px 0;
    }

    .formkit-form[data-uid="44f1fea9fb"] .formkit-input {
      width: 100%;
      border: 0;
      padding-left: 12px;
      padding-right: 0;
      height: 47px;
      font-size: 14px;
    }

    .formkit-form[data-uid="44f1fea9fb"] .formkit-select {
      padding-top: 13px !important;
      padding-bottom: 13px !important;
      border: 0 !important;
    }

    .formkit-form[data-uid="44f1fea9fb"] .formkit-checkboxes {
      background: transparent !important;
      color: inherit !important;
    }

    .formkit-form[data-uid="44f1fea9fb"] .formkit-fields .formkit-submit {
      margin-top: 8px;
      font-size: 12px;
      height: 47px;
    }

    .formkit-form[data-uid="44f1fea9fb"] .formkit-fields .formkit-submit span {
      padding: 15px 14px;
    }

    .formkit-form[data-uid="44f1fea9fb"] .formkit-fields[data-stacked="false"] {
      margin-left: -4px;
      margin-right: -4px;
      display: -webkit-box;
      display: -webkit-flex;
      display: -ms-flexbox;
      display: flex;
    }

    .formkit-form[data-uid="44f1fea9fb"] .formkit-fields[data-stacked="false"] .formkit-submit {
      -webkit-flex: 1 1 auto !important;
      -ms-flex: 1 1 auto !important;
      flex: 1 1 auto !important;
      margin: 0 !important;
      min-width: 90px;
    }

    .formkit-form[data-uid="44f1fea9fb"] .formkit-fields[data-stacked="false"] .formkit-field,
    .formkit-form[data-uid="44f1fea9fb"] .formkit-fields[data-stacked="false"] .formkit-submit {
      margin: 0 4px 8px 4px !important;
    }

    .formkit-form[data-uid="44f1fea9fb"] .formkit-fields[data-stacked="false"] .formkit-field {
      -webkit-flex: 100 1 auto !important;
      -ms-flex: 100 1 auto !important;
      flex: 100 1 auto !important;
      margin: 0;
    }

    .formkit-form[data-uid="44f1fea9fb"] .formkit-powered-by-convertkit-container {
      margin: 20px 0 0 0;
    }

    .formkit-form[data-uid="44f1fea9fb"] .formkit-disclaimer {
      font-size: 12px;
      opacity: 0.6;
      margin-top: 6px;
    }

    .formkit-form[data-uid="44f1fea9fb"] .formkit-field,
    .formkit-form[data-uid="44f1fea9fb"] .formkit-submit {
      margin: 0 0 8px 0;
      -webkit-flex: 1 0 100%;
      -ms-flex: 1 0 100%;
      flex: 1 0 100%;
    }

    @media screen and (min-width:600px) {
      .formkit-form[data-uid="44f1fea9fb"] [data-style="full"] {
        -webkit-flex-direction: row;
        -ms-flex-direction: row;
        flex-direction: row;
      }

      .formkit-form[data-uid="44f1fea9fb"] [data-style="full"] .formkit-column {
        width: 57%;
      }

      .formkit-form[data-uid="44f1fea9fb"] [data-style="full"] .formkit-background {
        width: 44%;
        height: auto;
        margin-left: 0;
        -webkit-order: 2;
        -ms-flex-order: 2;
        order: 2;
      }

      .formkit-slide-in,
      .preview .formkit-form[data-uid="44f1fea9fb"][data-format="slide in"],
      .formkit-form[data-uid="44f1fea9fb"][data-format="slide in-editing"] {
        max-width: 450px !important;
      }

      .formkit-slide-in [data-style="full"],
      .preview .formkit-form[data-uid="44f1fea9fb"][data-format="slide in"] [data-style="full"],
      .formkit-form[data-uid="44f1fea9fb"][data-format="slide in-editing"] [data-style="full"] {
        -webkit-flex-direction: column !important;
        -ms-flex-direction: column !important;
        flex-direction: column !important;
        max-width: 450px !important;
      }

      .formkit-slide-in .formkit-background,
      .preview .formkit-form[data-uid="44f1fea9fb"][data-format="slide in"] .formkit-background,
      .formkit-form[data-uid="44f1fea9fb"][data-format="slide in-editing"] .formkit-background {
        width: auto !important;
        height: 280px !important;
        margin: 20px !important;
        -webkit-order: 0 !important;
        -ms-flex-order: 0 !important;
        order: 0 !important;
      }

      .formkit-slide-in .formkit-column,
      .preview .formkit-form[data-uid="44f1fea9fb"][data-format="slide in"] .formkit-column,
      .formkit-form[data-uid="44f1fea9fb"][data-format="slide in-editing"] .formkit-column {
        width: 100% !important;
        -webkit-order: 2 !important;
        -ms-flex-order: 2 !important;
        order: 2 !important;
        padding: 20px 20px 30px 20px !important;
      }

      .formkit-slide-in .formkit-content,
      .preview .formkit-form[data-uid="44f1fea9fb"][data-format="slide in"] .formkit-content,
      .formkit-form[data-uid="44f1fea9fb"][data-format="slide in-editing"] .formkit-content {
        margin-bottom: 25px !important;
      }

      .formkit-form[data-uid="44f1fea9fb"] .formkit-column {
        padding: 55px 60px 55px 45px;
      }
    }

    .formkit-form[data-uid="44f1fea9fb"] {
      border: 5px solid #e8e8e8;
      box-shadow: none;
      max-width: 800px !important;
    }

    .formkit-form[data-uid="44f1fea9fb"] p {
      margin: 0;
    }

    .formkit-form[data-uid="44f1fea9fb"] .formkit-column {
      padding: 20px;
    }

    .formkit-form[data-uid="44f1fea9fb"] .formkit-header {
      margin: 0;
    }

    .formkit-form[data-uid="44f1fea9fb"] .formkit-header h2 {
      font-family: "Open Sans", sans-serif;
      font-size: 24px !important;
      overflow: visible;
      margin: 0;
    }

    .formkit-form[data-uid="44f1fea9fb"] .formkit-content {
      margin-bottom: 20px;
    }

    .formkit-form[data-uid="44f1fea9fb"] .formkit-content h2 {
      font-size: 40px !important;
      font-family: "Open Sans", sans-serif;
      font-weight: 600;
      color: #1080b6;
      overflow: visible;
      margin: 0;
      line-height: 1.1;
    }

    .formkit-form[data-uid="44f1fea9fb"] .formkit-content h3 {
      font-family: "Open Sans", sans-serif;
      font-size: 22px !important;
      font-weight: 400;
      color: #222;
      margin: 0 0 20px 0;
    }

    .formkit-form[data-uid="44f1fea9fb"] .formkit-input {
      font-size: 16px;
    }

    .formkit-form[data-uid="44f1fea9fb"] .formkit-fields .formkit-submit {
      font-family: "Open Sans", sans-serif;
      font-size: 16px;
      height: auto;
    }

    @media screen and (min-width:600px) {
      .formkit-form[data-uid="44f1fea9fb"] .formkit-column {
        width: 62% !important;
      }
    }

    @media screen and (max-width:480px) {
      .formkit-form[data-uid="44f1fea9fb"] .formkit-content h2 {
        font-size: 32px !important;
      }

      .formkit-form[data-uid="44f1fea9fb"] .formkit-content h3 {
        font-size: 17px !important;
      }
    }
  </style>
</form>

POST https://app.convertkit.com/forms/2803997/subscriptions

<form action="https://app.convertkit.com/forms/2803997/subscriptions" style="background-color:#ffffff;border-radius:0" class="seva-form formkit-form" method="post" data-sv-form="2803997" data-uid="f24402b59d" data-format="inline" data-version="5"
  min-width="400 500 600 700 800">
  <div data-style="full" style="--bg-border-radius:0px">
    <div data-element="column" class="formkit-column">
      <div class="formkit-header" style="color:#e67c00;font-weight:700" data-element="header">
        <h2>Free Bonus:</h2>
      </div>
      <div class="formkit-content" style="color:#444444" data-element="content">
        <h2>Big O Cheat Sheet</h2>
        <h3>[7 Time Complexity Classes on 1 Page] </h3>
        <h2>
        </h2>
        <p>Use this 1-page PDF cheat sheet as a reference to quickly look up the seven most important time complexity classes (with descriptions and examples). </p>
        <p>
        </p>
      </div>
      <ul class="formkit-alert formkit-alert-error" data-element="errors" data-group="alert"></ul>
      <div data-element="fields" data-stacked="true" class="seva-fields formkit-fields">
        <div class="formkit-field"><input type="text" class="formkit-input" aria-label="First name..." style="color:#222222;background-color:#F3F6F9;border-radius:5px;font-weight:400" name="fields[first_name]" required="" placeholder="First name...">
        </div>
        <div class="formkit-field"><input type="text" class="formkit-input" name="email_address" style="color:#222222;background-color:#F3F6F9;border-radius:5px;font-weight:400" aria-label="Email address..." placeholder="Email address..."
            required=""></div><button data-element="submit" class="formkit-submit formkit-submit" style="color:#ffffff;background-color:#1080b6;border-radius:5px;font-weight:700">
          <div class="formkit-spinner">
            <div></div>
            <div></div>
            <div></div>
          </div><span class="">Send Me the Cheat Sheet Now!</span>
        </button>
      </div>
      <div class="formkit-disclaimer" style="color:#000000" data-element="disclaimer">
        <p style="text-align:center">You get access to this PDF by signing up for my newsletter. I won’t send any spam, and you can opt-out at any time. </p>
      </div>
    </div>
    <div data-element="column" style="background-image:url('https://embed.filekitcdn.com/e/jmhVdGmaCp95jv6nesQHe/8Hx1tGdnVsX5gbyqoUwwmv')" class="formkit-background"></div>
  </div>
  <style>
    .formkit-form[data-uid="f24402b59d"] * {
      box-sizing: border-box;
    }

    .formkit-form[data-uid="f24402b59d"] {
      -webkit-font-smoothing: antialiased;
      -moz-osx-font-smoothing: grayscale;
    }

    .formkit-form[data-uid="f24402b59d"] legend {
      border: none;
      font-size: inherit;
      margin-bottom: 10px;
      padding: 0;
      position: relative;
      display: table;
    }

    .formkit-form[data-uid="f24402b59d"] fieldset {
      border: 0;
      padding: 0.01em 0 0 0;
      margin: 0;
      min-width: 0;
    }

    .formkit-form[data-uid="f24402b59d"] body:not(:-moz-handler-blocked) fieldset {
      display: table-cell;
    }

    .formkit-form[data-uid="f24402b59d"] h1,
    .formkit-form[data-uid="f24402b59d"] h2,
    .formkit-form[data-uid="f24402b59d"] h3,
    .formkit-form[data-uid="f24402b59d"] h4,
    .formkit-form[data-uid="f24402b59d"] h5,
    .formkit-form[data-uid="f24402b59d"] h6 {
      color: inherit;
      font-size: inherit;
      font-weight: inherit;
    }

    .formkit-form[data-uid="f24402b59d"] h2 {
      font-size: 1.5em;
      margin: 1em 0;
    }

    .formkit-form[data-uid="f24402b59d"] h3 {
      font-size: 1.17em;
      margin: 1em 0;
    }

    .formkit-form[data-uid="f24402b59d"] p {
      color: inherit;
      font-size: inherit;
      font-weight: inherit;
    }

    .formkit-form[data-uid="f24402b59d"] ol:not([template-default]),
    .formkit-form[data-uid="f24402b59d"] ul:not([template-default]),
    .formkit-form[data-uid="f24402b59d"] blockquote:not([template-default]) {
      text-align: left;
    }

    .formkit-form[data-uid="f24402b59d"] p:not([template-default]),
    .formkit-form[data-uid="f24402b59d"] hr:not([template-default]),
    .formkit-form[data-uid="f24402b59d"] blockquote:not([template-default]),
    .formkit-form[data-uid="f24402b59d"] ol:not([template-default]),
    .formkit-form[data-uid="f24402b59d"] ul:not([template-default]) {
      color: inherit;
      font-style: initial;
    }

    .formkit-form[data-uid="f24402b59d"] .ordered-list,
    .formkit-form[data-uid="f24402b59d"] .unordered-list {
      list-style-position: outside !important;
      padding-left: 1em;
    }

    .formkit-form[data-uid="f24402b59d"] .list-item {
      padding-left: 0;
    }

    .formkit-form[data-uid="f24402b59d"][data-format="modal"] {
      display: none;
    }

    .formkit-form[data-uid="f24402b59d"][data-format="slide in"] {
      display: none;
    }

    .formkit-form[data-uid="f24402b59d"][data-format="sticky bar"] {
      display: none;
    }

    .formkit-sticky-bar .formkit-form[data-uid="f24402b59d"][data-format="sticky bar"] {
      display: block;
    }

    .formkit-form[data-uid="f24402b59d"] .formkit-input,
    .formkit-form[data-uid="f24402b59d"] .formkit-select,
    .formkit-form[data-uid="f24402b59d"] .formkit-checkboxes {
      width: 100%;
    }

    .formkit-form[data-uid="f24402b59d"] .formkit-button,
    .formkit-form[data-uid="f24402b59d"] .formkit-submit {
      border: 0;
      border-radius: 5px;
      color: #ffffff;
      cursor: pointer;
      display: inline-block;
      text-align: center;
      font-size: 15px;
      font-weight: 500;
      cursor: pointer;
      margin-bottom: 15px;
      overflow: hidden;
      padding: 0;
      position: relative;
      vertical-align: middle;
    }

    .formkit-form[data-uid="f24402b59d"] .formkit-button:hover,
    .formkit-form[data-uid="f24402b59d"] .formkit-submit:hover,
    .formkit-form[data-uid="f24402b59d"] .formkit-button:focus,
    .formkit-form[data-uid="f24402b59d"] .formkit-submit:focus {
      outline: none;
    }

    .formkit-form[data-uid="f24402b59d"] .formkit-button:hover>span,
    .formkit-form[data-uid="f24402b59d"] .formkit-submit:hover>span,
    .formkit-form[data-uid="f24402b59d"] .formkit-button:focus>span,
    .formkit-form[data-uid="f24402b59d"] .formkit-submit:focus>span {
      background-color: rgba(0, 0, 0, 0.1);
    }

    .formkit-form[data-uid="f24402b59d"] .formkit-button>span,
    .formkit-form[data-uid="f24402b59d"] .formkit-submit>span {
      display: block;
      -webkit-transition: all 300ms ease-in-out;
      transition: all 300ms ease-in-out;
      padding: 12px 24px;
    }

    .formkit-form[data-uid="f24402b59d"] .formkit-input {
      background: #ffffff;
      font-size: 15px;
      padding: 12px;
      border: 1px solid #e3e3e3;
      -webkit-flex: 1 0 auto;
      -ms-flex: 1 0 auto;
      flex: 1 0 auto;
      line-height: 1.4;
      margin: 0;
      -webkit-transition: border-color ease-out 300ms;
      transition: border-color ease-out 300ms;
    }

    .formkit-form[data-uid="f24402b59d"] .formkit-input:focus {
      outline: none;
      border-color: #1677be;
      -webkit-transition: border-color ease 300ms;
      transition: border-color ease 300ms;
    }

    .formkit-form[data-uid="f24402b59d"] .formkit-input::-webkit-input-placeholder {
      color: inherit;
      opacity: 0.8;
    }

    .formkit-form[data-uid="f24402b59d"] .formkit-input::-moz-placeholder {
      color: inherit;
      opacity: 0.8;
    }

    .formkit-form[data-uid="f24402b59d"] .formkit-input:-ms-input-placeholder {
      color: inherit;
      opacity: 0.8;
    }

    .formkit-form[data-uid="f24402b59d"] .formkit-input::placeholder {
      color: inherit;
      opacity: 0.8;
    }

    .formkit-form[data-uid="f24402b59d"] [data-group="dropdown"] {
      position: relative;
      display: inline-block;
      width: 100%;
    }

    .formkit-form[data-uid="f24402b59d"] [data-group="dropdown"]::before {
      content: "";
      top: calc(50% - 2.5px);
      right: 10px;
      position: absolute;
      pointer-events: none;
      border-color: #4f4f4f transparent transparent transparent;
      border-style: solid;
      border-width: 6px 6px 0 6px;
      height: 0;
      width: 0;
      z-index: 999;
    }

    .formkit-form[data-uid="f24402b59d"] [data-group="dropdown"] select {
      height: auto;
      width: 100%;
      cursor: pointer;
      color: #333333;
      line-height: 1.4;
      margin-bottom: 0;
      padding: 0 6px;
      -webkit-appearance: none;
      -moz-appearance: none;
      appearance: none;
      font-size: 15px;
      padding: 12px;
      padding-right: 25px;
      border: 1px solid #e3e3e3;
      background: #ffffff;
    }

    .formkit-form[data-uid="f24402b59d"] [data-group="dropdown"] select:focus {
      outline: none;
    }

    .formkit-form[data-uid="f24402b59d"] [data-group="checkboxes"] {
      text-align: left;
      margin: 0;
    }

    .formkit-form[data-uid="f24402b59d"] [data-group="checkboxes"] [data-group="checkbox"] {
      margin-bottom: 10px;
    }

    .formkit-form[data-uid="f24402b59d"] [data-group="checkboxes"] [data-group="checkbox"] * {
      cursor: pointer;
    }

    .formkit-form[data-uid="f24402b59d"] [data-group="checkboxes"] [data-group="checkbox"]:last-of-type {
      margin-bottom: 0;
    }

    .formkit-form[data-uid="f24402b59d"] [data-group="checkboxes"] [data-group="checkbox"] input[type="checkbox"] {
      display: none;
    }

    .formkit-form[data-uid="f24402b59d"] [data-group="checkboxes"] [data-group="checkbox"] input[type="checkbox"]+label::after {
      content: none;
    }

    .formkit-form[data-uid="f24402b59d"] [data-group="checkboxes"] [data-group="checkbox"] input[type="checkbox"]:checked+label::after {
      border-color: #ffffff;
      content: "";
    }

    .formkit-form[data-uid="f24402b59d"] [data-group="checkboxes"] [data-group="checkbox"] input[type="checkbox"]:checked+label::before {
      background: #10bf7a;
      border-color: #10bf7a;
    }

    .formkit-form[data-uid="f24402b59d"] [data-group="checkboxes"] [data-group="checkbox"] label {
      position: relative;
      display: inline-block;
      padding-left: 28px;
    }

    .formkit-form[data-uid="f24402b59d"] [data-group="checkboxes"] [data-group="checkbox"] label::before,
    .formkit-form[data-uid="f24402b59d"] [data-group="checkboxes"] [data-group="checkbox"] label::after {
      position: absolute;
      content: "";
      display: inline-block;
    }

    .formkit-form[data-uid="f24402b59d"] [data-group="checkboxes"] [data-group="checkbox"] label::before {
      height: 16px;
      width: 16px;
      border: 1px solid #e3e3e3;
      background: #ffffff;
      left: 0px;
      top: 3px;
    }

    .formkit-form[data-uid="f24402b59d"] [data-group="checkboxes"] [data-group="checkbox"] label::after {
      height: 4px;
      width: 8px;
      border-left: 2px solid #4d4d4d;
      border-bottom: 2px solid #4d4d4d;
      -webkit-transform: rotate(-45deg);
      -ms-transform: rotate(-45deg);
      transform: rotate(-45deg);
      left: 4px;
      top: 8px;
    }

    .formkit-form[data-uid="f24402b59d"] .formkit-alert {
      background: #f9fafb;
      border: 1px solid #e3e3e3;
      border-radius: 5px;
      -webkit-flex: 1 0 auto;
      -ms-flex: 1 0 auto;
      flex: 1 0 auto;
      list-style: none;
      margin: 25px auto;
      padding: 12px;
      text-align: center;
      width: 100%;
    }

    .formkit-form[data-uid="f24402b59d"] .formkit-alert:empty {
      display: none;
    }

    .formkit-form[data-uid="f24402b59d"] .formkit-alert-success {
      background: #d3fbeb;
      border-color: #10bf7a;
      color: #0c905c;
    }

    .formkit-form[data-uid="f24402b59d"] .formkit-alert-error {
      background: #fde8e2;
      border-color: #f2643b;
      color: #ea4110;
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    }

    @-webkit-keyframes formkit-bouncedelay-formkit-form-data-uid-f24402b59d- {

      0%,
      80%,
      100% {
        -webkit-transform: scale(0);
        -ms-transform: scale(0);
        transform: scale(0);
      }

      40% {
        -webkit-transform: scale(1);
        -ms-transform: scale(1);
        transform: scale(1);
      }
    }

    @keyframes formkit-bouncedelay-formkit-form-data-uid-f24402b59d- {

      0%,
      80%,
      100% {
        -webkit-transform: scale(0);
        -ms-transform: scale(0);
        transform: scale(0);
      }

      40% {
        -webkit-transform: scale(1);
        -ms-transform: scale(1);
        transform: scale(1);
      }
    }

    .formkit-form[data-uid="f24402b59d"] blockquote {
      padding: 10px 20px;
      margin: 0 0 20px;
      border-left: 5px solid #e1e1e1;
    }

    .formkit-form[data-uid="f24402b59d"] .seva-custom-content {
      padding: 15px;
      font-size: 16px;
      color: #fff;
      mix-blend-mode: difference;
    }

    .formkit-form[data-uid="f24402b59d"] {
      box-shadow: 0px 4px 8px rgba(105, 113, 119, 0.2);
      max-width: 740px !important;
      overflow: hidden;
    }

    .formkit-form[data-uid="f24402b59d"] [data-style="full"] {
      width: 100%;
      display: -webkit-box;
      display: -webkit-flex;
      display: -ms-flexbox;
      display: flex;
      -webkit-flex-direction: column;
      -ms-flex-direction: column;
      flex-direction: column;
    }

    .formkit-form[data-uid="f24402b59d"] .formkit-background {
      background-position: center center;
      background-size: cover;
      height: 280px;
      margin: 20px;
      border-radius: var(--bg-border-radius) !important;
    }

    .formkit-form[data-uid="f24402b59d"] .formkit-column {
      padding: 20px;
      position: relative;
      -webkit-order: 2;
      -ms-flex-order: 2;
      order: 2;
    }

    .formkit-form[data-uid="f24402b59d"] .formkit-header {
      margin-top: 0;
      margin-bottom: 24px;
      font-weight: 700;
      font-size: calc(30px + (36 - 30) * ((100vw - 400px) / (600 - 400)));
    }

    @media all and (min-width:800px) {
      .formkit-form[data-uid="f24402b59d"] .formkit-header {
        font-size: 36px;
      }
    }

    .formkit-form[data-uid="f24402b59d"] .formkit-header h2 {
      line-height: 1.2;
      margin-top: 0;
    }

    .formkit-form[data-uid="f24402b59d"] .formkit-content {
      margin-bottom: 45px;
      font-size: 16px;
    }

    .formkit-form[data-uid="f24402b59d"] .formkit-fields {
      display: -webkit-box;
      display: -webkit-flex;
      display: -ms-flexbox;
      display: flex;
      -webkit-flex-wrap: wrap;
      -ms-flex-wrap: wrap;
      flex-wrap: wrap;
    }

    .formkit-form[data-uid="f24402b59d"] .formkit-field {
      margin: 0 0 10px 0;
    }

    .formkit-form[data-uid="f24402b59d"] .formkit-input {
      width: 100%;
      border: 0;
      padding-left: 12px;
      padding-right: 0;
      height: 47px;
      font-size: 14px;
    }

    .formkit-form[data-uid="f24402b59d"] .formkit-select {
      padding-top: 13px !important;
      padding-bottom: 13px !important;
      border: 0 !important;
    }

    .formkit-form[data-uid="f24402b59d"] .formkit-checkboxes {
      background: transparent !important;
      color: inherit !important;
    }

    .formkit-form[data-uid="f24402b59d"] .formkit-fields .formkit-submit {
      margin-top: 8px;
      font-size: 12px;
      height: 47px;
    }

    .formkit-form[data-uid="f24402b59d"] .formkit-fields .formkit-submit span {
      padding: 15px 14px;
    }

    .formkit-form[data-uid="f24402b59d"] .formkit-fields[data-stacked="false"] {
      margin-left: -4px;
      margin-right: -4px;
      display: -webkit-box;
      display: -webkit-flex;
      display: -ms-flexbox;
      display: flex;
    }

    .formkit-form[data-uid="f24402b59d"] .formkit-fields[data-stacked="false"] .formkit-submit {
      -webkit-flex: 1 1 auto !important;
      -ms-flex: 1 1 auto !important;
      flex: 1 1 auto !important;
      margin: 0 !important;
      min-width: 90px;
    }

    .formkit-form[data-uid="f24402b59d"] .formkit-fields[data-stacked="false"] .formkit-field,
    .formkit-form[data-uid="f24402b59d"] .formkit-fields[data-stacked="false"] .formkit-submit {
      margin: 0 4px 8px 4px !important;
    }

    .formkit-form[data-uid="f24402b59d"] .formkit-fields[data-stacked="false"] .formkit-field {
      -webkit-flex: 100 1 auto !important;
      -ms-flex: 100 1 auto !important;
      flex: 100 1 auto !important;
      margin: 0;
    }

    .formkit-form[data-uid="f24402b59d"] .formkit-powered-by-convertkit-container {
      margin: 20px 0 0 0;
    }

    .formkit-form[data-uid="f24402b59d"] .formkit-disclaimer {
      font-size: 12px;
      opacity: 0.6;
      margin-top: 6px;
    }

    .formkit-form[data-uid="f24402b59d"] .formkit-field,
    .formkit-form[data-uid="f24402b59d"] .formkit-submit {
      margin: 0 0 8px 0;
      -webkit-flex: 1 0 100%;
      -ms-flex: 1 0 100%;
      flex: 1 0 100%;
    }

    @media screen and (min-width:600px) {
      .formkit-form[data-uid="f24402b59d"] [data-style="full"] {
        -webkit-flex-direction: row;
        -ms-flex-direction: row;
        flex-direction: row;
      }

      .formkit-form[data-uid="f24402b59d"] [data-style="full"] .formkit-column {
        width: 57%;
      }

      .formkit-form[data-uid="f24402b59d"] [data-style="full"] .formkit-background {
        width: 44%;
        height: auto;
        margin-left: 0;
        -webkit-order: 2;
        -ms-flex-order: 2;
        order: 2;
      }

      .formkit-slide-in,
      .preview .formkit-form[data-uid="f24402b59d"][data-format="slide in"],
      .formkit-form[data-uid="f24402b59d"][data-format="slide in-editing"] {
        max-width: 450px !important;
      }

      .formkit-slide-in [data-style="full"],
      .preview .formkit-form[data-uid="f24402b59d"][data-format="slide in"] [data-style="full"],
      .formkit-form[data-uid="f24402b59d"][data-format="slide in-editing"] [data-style="full"] {
        -webkit-flex-direction: column !important;
        -ms-flex-direction: column !important;
        flex-direction: column !important;
        max-width: 450px !important;
      }

      .formkit-slide-in .formkit-background,
      .preview .formkit-form[data-uid="f24402b59d"][data-format="slide in"] .formkit-background,
      .formkit-form[data-uid="f24402b59d"][data-format="slide in-editing"] .formkit-background {
        width: auto !important;
        height: 280px !important;
        margin: 20px !important;
        -webkit-order: 0 !important;
        -ms-flex-order: 0 !important;
        order: 0 !important;
      }

      .formkit-slide-in .formkit-column,
      .preview .formkit-form[data-uid="f24402b59d"][data-format="slide in"] .formkit-column,
      .formkit-form[data-uid="f24402b59d"][data-format="slide in-editing"] .formkit-column {
        width: 100% !important;
        -webkit-order: 2 !important;
        -ms-flex-order: 2 !important;
        order: 2 !important;
        padding: 20px 20px 30px 20px !important;
      }

      .formkit-slide-in .formkit-content,
      .preview .formkit-form[data-uid="f24402b59d"][data-format="slide in"] .formkit-content,
      .formkit-form[data-uid="f24402b59d"][data-format="slide in-editing"] .formkit-content {
        margin-bottom: 25px !important;
      }

      .formkit-form[data-uid="f24402b59d"] .formkit-column {
        padding: 55px 60px 55px 45px;
      }
    }

    .formkit-form[data-uid="f24402b59d"] {
      border: 5px solid #e8e8e8;
      box-shadow: none;
      max-width: 800px !important;
    }

    .formkit-form[data-uid="f24402b59d"] p {
      margin: 0;
    }

    .formkit-form[data-uid="f24402b59d"] .formkit-column {
      padding: 20px;
    }

    .formkit-form[data-uid="f24402b59d"] .formkit-header {
      margin: 0;
    }

    .formkit-form[data-uid="f24402b59d"] .formkit-header h2 {
      font-family: "Open Sans", sans-serif;
      font-size: 24px !important;
      overflow: visible;
      margin: 0;
    }

    .formkit-form[data-uid="f24402b59d"] .formkit-content {
      margin-bottom: 20px;
    }

    .formkit-form[data-uid="f24402b59d"] .formkit-content h2 {
      font-size: 40px !important;
      font-family: "Open Sans", sans-serif;
      font-weight: 600;
      color: #1080b6;
      overflow: visible;
      margin: 0;
      line-height: 1.1;
    }

    .formkit-form[data-uid="f24402b59d"] .formkit-content h3 {
      font-family: "Open Sans", sans-serif;
      font-size: 22px !important;
      font-weight: 400;
      color: #222;
      margin: 0 0 20px 0;
    }

    .formkit-form[data-uid="f24402b59d"] .formkit-input {
      font-size: 16px;
    }

    .formkit-form[data-uid="f24402b59d"] .formkit-fields .formkit-submit {
      font-family: "Open Sans", sans-serif;
      font-size: 16px;
      height: auto;
    }

    @media screen and (min-width:600px) {
      .formkit-form[data-uid="f24402b59d"] .formkit-column {
        width: 62% !important;
      }
    }

    @media screen and (max-width:480px) {
      .formkit-form[data-uid="f24402b59d"] .formkit-content h2 {
        font-size: 32px !important;
      }

      .formkit-form[data-uid="f24402b59d"] .formkit-content h3 {
        font-size: 17px !important;
      }
    }
  </style>
</form>

POST https://www.happycoders.eu/wp-comments-post.php

<form action="https://www.happycoders.eu/wp-comments-post.php" method="post" id="commentform" class="comment-form">
  <p class="comment-notes"><span id="email-notes">Your email address will not be published.</span> <span class="required-field-message">Required fields are marked <span class="required">*</span></span></p>
  <p class="comment-form-comment"><label for="comment">Comment <span class="required">*</span></label> <textarea autocomplete="new-password" id="comment" name="e98bb0e3c5" cols="45" rows="8" maxlength="65525" required="required"></textarea><textarea
      id="a88e639b1808a60cd4eec9e05d4004d8" aria-label="hp-comment" aria-hidden="true" name="comment" autocomplete="new-password"
      style="padding:0 !important;clip:rect(1px, 1px, 1px, 1px) !important;position:absolute !important;white-space:nowrap !important;height:1px !important;width:1px !important;overflow:hidden !important;" tabindex="-1"></textarea>
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  </p><input name="wpml_language_code" type="hidden" value="en">
  <p class="comment-form-author"><label for="author">Name <span class="required">*</span></label> <input id="author" name="author" type="text" value="" size="30" maxlength="245" autocomplete="name" required="required"></p>
  <p class="comment-form-email"><label for="email">Email <span class="required">*</span></label> <input id="email" name="email" type="text" value="" size="30" maxlength="100" aria-describedby="email-notes" autocomplete="email" required="required">
  </p>
  <p class="form-submit"><input name="submit" type="submit" id="submit" class="submit" value="Post Comment"> <input type="hidden" name="comment_post_ID" value="12674" id="comment_post_ID">
    <input type="hidden" name="comment_parent" id="comment_parent" value="0">
  </p>
</form>

POST https://app.convertkit.com/forms/2803747/subscriptions

<form action="https://app.convertkit.com/forms/2803747/subscriptions" style="background-color:#f9fafb;border-radius:4px" class="seva-form formkit-form" method="post" data-sv-form="2803747" data-uid="bebaa18901" data-format="modal" data-version="5"
  min-width="400 500 600 700 800">
  <div style="background-image:;opacity:0.2" class="formkit-background"></div>
  <div data-style="minimal">
    <div class="formkit-header" style="color:#222222;font-size:28px;font-weight:700" data-element="header">
      <h2>Become a better Java programmer <br>with this FREE newsletter. </h2>
    </div>
    <div class="formkit-subheader" style="color:#444444;font-size:18px" data-element="subheader">
      <p>Receive regular tips and tutorials about Java programming, <br>algorithms and data structures. </p>
    </div>
    <ul class="formkit-alert formkit-alert-error" data-element="errors" data-group="alert"></ul>
    <div data-element="fields" data-stacked="true" class="seva-fields formkit-fields">
      <div class="formkit-field"><input type="text" class="formkit-input" aria-label="First name..." style="color:#000;border-color:#e3e3e3;border-radius:4px;font-weight:400" name="fields[first_name]" required="" placeholder="First name..."></div>
      <div class="formkit-field"><input type="text" class="formkit-input" name="email_address" style="color:#000;border-color:#e3e3e3;border-radius:4px;font-weight:400" aria-label="Email address..." placeholder="Email address..." required=""></div>
      <button data-element="submit" class="formkit-submit formkit-submit" style="color:#fff;background-color:#1080b6;border-radius:4px;font-weight:400">
        <div class="formkit-spinner">
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    <div class="formkit-guarantee" style="color:#4d4d4d;font-size:13px;font-weight:400" data-element="guarantee">
      <p>Unsubscribe whenever you want. Read my <a href="https://www.happycoders.eu/privacy-policy/" target="_blank" rel="noopener noreferrer">Privacy Policy</a>. </p>
    </div>
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    .formkit-form[data-uid="bebaa18901"] .formkit-guarantee>p {
      margin: 0;
    }

    .formkit-form[data-uid="bebaa18901"] .formkit-powered-by-convertkit-container {
      margin-bottom: 0;
    }

    .formkit-form[data-uid="bebaa18901"] .formkit-fields {
      display: -webkit-box;
      display: -webkit-flex;
      display: -ms-flexbox;
      display: flex;
      -webkit-flex-wrap: wrap;
      -ms-flex-wrap: wrap;
      flex-wrap: wrap;
      margin: 25px auto 0 auto;
    }

    .formkit-form[data-uid="bebaa18901"] .formkit-field {
      min-width: 220px;
    }

    .formkit-form[data-uid="bebaa18901"] .formkit-field,
    .formkit-form[data-uid="bebaa18901"] .formkit-submit {
      margin: 0 0 15px 0;
      -webkit-flex: 1 0 100%;
      -ms-flex: 1 0 100%;
      flex: 1 0 100%;
    }

    .formkit-form[data-uid="bebaa18901"][min-width~="600"] [data-style="minimal"] {
      padding: 40px;
    }

    .formkit-form[data-uid="bebaa18901"][min-width~="600"] .formkit-fields[data-stacked="false"] {
      margin-left: -5px;
      margin-right: -5px;
    }

    .formkit-form[data-uid="bebaa18901"][min-width~="600"] .formkit-fields[data-stacked="false"] .formkit-field,
    .formkit-form[data-uid="bebaa18901"][min-width~="600"] .formkit-fields[data-stacked="false"] .formkit-submit {
      margin: 0 5px 15px 5px;
    }

    .formkit-form[data-uid="bebaa18901"][min-width~="600"] .formkit-fields[data-stacked="false"] .formkit-field {
      -webkit-flex: 100 1 auto;
      -ms-flex: 100 1 auto;
      flex: 100 1 auto;
    }

    .formkit-form[data-uid="bebaa18901"][min-width~="600"] .formkit-fields[data-stacked="false"] .formkit-submit {
      -webkit-flex: 1 1 auto;
      -ms-flex: 1 1 auto;
      flex: 1 1 auto;
    }

    .formkit-form[data-uid="bebaa18901"] h2 {
      font-size: 32px;
      margin: 0 0 1em 0;
    }

    .formkit-form[data-uid="bebaa18901"] .formkit-input,
    .formkit-form[data-uid="bebaa18901"] .formkit-submit {
      font-size: 17px;
    }
  </style>
</form>

POST https://app.convertkit.com/forms/2803748/subscriptions

<form action="https://app.convertkit.com/forms/2803748/subscriptions" style="background-color:#f9fafb;border-radius:4px" class="seva-form formkit-form" method="post" data-sv-form="2803748" data-uid="c5fd58ecdd" data-format="modal" data-version="5"
  min-width="400 500 600 700 800">
  <div style="background-image:;opacity:0.2" class="formkit-background"></div>
  <div data-style="minimal">
    <div class="formkit-header" style="color:#222222;font-size:28px;font-weight:700" data-element="header">
      <h2>Become a better Java programmer <br>with this FREE newsletter. </h2>
    </div>
    <div class="formkit-subheader" style="color:#444444;font-size:18px" data-element="subheader">
      <p>Receive regular tips and tutorials about Java programming, <br>algorithms and data structures. </p>
    </div>
    <ul class="formkit-alert formkit-alert-error" data-element="errors" data-group="alert"></ul>
    <div data-element="fields" data-stacked="true" class="seva-fields formkit-fields">
      <div class="formkit-field"><input type="text" class="formkit-input" aria-label="First name..." style="color:#000;border-color:#e3e3e3;border-radius:4px;font-weight:400" name="fields[first_name]" required="" placeholder="First name..."></div>
      <div class="formkit-field"><input type="text" class="formkit-input" name="email_address" style="color:#000;border-color:#e3e3e3;border-radius:4px;font-weight:400" aria-label="Email address..." placeholder="Email address..." required=""></div>
      <button data-element="submit" class="formkit-submit formkit-submit" style="color:#fff;background-color:#1080b6;border-radius:4px;font-weight:400">
        <div class="formkit-spinner">
          <div></div>
          <div></div>
          <div></div>
        </div><span class="">CLICK HERE TO SUBSCRIBE</span>
      </button>
    </div>
    <div class="formkit-guarantee" style="color:#4d4d4d;font-size:13px;font-weight:400" data-element="guarantee">
      <p>Unsubscribe whenever you want. Read my <a href="https://www.happycoders.eu/privacy-policy/" target="_blank" rel="noopener noreferrer">Privacy Policy</a>. </p>
    </div>
  </div>
  <style>
    .formkit-form[data-uid="c5fd58ecdd"] * {
      box-sizing: border-box;
    }

    .formkit-form[data-uid="c5fd58ecdd"] {
      -webkit-font-smoothing: antialiased;
      -moz-osx-font-smoothing: grayscale;
    }

    .formkit-form[data-uid="c5fd58ecdd"] legend {
      border: none;
      font-size: inherit;
      margin-bottom: 10px;
      padding: 0;
      position: relative;
      display: table;
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    .formkit-form[data-uid="c5fd58ecdd"] fieldset {
      border: 0;
      padding: 0.01em 0 0 0;
      margin: 0;
      min-width: 0;
    }

    .formkit-form[data-uid="c5fd58ecdd"] body:not(:-moz-handler-blocked) fieldset {
      display: table-cell;
    }

    .formkit-form[data-uid="c5fd58ecdd"] h1,
    .formkit-form[data-uid="c5fd58ecdd"] h2,
    .formkit-form[data-uid="c5fd58ecdd"] h3,
    .formkit-form[data-uid="c5fd58ecdd"] h4,
    .formkit-form[data-uid="c5fd58ecdd"] h5,
    .formkit-form[data-uid="c5fd58ecdd"] h6 {
      color: inherit;
      font-size: inherit;
      font-weight: inherit;
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    .formkit-form[data-uid="c5fd58ecdd"] h2 {
      font-size: 1.5em;
      margin: 1em 0;
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    .formkit-form[data-uid="c5fd58ecdd"] h3 {
      font-size: 1.17em;
      margin: 1em 0;
    }

    .formkit-form[data-uid="c5fd58ecdd"] p {
      color: inherit;
      font-size: inherit;
      font-weight: inherit;
    }

    .formkit-form[data-uid="c5fd58ecdd"] ol:not([template-default]),
    .formkit-form[data-uid="c5fd58ecdd"] ul:not([template-default]),
    .formkit-form[data-uid="c5fd58ecdd"] blockquote:not([template-default]) {
      text-align: left;
    }

    .formkit-form[data-uid="c5fd58ecdd"] p:not([template-default]),
    .formkit-form[data-uid="c5fd58ecdd"] hr:not([template-default]),
    .formkit-form[data-uid="c5fd58ecdd"] blockquote:not([template-default]),
    .formkit-form[data-uid="c5fd58ecdd"] ol:not([template-default]),
    .formkit-form[data-uid="c5fd58ecdd"] ul:not([template-default]) {
      color: inherit;
      font-style: initial;
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    .formkit-form[data-uid="c5fd58ecdd"] .ordered-list,
    .formkit-form[data-uid="c5fd58ecdd"] .unordered-list {
      list-style-position: outside !important;
      padding-left: 1em;
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    .formkit-form[data-uid="c5fd58ecdd"] .list-item {
      padding-left: 0;
    }

    .formkit-form[data-uid="c5fd58ecdd"][data-format="modal"] {
      display: none;
    }

    .formkit-form[data-uid="c5fd58ecdd"][data-format="slide in"] {
      display: none;
    }

    .formkit-form[data-uid="c5fd58ecdd"][data-format="sticky bar"] {
      display: none;
    }

    .formkit-sticky-bar .formkit-form[data-uid="c5fd58ecdd"][data-format="sticky bar"] {
      display: block;
    }

    .formkit-form[data-uid="c5fd58ecdd"] .formkit-input,
    .formkit-form[data-uid="c5fd58ecdd"] .formkit-select,
    .formkit-form[data-uid="c5fd58ecdd"] .formkit-checkboxes {
      width: 100%;
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    .formkit-form[data-uid="c5fd58ecdd"] .formkit-button,
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      border: 0;
      border-radius: 5px;
      color: #ffffff;
      cursor: pointer;
      display: inline-block;
      text-align: center;
      font-size: 15px;
      font-weight: 500;
      cursor: pointer;
      margin-bottom: 15px;
      overflow: hidden;
      padding: 0;
      position: relative;
      vertical-align: middle;
    }

    .formkit-form[data-uid="c5fd58ecdd"] .formkit-button:hover,
    .formkit-form[data-uid="c5fd58ecdd"] .formkit-submit:hover,
    .formkit-form[data-uid="c5fd58ecdd"] .formkit-button:focus,
    .formkit-form[data-uid="c5fd58ecdd"] .formkit-submit:focus {
      outline: none;
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    .formkit-form[data-uid="c5fd58ecdd"] .formkit-button:hover>span,
    .formkit-form[data-uid="c5fd58ecdd"] .formkit-submit:hover>span,
    .formkit-form[data-uid="c5fd58ecdd"] .formkit-button:focus>span,
    .formkit-form[data-uid="c5fd58ecdd"] .formkit-submit:focus>span {
      background-color: rgba(0, 0, 0, 0.1);
    }

    .formkit-form[data-uid="c5fd58ecdd"] .formkit-button>span,
    .formkit-form[data-uid="c5fd58ecdd"] .formkit-submit>span {
      display: block;
      -webkit-transition: all 300ms ease-in-out;
      transition: all 300ms ease-in-out;
      padding: 12px 24px;
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    .formkit-form[data-uid="c5fd58ecdd"] .formkit-input {
      background: #ffffff;
      font-size: 15px;
      padding: 12px;
      border: 1px solid #e3e3e3;
      -webkit-flex: 1 0 auto;
      -ms-flex: 1 0 auto;
      flex: 1 0 auto;
      line-height: 1.4;
      margin: 0;
      -webkit-transition: border-color ease-out 300ms;
      transition: border-color ease-out 300ms;
    }

    .formkit-form[data-uid="c5fd58ecdd"] .formkit-input:focus {
      outline: none;
      border-color: #1677be;
      -webkit-transition: border-color ease 300ms;
      transition: border-color ease 300ms;
    }

    .formkit-form[data-uid="c5fd58ecdd"] .formkit-input::-webkit-input-placeholder {
      color: inherit;
      opacity: 0.8;
    }

    .formkit-form[data-uid="c5fd58ecdd"] .formkit-input::-moz-placeholder {
      color: inherit;
      opacity: 0.8;
    }

    .formkit-form[data-uid="c5fd58ecdd"] .formkit-input:-ms-input-placeholder {
      color: inherit;
      opacity: 0.8;
    }

    .formkit-form[data-uid="c5fd58ecdd"] .formkit-input::placeholder {
      color: inherit;
      opacity: 0.8;
    }

    .formkit-form[data-uid="c5fd58ecdd"] [data-group="dropdown"] {
      position: relative;
      display: inline-block;
      width: 100%;
    }

    .formkit-form[data-uid="c5fd58ecdd"] [data-group="dropdown"]::before {
      content: "";
      top: calc(50% - 2.5px);
      right: 10px;
      position: absolute;
      pointer-events: none;
      border-color: #4f4f4f transparent transparent transparent;
      border-style: solid;
      border-width: 6px 6px 0 6px;
      height: 0;
      width: 0;
      z-index: 999;
    }

    .formkit-form[data-uid="c5fd58ecdd"] [data-group="dropdown"] select {
      height: auto;
      width: 100%;
      cursor: pointer;
      color: #333333;
      line-height: 1.4;
      margin-bottom: 0;
      padding: 0 6px;
      -webkit-appearance: none;
      -moz-appearance: none;
      appearance: none;
      font-size: 15px;
      padding: 12px;
      padding-right: 25px;
      border: 1px solid #e3e3e3;
      background: #ffffff;
    }

    .formkit-form[data-uid="c5fd58ecdd"] [data-group="dropdown"] select:focus {
      outline: none;
    }

    .formkit-form[data-uid="c5fd58ecdd"] [data-group="checkboxes"] {
      text-align: left;
      margin: 0;
    }

    .formkit-form[data-uid="c5fd58ecdd"] [data-group="checkboxes"] [data-group="checkbox"] {
      margin-bottom: 10px;
    }

    .formkit-form[data-uid="c5fd58ecdd"] [data-group="checkboxes"] [data-group="checkbox"] * {
      cursor: pointer;
    }

    .formkit-form[data-uid="c5fd58ecdd"] [data-group="checkboxes"] [data-group="checkbox"]:last-of-type {
      margin-bottom: 0;
    }

    .formkit-form[data-uid="c5fd58ecdd"] [data-group="checkboxes"] [data-group="checkbox"] input[type="checkbox"] {
      display: none;
    }

    .formkit-form[data-uid="c5fd58ecdd"] [data-group="checkboxes"] [data-group="checkbox"] input[type="checkbox"]+label::after {
      content: none;
    }

    .formkit-form[data-uid="c5fd58ecdd"] [data-group="checkboxes"] [data-group="checkbox"] input[type="checkbox"]:checked+label::after {
      border-color: #ffffff;
      content: "";
    }

    .formkit-form[data-uid="c5fd58ecdd"] [data-group="checkboxes"] [data-group="checkbox"] input[type="checkbox"]:checked+label::before {
      background: #10bf7a;
      border-color: #10bf7a;
    }

    .formkit-form[data-uid="c5fd58ecdd"] [data-group="checkboxes"] [data-group="checkbox"] label {
      position: relative;
      display: inline-block;
      padding-left: 28px;
    }

    .formkit-form[data-uid="c5fd58ecdd"] [data-group="checkboxes"] [data-group="checkbox"] label::before,
    .formkit-form[data-uid="c5fd58ecdd"] [data-group="checkboxes"] [data-group="checkbox"] label::after {
      position: absolute;
      content: "";
      display: inline-block;
    }

    .formkit-form[data-uid="c5fd58ecdd"] [data-group="checkboxes"] [data-group="checkbox"] label::before {
      height: 16px;
      width: 16px;
      border: 1px solid #e3e3e3;
      background: #ffffff;
      left: 0px;
      top: 3px;
    }

    .formkit-form[data-uid="c5fd58ecdd"] [data-group="checkboxes"] [data-group="checkbox"] label::after {
      height: 4px;
      width: 8px;
      border-left: 2px solid #4d4d4d;
      border-bottom: 2px solid #4d4d4d;
      -webkit-transform: rotate(-45deg);
      -ms-transform: rotate(-45deg);
      transform: rotate(-45deg);
      left: 4px;
      top: 8px;
    }

    .formkit-form[data-uid="c5fd58ecdd"] .formkit-alert {
      background: #f9fafb;
      border: 1px solid #e3e3e3;
      border-radius: 5px;
      -webkit-flex: 1 0 auto;
      -ms-flex: 1 0 auto;
      flex: 1 0 auto;
      list-style: none;
      margin: 25px auto;
      padding: 12px;
      text-align: center;
      width: 100%;
    }

    .formkit-form[data-uid="c5fd58ecdd"] .formkit-alert:empty {
      display: none;
    }

    .formkit-form[data-uid="c5fd58ecdd"] .formkit-alert-success {
      background: #d3fbeb;
      border-color: #10bf7a;
      color: #0c905c;
    }

    .formkit-form[data-uid="c5fd58ecdd"] .formkit-alert-error {
      background: #fde8e2;
      border-color: #f2643b;
      color: #ea4110;
    }

    .formkit-form[data-uid="c5fd58ecdd"] .formkit-spinner {
      display: -webkit-box;
      display: -webkit-flex;
      display: -ms-flexbox;
      display: flex;
      height: 0px;
      width: 0px;
      margin: 0 auto;
      position: absolute;
      top: 0;
      left: 0;
      right: 0;
      width: 0px;
      overflow: hidden;
      text-align: center;
      -webkit-transition: all 300ms ease-in-out;
      transition: all 300ms ease-in-out;
    }

    .formkit-form[data-uid="c5fd58ecdd"] .formkit-spinner>div {
      margin: auto;
      width: 12px;
      height: 12px;
      background-color: #fff;
      opacity: 0.3;
      border-radius: 100%;
      display: inline-block;
      -webkit-animation: formkit-bouncedelay-formkit-form-data-uid-c5fd58ecdd- 1.4s infinite ease-in-out both;
      animation: formkit-bouncedelay-formkit-form-data-uid-c5fd58ecdd- 1.4s infinite ease-in-out both;
    }

    .formkit-form[data-uid="c5fd58ecdd"] .formkit-spinner>div:nth-child(1) {
      -webkit-animation-delay: -0.32s;
      animation-delay: -0.32s;
    }

    .formkit-form[data-uid="c5fd58ecdd"] .formkit-spinner>div:nth-child(2) {
      -webkit-animation-delay: -0.16s;
      animation-delay: -0.16s;
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    .formkit-form[data-uid="c5fd58ecdd"] .formkit-submit[data-active] .formkit-spinner {
      opacity: 1;
      height: 100%;
      width: 50px;
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    .formkit-form[data-uid="c5fd58ecdd"] .formkit-submit[data-active] .formkit-spinner~span {
      opacity: 0;
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    .formkit-form[data-uid="c5fd58ecdd"] .formkit-powered-by[data-active="false"] {
      opacity: 0.35;
    }

    .formkit-form[data-uid="c5fd58ecdd"] .formkit-powered-by-convertkit-container {
      display: -webkit-box;
      display: -webkit-flex;
      display: -ms-flexbox;
      display: flex;
      width: 100%;
      z-index: 5;
      margin: 10px 0;
      position: relative;
    }

    .formkit-form[data-uid="c5fd58ecdd"] .formkit-powered-by-convertkit-container[data-active="false"] {
      opacity: 0.35;
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    .formkit-form[data-uid="c5fd58ecdd"] .formkit-powered-by-convertkit {
      -webkit-align-items: center;
      -webkit-box-align: center;
      -ms-flex-align: center;
      align-items: center;
      background-color: #ffffff;
      border: 1px solid #dce1e5;
      border-radius: 4px;
      color: #373f45;
      cursor: pointer;
      display: block;
      height: 36px;
      margin: 0 auto;
      opacity: 0.95;
      padding: 0;
      -webkit-text-decoration: none;
      text-decoration: none;
      text-indent: 100%;
      -webkit-transition: ease-in-out all 200ms;
      transition: ease-in-out all 200ms;
      white-space: nowrap;
      overflow: hidden;
      -webkit-user-select: none;
      -moz-user-select: none;
      -ms-user-select: none;
      user-select: none;
      width: 190px;
      background-repeat: no-repeat;
      background-position: center;
      background-image: url("data:image/svg+xml;charset=utf8,%3Csvg width='162' height='20' viewBox='0 0 162 20' fill='none' xmlns='http://www.w3.org/2000/svg'%3E%3Cpath d='M83.0561 15.2457C86.675 15.2457 89.4722 12.5154 89.4722 9.14749C89.4722 5.99211 86.8443 4.06563 85.1038 4.06563C82.6801 4.06563 80.7373 5.76407 80.4605 8.28551C80.4092 8.75244 80.0387 9.14403 79.5686 9.14069C78.7871 9.13509 77.6507 9.12841 76.9314 9.13092C76.6217 9.13199 76.3658 8.88106 76.381 8.57196C76.4895 6.38513 77.2218 4.3404 78.618 2.76974C80.1695 1.02445 82.4289 0 85.1038 0C89.5979 0 93.8406 4.07791 93.8406 9.14749C93.8406 14.7608 89.1832 19.3113 83.1517 19.3113C78.8502 19.3113 74.5179 16.5041 73.0053 12.5795C72.9999 12.565 72.9986 12.5492 73.0015 12.534C73.0218 12.4179 73.0617 12.3118 73.1011 12.2074C73.1583 12.0555 73.2143 11.907 73.2062 11.7359L73.18 11.1892C73.174 11.0569 73.2075 10.9258 73.2764 10.8127C73.3452 10.6995 73.4463 10.6094 73.5666 10.554L73.7852 10.4523C73.9077 10.3957 74.0148 10.3105 74.0976 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BIG O NOTATION AND TIME COMPLEXITY – EASILY EXPLAINED

by Sven Woltmann – May 28, 2020

The big O notation¹ is used to describe the complexity of algorithms.

On Google and YouTube, you can find numerous articles and videos explaining the
big O notation. But to understand most of them (like this Wikipedia article),
you should have studied mathematics as a preparation. ;-)

That' s why, in this article, I will explain the big O notation (and the time
and space complexity described with it) only using examples and diagrams – and
entirely without mathematical formulas, proofs and symbols like θ, Ω, ω, ∈, ∀, ∃
and ε.

You can find all source codes from this article in this GitHub repository.

¹ also known as "Bachmann-Landau notation" or "asymptotic notation"

Contents hide
1 Types of Complexity
1.1 Computational Time Complexity
1.2 Space Complexity
2 Complexity Classes
2.1 O(1) – Constant Time
2.2 O(n) – Linear Time
2.3 O(n²) – Quadratic Time
2.4 O(log n) – Logarithmic Time
2.5 O(n log n) – Quasilinear Time
2.6 Big O Notation Order
2.7 Other Complexity Classes
3 Summary


TYPES OF COMPLEXITY


COMPUTATIONAL TIME COMPLEXITY

Computational time complexity describes the change in the runtime of an
algorithm, depending on the change in the input data's size.

In other words: "How much does an algorithm degrade when the amount of input
data increases?"

Examples:

 * How much longer does it take to find an element within an unsorted array when
   the size of the array doubles? (Answer: twice as long)
 * How much longer does it take to find an element within a sorted array when
   the size of the array doubles? (Answer: one more step)


SPACE COMPLEXITY

Space complexity describes how much additional memory an algorithm needs
depending on the size of the input data.

This does not refer to the memory required for the input data itself (i.e., that
twice as much space is naturally needed for an input array twice as large), but
the additional memory needed by the algorithm for loop and helper variables,
temporary data structures, and the call stack (e.g., due to recursion).


COMPLEXITY CLASSES

We divide algorithms into so-called complexity classes. A complexity class is
identified by the Landau symbol O ("big O").

In the following section, I will explain the most common complexity classes,
starting with the easy-to-understand classes and moving on to the more complex
ones. Accordingly, the classes are not sorted by complexity.


FREE BONUS:


BIG O CHEAT SHEET


[7 TIME COMPLEXITY CLASSES ON 1 PAGE]




Use this 1-page PDF cheat sheet as a reference to quickly look up the seven most
important time complexity classes (with descriptions and examples).




Send Me the Cheat Sheet Now!

You get access to this PDF by signing up for my newsletter. I won’t send any
spam, and you can opt-out at any time.




O(1) – CONSTANT TIME

Pronounced: "Order 1", "O of 1", "big O of 1"

The runtime is constant, i.e., independent of the number of input elements n.

In the following graph, the horizontal axis represents the number of input
elements n (or more generally: the size of the input problem), and the vertical
axis represents the time required.

Since complexity classes can only be used to classify algorithms, but not to
calculate their exact running time, the axes are not labeled.



O(1) EXAMPLES

The following two problems are examples of constant time:

 * Accessing a specific element of an array of size n: No matter how large the
   array is, accessing it via array[index] always takes the same time².
 * Inserting an element at the beginning of a linked list: This always requires
   setting one or two (for a doubly linked list) pointers (or references),
   regardless of the list's size. (In an array, on the other hand, this would
   require moving all values one field to the right, which takes longer with a
   larger array than with a smaller one).

² This statement is not one hundred percent correct. Effects from CPU caches
also come into play here: If the data block containing the element to be read is
already (or still) in the CPU cache (which is more likely the smaller the array
is), then access is faster than if it first has to be read from RAM.

O(1) EXAMPLE SOURCE CODE

The following source code (class ConstantTimeSimpleDemo in the GitHub
repository) shows a simple example to measure the time required to insert an
element at the beginning of a linked list:

public static void main(String[] args) {
  for (int n = 32; n <= 8_388_608; n *= 2) {
    LinkedList<Integer> list = createLinkedListOfSize(n);

    long time = System.nanoTime();
    list.add(0, 1);
    time = System.nanoTime() - time;

    System.out.printf("n = %d -> time = %d ns%n", n, time);
  }
}

private static LinkedList<Integer> createLinkedListOfSize(int n) {
  LinkedList<Integer> list = new LinkedList<>();
  for (int i = 0; i < n; i++) {
    list.add(i);
  }
  return list;
}Code language: Java (java)

On my system, the times are between 1,200 ns and 19,000 ns, unevenly distributed
over the various measurements. This is sufficient for a quick test. But we don't
get particularly good measurement results here, as both the HotSpot compiler and
the garbage collector can kick in at any time.

The test program TimeComplexityDemo with the ConstantTime class provides better
measurement results. The test program first runs several warmup rounds to allow
the HotSpot compiler to optimize the code. Only after that are measurements
performed five times, and the median of the measured values is displayed.

Here is an extract of the results:

--- ConstantTime (results 5 of 5) ---
ConstantTime, n =        32 -> fastest: 31,700 ns, median: 44,900 ns
ConstantTime, n =    16,384 -> fastest: 14,400 ns, median: 40,200 ns
ConstantTime, n = 8,388,608 -> fastest: 34,000 ns, median: 51,100 nsCode language: plaintext (plaintext)

The effort remains about the same, regardless of the size of the list. The
complete test results can be found in the file test-results.txt.


O(N) – LINEAR TIME

Pronounced: "Order n", "O of n", "big O of n"

The time grows linearly with the number of input elements n: If n doubles, then
the time approximately doubles, too.

"Approximately" because the effort may also include components with lower
complexity classes. These become insignificant if n is sufficiently large so
they are omitted in the notation.

In the following diagram, I have demonstrated this by starting the graph
slightly above zero (meaning that the effort also contains a constant
component):



O(N) EXAMPLES

The following problems are examples for linear time:

 * Finding a specific element in an array: All elements of the array have to be
   examined – if there are twice as many elements, it takes twice as long.
 * Summing up all elements of an array: Again, all elements must be looked at
   once – if the array is twice as large, it takes twice as long.

It is essential to understand that the complexity class makes no statement about
the absolute time required, but only about the change in the time required
depending on the change in the input size. The two examples above would take
much longer with a linked list than with an array – but that is irrelevant for
the complexity class.

O(N) EXAMPLE SOURCE CODE

The following source code (class LinearTimeSimpleDemo) measures the time for
summing up all elements of an array:

public static void main(String[] args) {
  for (int n = 32; n <= 536_870_912; n *= 2) {
    int[] array = createArrayOfSize(n);

    long sum = 0;

    long time = System.nanoTime();
    for (int i = 0; i < n; i++) {
      sum += array[i];
    }
    time = System.nanoTime() - time;

    System.out.printf("n = %d -> time = %d ns%n", n, time);
  }
}

private static int[] createArrayOfSize(int n) {
  int[] array = new int[n];
  for (int i = 0; i < n; i++) {
    array[i] = i;
  }
  return array;
}
Code language: Java (java)

On my system, the time degrades approximately linearly from 1,100 ns to
155,911,900 ns. Better measurement results are again provided by the test
program TimeComplexityDemo and the LinearTime algorithm class. Here is an
extract of the results:

--- LinearTime (results 5 of 5) ---
LinearTime, n =         512 -> fastest:         300 ns, median:         300 ns
LinearTime, n =     524,288 -> fastest:     159,300 ns, median:     189,400 ns
LinearTime, n = 536,870,912 -> fastest: 164,322,600 ns, median: 168,681,700 nsCode language: plaintext (plaintext)

You can find the complete test results again in test-results.txt.

WHAT IS THE DIFFERENCE BETWEEN "LINEAR" AND "PROPORTIONAL"?

A function is linear if it can be represented by a straight line, e.g. f(x) = 5x
+ 3.

Proportional is a particular case of linear, where the line passes through the
point (0,0) of the coordinate system, for example, f(x) = 3x.

As there may be a constant component in O(n), it's time is linear.


O(N²) – QUADRATIC TIME

Pronounced: "Order n squared", "O of n squared", "big O of n squared"

The time grows linearly to the square of the number of input elements: If the
number of input elements n doubles, then the time roughly quadruples. (And if
the number of elements increases tenfold, the effort increases by a factor of
one hundred!)



O(N²) EXAMPLES

Examples of quadratic time are simple sorting algorithms like Insertion Sort,
Selection Sort, and Bubble Sort.

O(N²) EXAMPLE SOURCE CODE

The following example (QuadraticTimeSimpleDemo) shows how the time for sorting
an array using Insertion Sort changes depending on the size of the array:

public static void main(String[] args) {
  for (int n = 32; n <= 262_144; n *= 2) {
    int[] array = createRandomArrayOfSize(n);

    long time = System.nanoTime();
    insertionSort(array);
    time = System.nanoTime() - time;

    System.out.printf("n = %d -> time = %d ns%n", n, time);
  }
}

private static int[] createRandomArrayOfSize(int n) {
  ThreadLocalRandom random = ThreadLocalRandom.current();
  int[] array = new int[n];
  for (int i = 0; i < n; i++) {
    array[i] = random.nextInt();
  }
  return array;
}

private static void insertionSort(int[] elements) {
  for (int i = 1; i < elements.length; i++) {
    int elementToSort = elements[i];
    int j = i;
    while (j > 0 && elementToSort < elements[j - 1]) {
      elements[j] = elements[j - 1];
      j--;
    }
    elements[j] = elementToSort;
  }
}
Code language: Java (java)

We can obtain better results with the test program TimeComplexityDemo and the
QuadraticTime class. Here is an excerpt of the results, where you can see the
approximate quadrupling of the effort each time the problem size doubles:

QuadraticTime, n =   8,192 -> fastest:     4,648,400 ns, median:     4,720,200 ns
QuadraticTime, n =  16,384 -> fastest:    19,189,100 ns, median:    19,440,400 ns
QuadraticTime, n =  32,768 -> fastest:    78,416,700 ns, median:    79,896,000 ns
QuadraticTime, n =  65,536 -> fastest:   319,905,300 ns, median:   330,530,600 ns
QuadraticTime, n = 131,072 -> fastest: 1,310,702,600 ns, median: 1,323,919,500 nsCode language: plaintext (plaintext)

You can find the complete test results in test-results.txt.

O(N) VS. O(N²)

At this point, I would like to point out again that the effort can contain
components of lower complexity classes and constant factors. Both are irrelevant
for the big O notation since they are no longer of importance if n is
sufficiently large.

It is therefore possible that, for example, O(n²) is faster than O(n) – at least
up to a certain size of n.

The following diagram compares three fictitious algorithms: one with complexity
class O(n²) and two with O(n), one of which is faster than the other. It is good
to see how up to n = 4, the orange O(n²) algorithm takes less time than the
yellow O(n) algorithm. And even up to n = 8, less time than the cyan O(n)
algorithm.

Above a sufficiently large n (that is n = 9), O(n²) is and remains the slowest
algorithm.



Let's move on to two, not-so-intuitive complexity classes.


O(LOG N) – LOGARITHMIC TIME

Pronounced: "Order log n", "O of log n", "big O of log n"

The effort increases approximately by a constant amount when the number of input
elements doubles.

For example, if the time increases by one second when the number of input
elements increases from 1,000 to 2,000, it only increases by another second when
the effort increases to 4,000. And again by one more second when the effort
grows to 8,000.



O(LOG N) EXAMPLE

An example of logarithmic growth is the binary search for a specific element in
a sorted array of size n.

Since we halve the area to be searched with each search step, we can, in turn,
search an array twice as large with only one more search step.

(The older ones among us may remember searching the telephone book or an
encyclopedia.)

O(LOG N) EXAMPLE SOURCE CODE

The following example (LogarithmicTimeSimpleDemo) measures how the time for
binary search changes in relation to the array size.

public static void main(String[] args) {
  for (int n = 32; n <= 536_870_912; n *= 2) {
    int[] array = createArrayOfSize(n);

    long time = System.nanoTime();
    Arrays.binarySearch(array, 0);
    time = System.nanoTime() - time;

    System.out.printf("n = %d -> time = %d ns%n", n, time);
  }
}

private static int[] createArrayOfSize(int n) {
  int[] array = new int[n];
  for (int i = 0; i < n; i++) {
    array[i] = i;
  }
  return array;
}Code language: Java (java)

We get better measurement results with the test program TimeComplexityDemo and
the class LogarithmicTime. Here are the results:

LogarithmicTime, n =          32 -> fastest:  77,800 ns, median: 107,200 ns
LogarithmicTime, n =       2,048 -> fastest: 173,500 ns, median: 257,400 ns
LogarithmicTime, n =     131,072 -> fastest: 363,400 ns, median: 413,100 ns
LogarithmicTime, n =   8,388,608 -> fastest: 661,100 ns, median: 670,800 ns
LogarithmicTime, n = 536,870,912 -> fastest: 770,500 ns, median: 875,700 nsCode language: plaintext (plaintext)

In each step, the problem size n increases by factor 64. The time does not
always increase by exactly the same value, but it does so sufficiently precisely
to demonstrate that logarithmic time is significantly cheaper than linear time
(for which the time required would also increase by factor 64 each step).

As before, you can find the complete test results in the file test-results.txt.


O(N LOG N) – QUASILINEAR TIME

Pronounced: "Order n log n", "O of n log n", "big O of n log n"

The effort grows slightly faster than linear because the linear component is
multiplied by a logarithmic one. For clarification, you can also insert a
multiplication sign: O(n × log n).

This is best illustrated by the following graph. We see a curve whose gradient
is visibly growing at the beginning, but soon approaches a straight line as n
increases:



O(N LOG N) EXAMPLE

Efficient sorting algorithms like Quicksort, Merge Sort, and Heapsort are
examples for quasilinear time.

O(N LOG N) EXAMPLE SOURCE CODE

The following sample code (class QuasiLinearTimeSimpleDemo) shows how the time
for sorting an array with Quicksort³ grows in relation to the array size:

public static void main(String[] args) {
  for (int n = 32; n <= 536_870_912; n *= 2) {
    int[] array = createArrayOfSize(n);

    long time = System.nanoTime();
    Arrays.binarySearch(array, 0);
    time = System.nanoTime() - time;

    System.out.printf("n = %d -> time = %d ns%n", n, time);
  }
}

private static int[] createArrayOfSize(int n) {
  int[] array = new int[n];
  for (int i = 0; i < n; i++) {
    array[i] = i;
  }
  return array;
}Code language: Java (java)

The test program TimeComplexityDemo with the class QuasiLinearTime delivers more
precise results. Here is an extract:

QuasiLinearTime, n =        256 -> fastest:        12,200 ns, med.:        12,500 ns
QuasiLinearTime, n =      4,096 -> fastest:       228,600 ns, med.:       234,200 ns
QuasiLinearTime, n =     65,536 -> fastest:     4,606,500 ns, med.:     4,679,800 ns
QuasiLinearTime, n =  1,048,576 -> fastest:    93,933,500 ns, med.:    95,216,300 ns
QuasiLinearTime, n = 16,777,216 -> fastest: 1,714,541,900 ns, med.: 1,755,715,000 nsCode language: plaintext (plaintext)

The problem size increases each time by factor 16, and the time required by
factor 18.5 to 20.3. You can find the complete test result, as always, in
test-results.txt.

³ More precisely: Dual-Pivot Quicksort, which switches to Insertion Sort for
arrays with less than 44 elements. For this reason, this test starts at 64
elements, not at 32 like the others.


BIG O NOTATION ORDER

Here are, once again, the complexity classes, sorted in ascending order of
complexity:

 * O(1) – constant time
 * O(log n) – logarithmic time
 * O(n) – linear time
 * O(n log n) – quasilinear time
 * O(n²) – quadratic time

And here the comparison graphically:



I intentionally shifted the curves along the time axis so that the worst
complexity class O(n²) is fastest for low values of n, and the best complexity
class O(1) is slowest. To then show how, for sufficiently high values of n, the
efforts shift as expected.


OTHER COMPLEXITY CLASSES

Further complexity classes are, for example:

 * O(nm) – polynomial time
 * O(2n) – exponential time
 * O(n!) – factorial time

However, these are so bad that we should avoid algorithms with these
complexities, if possible.

I have included these classes in the following diagram (O(nm) with m=3):



I had to compress the y-axis by factor 10 compared to the previous diagram to
display the three new curves.


SUMMARY

Time complexity describes how the runtime of an algorithm changes depending on
the amount of input data. The most common complexity classes are (in ascending
order of complexity): O(1), O(log n), O(n), O(n log n), O(n²).

Algorithms with constant, logarithmic, linear, and quasilinear time usually lead
to an end in a reasonable time for input sizes up to several billion elements.
Algorithms with quadratic time can quickly reach theoretical execution times of
several years for the same problem sizes⁴. You should, therefore, avoid them as
far as possible.

⁴ Quicksort, for example, sorts a billion items in 90 seconds on my laptop;
Insertion Sort, on the other hand, needs 85 seconds for a million items; that
would be 85 million seconds for a billion items – or in other words: two years
and eight months!

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ABOUT THE AUTHOR

I'm a freelance software developer with more than two decades of experience in
scalable Java enterprise applications. My focus is on optimizing complex
algorithms and on advanced topics such as concurrency, the Java memory model,
and garbage collection. Here on HappyCoders.eu, I want to help you become a
better Java programmer. Read more about me here.



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7 COMMENTS ON “BIG O NOTATION AND TIME COMPLEXITY – EASILY EXPLAINED”

 1. Mike says:
    February 11, 2021 at 4:40 pm
    
    Thanks, great explanation. I'm happy coder now ;)
    
    Reply
    1. Sven Woltmann says:
       February 11, 2021 at 9:00 pm
       
       I am happy to hear that. I know it's a difficult subject, I had a great
       deal of trouble understanding it in college.
       
       Reply
 2. Tat says:
    March 1, 2022 at 1:02 pm
    
    Thanks for the beautiful article. It helps me to think now.
    
    Reply
 3. Conveyancing says:
    April 23, 2022 at 7:48 pm
    
    Hi Sven,
    Thanks for explaining Big O notation.
    I recently had an interview where it featured and I didn't do very well.
    Your article has helped cement it in my mind. I might print out your sheet
    so I can refer to it in future interviews.
    Matthew
    
    Reply
 4. Ampee says:
    July 16, 2022 at 11:53 am
    
    Your article was very helpful. Thank you!
    
    Reply
 5. Kamrul Hasan says:
    February 23, 2023 at 1:40 pm
    
    Wow. I like the detailed information
    
    Reply
 6. Ed Gerck says:
    August 10, 2023 at 12:42 am
    
    A faster FFT can have a complexity of O(N), and use only rational numbers.
    
    Reply




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