{"id":11334,"date":"2025-12-23T12:37:42","date_gmt":"2025-12-23T07:07:42","guid":{"rendered":"https:\/\/namastedev.com\/blog\/?p=11334"},"modified":"2025-12-24T18:00:58","modified_gmt":"2025-12-24T12:30:58","slug":"minimum-spanning-tree","status":"publish","type":"post","link":"https:\/\/namastedev.com\/blog\/minimum-spanning-tree\/","title":{"rendered":"Minimum Spanning Tree"},"content":{"rendered":"\n<!-- Shortest Path in unweighted graph -->\n<!-- PrismJS for Syntax Highlighting -->\n<link href=\"https:\/\/cdn.jsdelivr.net\/npm\/prismjs@1.29.0\/themes\/prism-tomorrow.min.css\" rel=\"stylesheet\">\n<script src=\"https:\/\/cdn.jsdelivr.net\/npm\/prismjs@1.29.0\/prism.min.js\"><\/script>\n<script src=\"https:\/\/cdn.jsdelivr.net\/npm\/prismjs@1.29.0\/plugins\/autoloader\/prism-autoloader.min.js\"><\/script>\n\n<style>\n.wp_blog_theme {\n  --primary: #E58C32;\n  --secondary: #030302;\n  --light-bg: #fef9f4;\n  --text-dark: #2d2d2d;\n  --tab-radius: 12px;\n  --shadow: 0 4px 12px rgba(0, 0, 0, 0.08);\n  --code-bg: #001f3f;\n  --code-text: #d4f1ff;\n}\n\n.wp_blog_container {\n  font-family: 'Segoe UI', sans-serif;\n  background: var(--light-bg);\n  margin: 0;\n  padding: 0;\n  color: var(--text-dark);\n}\n\n\/* Heading *\/\n.wp_blog_main-heading {\n  text-align: center;\n  font-size: 2.4rem;\n  color: var(--primary);\n  margin-top: 2.5rem;\n  font-weight: bold;\n}\n\n\/* Explanation Card *\/\n.wp_blog_explanation,\n.wp_blog_code-tabs-container {\n  max-width: 940px;\n  margin: 2rem auto;\n  padding: 2rem;\n  background: white;\n  border-radius: var(--tab-radius);\n  box-shadow: var(--shadow);\n}\n\n\/* Text and Visuals *\/\n.wp_blog_explanation h2 {\n  font-size: 1.4rem;\n  color: var(--primary);\n  margin-bottom: 0.5rem;\n}\n\n.wp_blog_explanation p,\n.wp_blog_explanation li {\n  font-size: 1.05rem;\n  line-height: 1.7;\n  margin: 0.5rem 0;\n}\n\n.wp_blog_explanation code {\n  background: #fef9f4; 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\/* makes it the reference for absolute children *\/\n}\n\n.wp_blog_toggle-btn {\n  position: absolute;\n  top: 1rem;\n  right: 1rem;\n  z-index: 9999;\n  padding: 0.5rem 0.8rem;\n  border-radius: 10%;\n  background: var(--primary);\n  color: white;\n  font-weight: bold;\n  cursor: pointer;\n  border: none;\n  box-shadow: var(--shadow);\n  transition: background 0.3s, transform 0.2s;\n}\n\n.wp_blog_toggle-btn:hover {\n  background: #cc772e;\n}\n\n.wp_blog_theme.dark-mode .wp_blog_code-tabs-container {\n  background: #1e1e1e;\n}\n<\/style>\n\n<div class=\"wp_blog_container wp_blog_theme\">\n  <button id=\"blogNotesThemeToggle\" class=\"wp_blog_toggle-btn\">\ud83c\udf19<\/button>\n  <h1 class=\"wp_blog_main-heading\"><\/h1>\n\n  <div class=\"wp_blog_explanation\">\n    <h2>Minimum Spanning Tree<\/h2>\n    <h2>Spanning Tree<\/h2>\n    <p><strong>It is a subgraph that connects all vertuces of the graph with no cycles and exactly n-1 edges.<\/strong><\/p>\n    <h2>Points to Remember:<\/h2>\n    <ul>\n            <li>All Nodes<\/li>\n            <li>Connected<\/li>\n            <li>No Cycles<\/li>\n            <li>(n-1) edges<\/li>\n    <\/ul>\n    <img decoding=\"async\" src=\"https:\/\/namastedev.com\/blog\/wp-content\/uploads\/2025\/12\/Screenshot-2025-12-23-at-12.03.16-PM.png\" alt=\"\">\n    <h4>Cost: <code>7 + 2 + 6 + 3 + 8 = 26<\/code><\/h4>\n\n    <h4>Minimum Spanning Tree<\/h4>\n    <img decoding=\"async\" src=\"https:\/\/namastedev.com\/blog\/wp-content\/uploads\/2025\/12\/Screenshot-2025-12-23-at-12.14.34-PM.png\" alt=\"spanning tree\">\n\n    <h2>Spaaning Tree<\/h2>\n    <img decoding=\"async\" src=\"https:\/\/namastedev.com\/blog\/wp-content\/uploads\/2025\/12\/Screenshot-2025-12-23-at-12.18.29-PM.png\" alt=\"\">\n    <h4>Minimum Cost Spanning Tree:<code>5 + 1 + 2 + 3 + 8 = 19<\/code><\/h4>\n\n    <h2>Why Minimum Spanning Tree?<\/h2>\n    <ul>\n        <li>Minimum edges to connect a network.<\/li>\n        <li>No Cycles.<\/li>\n        <li>Simplify the Structure.<\/li>\n    <\/ul>\n\n    <h2>Use Case:<\/h2>\n    <ul>\n        <li>Network<\/li>\n        <li>Routing<\/li>\n        <li>Broadcasting<\/li>\n        <li>Infrastructure design (roads, pipes, electricity)<\/li>\n    <\/ul>\n\n    <h2>Minimum Spanning Tree Algorithms<\/h2>\n    <h5><i>This will be covered in upcoming videos<\/i><\/h5>\n    <ul>\n        <code>\n            <li>Prim's Algorithm<\/li>\n            <li>Kruskal's Algorithm<\/li>\n        <\/code>\n    <\/ul>\n<\/div>  \n<\/div>\n<script>\ndocument.addEventListener(\"DOMContentLoaded\", () => {\n  const buttons = document.querySelectorAll(\".wp_blog_code-tab-button\");\n  const contents = document.querySelectorAll(\".wp_blog_code-tab-content\");\n\n  buttons.forEach((button) => {\n    button.addEventListener(\"click\", () => {\n      const lang = button.getAttribute(\"data-lang\");\n\n      buttons.forEach((btn) => btn.classList.remove(\"active\"));\n      contents.forEach((content) => content.classList.remove(\"active\"));\n\n      button.classList.add(\"active\");\n      document\n        .querySelector(`.wp_blog_code-tab-content[data-lang=\"${lang}\"]`)\n        .classList.add(\"active\");\n    });\n  });\n\n  const themeToggle = document.getElementById(\"blogNotesThemeToggle\");\n  const themeContainer = document.querySelector(\".wp_blog_theme\");\n\n  themeToggle.addEventListener(\"click\", () => {\n    themeContainer.classList.toggle(\"dark-mode\");\n    themeToggle.textContent =\n      themeContainer.classList.contains(\"dark-mode\") ? \"\u2600\ufe0f\" : \"\ud83c\udf19\";\n  });\n});\n<\/script>\n\n","protected":false},"excerpt":{"rendered":"<p>\ud83c\udf19 Minimum Spanning Tree Spanning Tree It is a subgraph that connects all vertuces of the graph with no cycles and exactly n-1 edges. Points to Remember: All Nodes Connected No Cycles (n-1) edges Cost: 7 + 2 + 6 + 3 + 8 = 26 Minimum Spanning Tree Spaaning Tree Minimum Cost Spanning Tree:5<\/p>\n","protected":false},"author":108,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"categories":[210,322,260,176,175,211,811,810,174,172,173],"tags":[],"class_list":["post-11334","post","type-post","status-publish","format-standard","category-algorithms","category-algorithms-and-data-structures","category-c-c-plus-plus","category-csharp","category-cplusplus","category-data-structures","category-data-structures-and-algorithms","category-dsa","category-java","category-javascript","category-python"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/11334","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/users\/108"}],"replies":[{"embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/comments?post=11334"}],"version-history":[{"count":1,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/11334\/revisions"}],"predecessor-version":[{"id":11335,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/11334\/revisions\/11335"}],"wp:attachment":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/media?parent=11334"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/categories?post=11334"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/tags?post=11334"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}