{"id":9359,"date":"2025-08-15T17:40:54","date_gmt":"2025-08-15T12:10:54","guid":{"rendered":"https:\/\/namastedev.com\/blog\/?p=9359"},"modified":"2025-10-15T16:16:42","modified_gmt":"2025-10-15T10:46:42","slug":"permutations","status":"publish","type":"post","link":"https:\/\/namastedev.com\/blog\/permutations\/","title":{"rendered":"Permutations"},"content":{"rendered":"\n<!-- Evaluate Reverse Polish Notation 10-->\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;   \/* light bg instead of dark blue *\/\n  color: #E58C32;        \/* brand orange *\/\n  padding: 3px 6px;\n  border-radius: 4px;\n  font-family: 'Courier New', monospace;\n  font-weight: 600;      \/* optional, makes it pop *\/\n}\n\n.wp_blog_explanation img {\n  max-width: 100%;\n  border-radius: var(--tab-radius);\n  margin-top: 1rem;\n  box-shadow: 0 2px 12px rgba(0, 0, 0, 0.06);\n}\n\n\/* Tab Buttons *\/\n.wp_blog_code-tabs-header {\n  display: flex;\n  flex-wrap: wrap;\n  gap: 0.5rem;\n  margin-bottom: 1rem;\n}\n\n.wp_blog_code-tab-button {\n  padding: 0.6rem 1.2rem;\n  border: 1px solid var(--primary);\n  background: white;\n  color: var(--primary);\n  border-radius: 50px;\n  font-weight: 600;\n  cursor: pointer;\n  transition: all 0.3s ease;\n}\n\n.wp_blog_code-tab-button:hover {\n  background: var(--secondary);\n}\n\n.wp_blog_code-tab-button.active {\n  background: var(--primary);\n  color: white;\n}\n\n\/* Code Content *\/\n.wp_blog_code-tab-content {\n  display: none;\n  background: var(--code-bg);\n  border-radius: var(--tab-radius);\n}\n\n.wp_blog_code-tab-content.active {\n  display: block;\n}\n\n.wp_blog_code-tab-content pre {\n  margin: 0;\n  padding: 1.5rem;\n  font-size: 1rem;\n  overflow-x: auto;\n  background: var(--code-bg);\n  border-radius: var(--tab-radius);\n  color: var(--code-text);\n}\n\n\/* Dark mode variables *\/\n.wp_blog_theme.dark-mode {\n  --light-bg: #121212;\n  --text-dark: #f5f5f5;\n  --shadow: 0 4px 12px rgba(255, 255, 255, 0.08);\n  --code-bg: #1e1e1e;\n  --code-text: #c5f0ff;\n}\n\n.wp_blog_theme.dark-mode .wp_blog_explanation {\n  background: #1e1e1e;\n}\n\n\/* Dark mode code highlight *\/\n.wp_blog_theme.dark-mode .wp_blog_explanation code {\n  background: #333;\n  color: #ffd27f;\n}\n\n.wp_blog_theme {\n  position: relative; \/* 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>Problem Statement:<\/h2>\n    <p>\n        Given an array <code>nums<\/code> of distinct integers, return all the possible permutations. You can return the answer in <strong>any order<\/strong>.\n    <\/p>\n    \n    <p><strong>Example 1:<\/strong><\/p>\n    <p><strong>Input:<\/strong>nums = [1,2,3]<\/p>\n    <p><strong>Output:<\/strong><code> [[1,2,3],[1,3,2],[2,1,3],[2,3,1],[3,1,2],[3,2,1]]<\/code><\/p>\n\n    <p><strong>Example 2:<\/strong><\/p>\n    <p><strong>Input:<\/strong> nums = [0,1]<\/p>\n    <p><strong>Output:<\/strong><code>[[0,1],[1,0]]<\/code><\/p>\n\n    <p><strong>Example 3:<\/strong><\/p>\n    <p><strong>Input:<\/strong> nums = [1]<\/p>\n    <p><strong>Output:<\/strong><code>[[1]]<\/code><\/p>\n\n\n    <h2>Constraints:<\/h2>\n    <ul>\n        <li><code>1 <= nums.length <= 10<\/code><\/li>\n        <li><code>-10 <= nums[i] <= 10<\/code><\/li>\n        <li>All the integer of <code>nums<\/code> are <strong>unique<\/strong>.<\/li>\n    <\/ul>\n\n    <h2>Approach:<\/h2>\n   <ul>\n        <li><code>Maintain a path<\/code> array for the current permutation.<\/li>\n        <li>At <strong>each step<\/strong>, try <code>adding an unused element<\/code> from arr.<\/li>\n        <li>If <code>path length equals<\/code> <strong>n, push<\/strong> a copy to result.<\/li>\n        <li><strong>Backtrack<\/strong> by removing the last element and trying the next option.<\/li>\n    <\/ul> \n\n    <h2>Time Complexity:<\/h2>\n    <li><p><strong>Time Complexity = O(n \u00d7 n!)<\/strong><\/p><\/li> \n    <h2>Space Complexity:<\/h2>\n    <li><p><strong>Space Complexity = O(n) for recursion + O(n!) output storage.<\/strong><\/p><\/li>\n\n<h2>Dry Run<\/h2>\n<div style=\"background: var(--light-bg); border-left: 4px solid var(--primary); padding: 1rem; border-radius: var(--tab-radius); margin: 1rem 0; color: var(--text-dark);\">\n\n  <p><strong>Input:<\/strong> <code>arr = [1, 2, 3]<\/code><\/p>\n\n  <pre style=\"white-space: pre-wrap; background: var(--code-bg); padding: 1rem; border-radius: 8px; overflow-x: auto; color: var(--code-text);\">\nStep 0: Start Function backtrackSubsets([1, 2, 3])\nn = 3\nInitialize:\nresult = []\npath = []\n\nCall backtrack([], 0)\n\u2192 Push [] \u2192 result = [[]]\n\nLoop i = 0 \u2192 arr[0] = 1\npath.push(1) \u2192 path = [1]\nCall backtrack([1], 1)\n  \u2192 Push [1] \u2192 result = [[], [1]]\n\n  Loop i = 1 \u2192 arr[1] = 2\n  path.push(2) \u2192 path = [1, 2]\n  Call backtrack([1, 2], 2)\n    \u2192 Push [1, 2] \u2192 result = [[], [1], [1, 2]]\n\n    Loop i = 2 \u2192 arr[2] = 3\n    path.push(3) \u2192 path = [1, 2, 3]\n    Call backtrack([1, 2, 3], 3)\n      \u2192 Push [1, 2, 3] \u2192 result = [[], [1], [1, 2], [1, 2, 3]]\n    Loop ends (start = 3 >= n)\n    path.pop() \u2192 path = [1, 2]\n\n  Loop ends\n  path.pop() \u2192 path = [1]\n\n  Loop i = 2 \u2192 arr[2] = 3\n  path.push(3) \u2192 path = [1, 3]\n  Call backtrack([1, 3], 3)\n    \u2192 Push [1, 3] \u2192 result = [[], [1], [1, 2], [1, 2, 3], [1, 3]]\n  Loop ends\n  path.pop() \u2192 path = [1]\n\nLoop ends\npath.pop() \u2192 path = []\n\nLoop i = 1 \u2192 arr[1] = 2\npath.push(2) \u2192 path = [2]\nCall backtrack([2], 2)\n  \u2192 Push [2] \u2192 result = [[], [1], [1, 2], [1, 2, 3], [1, 3], [2]]\n\n  Loop i = 2 \u2192 arr[2] = 3\n  path.push(3) \u2192 path = [2, 3]\n  Call backtrack([2, 3], 3)\n    \u2192 Push [2, 3] \u2192 result = [..., [2, 3]]\n  Loop ends\n  path.pop() \u2192 path = [2]\n\nLoop ends\npath.pop() \u2192 path = []\n\nLoop i = 2 \u2192 arr[2] = 3\npath.push(3) \u2192 path = [3]\nCall backtrack([3], 3)\n  \u2192 Push [3] \u2192 result = [..., [3]]\nLoop ends\npath.pop() \u2192 path = []\n\nStep 3: End\nReturn result = [[], [1], [1, 2], [1, 2, 3], [1, 3], [2], [2, 3], [3]]\n  <\/pre>\n\n  <p><strong>Output:<\/strong> \n    <code>[[], [1], [1, 2], [1, 2, 3], [1, 3], [2], [2, 3], [3]]<\/code>\n  <\/p>\n\n  <p><strong>Explanation:<\/strong> The backtracking algorithm pushes the current <code>path<\/code> to <code>result<\/code> at every call, then iterates choices from <code>start<\/code> to <code>n-1<\/code>. For each choice, it adds the element, recurses to explore deeper subsets, and then removes the element (backtracks) to explore the next choice.<\/p>\n  \n<\/div>\n\n<\/div>\n\n<div class=\"wp_blog_code-tabs-container\">\n    <div class=\"wp_blog_code-tabs-header\">\n        <button class=\"wp_blog_code-tab-button active\" data-lang=\"js\">JavaScript<\/button>\n        <button class=\"wp_blog_code-tab-button\" data-lang=\"py\">Python<\/button>\n        <button class=\"wp_blog_code-tab-button\" data-lang=\"java\">Java<\/button>\n        <button class=\"wp_blog_code-tab-button\" data-lang=\"cpp\">C++<\/button>\n        <button class=\"wp_blog_code-tab-button\" data-lang=\"c\">C<\/button>\n        <button class=\"wp_blog_code-tab-button\" data-lang=\"cs\">C#<\/button>\n    <\/div>\n\n    <div class=\"wp_blog_code-tab-content active\" data-lang=\"js\">\n<pre><code class=\"language-javascript\">\nvar permute = function(arr) {\n    let result = [];\n    let n = arr.length;\n    let backtrack = (path) => {\n        if(path.length === n){\n            result.push([...path]);\n        }\n        for(let i=0; i < n; i++){\n            if(!path.includes(arr[i])){\n                path.push(arr[i]);\n                backtrack(path);\n                path.pop();\n            }\n        }\n    }\n    backtrack([]);\n    return result;\n};\n<\/code><\/pre>\n<\/div>\n\n<div class=\"wp_blog_code-tab-content\" data-lang=\"py\">\n<pre><code class=\"language-python\">\ndef permute(arr):\n    result = []\n    n = len(arr)\n    \n    def backtrack(path):\n        if len(path) == n:\n            result.append(path[:])\n            return\n        for i in range(n):\n            if arr[i] not in path:\n                path.append(arr[i])\n                backtrack(path)\n                path.pop()\n    \n    backtrack([])\n    return result\n\n# Example\narr = [1, 2, 3]\nres = permute(arr)\nfor r in res:\n    print(r)\n<\/code><\/pre>\n<\/div>\n\n<div class=\"wp_blog_code-tab-content\" data-lang=\"java\">\n<pre><code class=\"language-java\">\npublic class Main {\n    static void backtrack(List<Integer> arr, List<Integer> path, List<List<Integer>> result, int n) {\n        if (path.size() == n) {\n            result.add(new ArrayList<>(path));\n            return;\n        }\n        for (int i = 0; i < n; i++) {\n            if (!path.contains(arr.get(i))) {\n                path.add(arr.get(i));\n                backtrack(arr, path, result, n);\n                path.remove(path.size() - 1);\n            }\n        }\n    }\n    static List<List<Integer>> permute(List<Integer> arr) {\n        List<List<Integer>> result = new ArrayList<>();\n        backtrack(arr, new ArrayList<>(), result, arr.size());\n        return result;\n    }\n    public static void main(String[] args) {\n        List<Integer> arr = Arrays.asList(1, 2, 3);\n        List<List<Integer>> res = permute(arr);\n        for (List<Integer> list : res) {\n            System.out.println(list);\n        }\n    }\n}\n<\/code><\/pre>\n<\/div>\n\n<div class=\"wp_blog_code-tab-content\" data-lang=\"cpp\">\n<pre><code class=\"language-cpp\">\nvoid backtrack(vector<int> &arr, vector<int> &path, vector<vector<int>> &result, int n) {\n    if (path.size() == n) {\n        result.push_back(path);\n        return;\n    }\n    for (int i = 0; i < n; i++) {\n        if (find(path.begin(), path.end(), arr[i]) == path.end()) {\n            path.push_back(arr[i]);\n            backtrack(arr, path, result, n);\n            path.pop_back();\n        }\n    }\n}\nvector<vector<int>> permute(vector<int> &arr) {\n    vector<vector<int>> result;\n    vector<int> path;\n    backtrack(arr, path, result, arr.size());\n    return result;\n}\nint main() {\n    vector<int> arr = {1, 2, 3};\n    vector<vector<int>> res = permute(arr);\n    for (auto &v : res) {\n        for (int x : v) cout << x << \" \";\n        cout << endl;\n    }\n    return 0;\n}\n<\/code><\/pre>\n<\/div>\n\n<div class=\"wp_blog_code-tab-content\" data-lang=\"c\">\n<pre><code class=\"language-c\">\nvoid printPermutation(int *path, int n) {\n    for (int i = 0; i < n; i++) printf(\"%d \", path[i]);\n    printf(\"\\n\");\n}\nbool contains(int *path, int pathSize, int val) {\n    for (int i = 0; i < pathSize; i++)\n        if (path[i] == val) return true;\n    return false;\n}\nvoid backtrack(int *arr, int *path, int n, int pathSize) {\n    if (pathSize == n) {\n        printPermutation(path, n);\n        return;\n    }\n    for (int i = 0; i < n; i++) {\n        if (!contains(path, pathSize, arr[i])) {\n            path[pathSize] = arr[i];\n            backtrack(arr, path, n, pathSize + 1);\n        }\n    }\n}\nint main() {\n    int arr[] = {1, 2, 3};\n    int n = sizeof(arr) \/ sizeof(arr[0]);\n    int *path = (int*)malloc(n * sizeof(int));\n    backtrack(arr, path, n, 0);\n    free(path);\n    return 0;\n}\n<\/code><\/pre>\n<\/div>\n\n<div class=\"wp_blog_code-tab-content\" data-lang=\"cs\">\n<pre><code class=\"language-csharp\">\nclass Program {\n    static void Backtrack(List<int> arr, List<int> path, List<List<int>> result, int n) {\n        if (path.Count == n) {\n            result.Add(new List<int>(path));\n            return;\n        }\n        for (int i = 0; i < n; i++) {\n            if (!path.Contains(arr[i])) {\n                path.Add(arr[i]);\n                Backtrack(arr, path, result, n);\n                path.RemoveAt(path.Count - 1);\n            }\n        }\n    }\n    static List<List<int>> Permute(List<int> arr) {\n        var result = new List<List<int>>();\n        Backtrack(arr, new List<int>(), result, arr.Count);\n        return result;\n    }\n    static void Main() {\n        var arr = new List<int> { 1, 2, 3 };\n        var res = Permute(arr);\n        foreach (var list in res) {\n            Console.WriteLine(string.Join(\" \", list));\n        }\n    }\n}\n<\/code><\/pre>\n<\/div>\n<\/div>\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 Problem Statement: Given an array nums of distinct integers, return all the possible permutations. You can return the answer in any order. Example 1: Input:nums = [1,2,3] Output: [[1,2,3],[1,3,2],[2,1,3],[2,3,1],[3,1,2],[3,2,1]] Example 2: Input: nums = [0,1] Output:[[0,1],[1,0]] Example 3: Input: nums = [1] Output:[[1]] Constraints: 1<\/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-9359","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\/9359","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=9359"}],"version-history":[{"count":2,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/9359\/revisions"}],"predecessor-version":[{"id":10325,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/9359\/revisions\/10325"}],"wp:attachment":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/media?parent=9359"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/categories?post=9359"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/tags?post=9359"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}