{"id":9515,"date":"2025-08-20T18:33:57","date_gmt":"2025-08-20T13:03:57","guid":{"rendered":"https:\/\/namastedev.com\/blog\/?p=9515"},"modified":"2025-10-15T13:16:40","modified_gmt":"2025-10-15T07:46:40","slug":"introduction-to-backtracking","status":"publish","type":"post","link":"https:\/\/namastedev.com\/blog\/introduction-to-backtracking\/","title":{"rendered":"Introduction to Backtracking"},"content":{"rendered":"\n<!-- Prism.js for Code Highlighting -->\n<link\n    href=\"https:\/\/cdn.jsdelivr.net\/npm\/prismjs@1.29.0\/themes\/prism-tomorrow.min.css\"\n    rel=\"stylesheet\"\n\/>\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>Backtracking<\/h2>\n        <p><strong>Recursive Algorithmic technique<\/strong> for solving problems <code>incrementally by trying partial solutions<\/code> and then abandoning them (backtracking) is they fail to satisfy <code>constraints<\/code>.<\/p>\n\n        <h2>Note:<\/h2>\n        <p><strong>Exploring all<\/strong> possibility but <code>being smart by abandoning wrong<\/code> path early.<\/p>\n\n        <p><code>Example<\/code>: Like trying <code>all the paths<\/code> in <strong>max and going back<\/strong> if you hit a wall.\n<\/p>\n        <h2>When to use Backtracking ?<\/h2>\n        <ul>\n            <li>You want to explore all combination\/permutations\/subsets.<\/li>\n            <li>When there is a Clear way to validate a partial solution.<\/li>\n            <li>Number of combinations is too large to brute force, so you abandon the invalid ones early.<\/li>\n        <\/ul>\n\n        <p><strong><i>Basically, Backtracking optimise Recursion.<\/i><\/strong><\/p>\n        <p><strong>Note: Try a choice -> work ?, continue -> if not, undo (backtrack).<\/strong><\/p>\n        \n        <h2>Example: <\/h2>\n        <h3>From the numbers [2, 3, 5, 10, 12], try to find a combination that gives a sum of 15. \nSolution.<\/h3>\n\n        <ul>\n            <li>* Label the numbers as <strong>x\u2080, x\u2081, x\u2082, x\u2083, x\u2084<\/strong>.<\/li>\n            <li>* Find <strong>all<\/strong> possible <code>combinations<\/code>.<\/li>\n            <li>* Think <strong>carefully about the choices<\/strong>.<\/li>\n            <li>* <code>Develop<\/code> the <strong>state space tree<\/strong> (or recursion tree, or path inside recursion) to find the solution.<\/li>\n            <li>* Initialize <strong>Sum = 0<\/strong>.<\/li>\n        <\/ul>\n        <p>Now, we have to make a decision: whether we want to include 2 or not.<\/p>\n\n        <img decoding=\"async\" src=\"https:\/\/namastedev.com\/blog\/wp-content\/uploads\/2025\/08\/Screenshot-2025-08-20-at-6.31.55\u202fPM.png\" alt=\"\">\n        <p>Above, This is a type of problem that uses <strong>backtracking<\/strong>.<\/p>\n        <p><code>Choices: 2<sup>5<\/sup><\/code><\/p>\n        <p>Tree have <strong>maximum choices: <\/strong><code>2<sup>n<\/sup><\/code>.<\/p>\n    \n    <h2>Use Cases:<\/h2>\n    <ul>\n        <li>Subset<\/li>\n        <li>Combinations<\/li>\n        <li>Permutations<\/li>\n        <li>N-Queens<\/li>\n        <li>A lot of <code>choices<\/code> and <code>decisions<\/code><\/li>\n    <\/ul>\n    <\/div>\n<\/div>\n\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","protected":false},"excerpt":{"rendered":"<p>\ud83c\udf19 Backtracking Recursive Algorithmic technique for solving problems incrementally by trying partial solutions and then abandoning them (backtracking) is they fail to satisfy constraints. Note: Exploring all possibility but being smart by abandoning wrong path early. Example: Like trying all the paths in max and going back if you hit a wall. When to use<\/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":[210,322,176,175,211,811,810,174,172,173],"tags":[],"class_list":{"0":"post-9515","1":"post","2":"type-post","3":"status-publish","4":"format-standard","6":"category-algorithms","7":"category-algorithms-and-data-structures","8":"category-csharp","9":"category-cplusplus","10":"category-data-structures","11":"category-data-structures-and-algorithms","12":"category-dsa","13":"category-java","14":"category-javascript","15":"category-python"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/9515","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=9515"}],"version-history":[{"count":2,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/9515\/revisions"}],"predecessor-version":[{"id":10316,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/9515\/revisions\/10316"}],"wp:attachment":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/media?parent=9515"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/categories?post=9515"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/tags?post=9515"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}