{"id":9509,"date":"2025-08-20T16:36:24","date_gmt":"2025-08-20T11:06:24","guid":{"rendered":"https:\/\/namastedev.com\/blog\/?p=9509"},"modified":"2025-10-13T16:12:05","modified_gmt":"2025-10-13T10:42:05","slug":"permutations-ii","status":"publish","type":"post","link":"https:\/\/namastedev.com\/blog\/permutations-ii\/","title":{"rendered":"Permutations  II"},"content":{"rendered":"\n<!-- Permutation_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\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>Problem Statement<\/h2>\n    <p>\n        Given a collection of numbers, <code>nums<\/code>, that might contain duplicates, return <i>all possible unique permutations <strong>in any order<\/strong><\/i>.\n    <\/p>\n\n    <p><strong>Example 1:<\/strong><\/p>\n    <p><strong>Input:<\/strong> nums = [1,1,2]<\/p>\n    <p><strong>Output:<\/strong><code> \n        [[1,1,2],\n        [1,2,1],\n        [2,1,1]]\n<\/code><\/p>\n\n    <p><strong>Example 2:<\/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    <h2>Constraints<\/h2>\n    <ul>\n        <li><code>1 <= nums.length <= 8<\/code><\/li>\n        <li><code>-10 <= nums[i] <= 10<\/code>.<\/li>\n    <\/ul>\n\n    <h2>Approach<\/h2>\n    <ul>\n        <li><strong>Sort the array<\/strong> \u2192 so duplicates are adjacent.<\/li>\n        <li><strong>Use backtracking<\/strong>\n            <ul>\n                <li><code>Maintain<\/code> a path (current permutation being built).<\/li>\n                <li>At each step, iterate over remaining <code>choices<\/code>.<\/li>\n                <li><strong>Skip duplicates<\/strong> If the current number is the same as the previous <code>(choices[i] === choices[i-1])<\/code> \u2192 continue.<\/li>\n                <li>Pick <code>choices[i]<\/code>, recurse with the rest of the elements, then backtrack.<\/li>\n            <\/ul>\n        <\/li>\n        <li>When path.length === arr.length, store it in result.<\/li>\n    <\/ul> \n\n    <h2>Time Complexity<\/h2>\n    <li><p><strong>Time Complexity = O(n * n!)<\/strong><\/p><\/li> \n    <h2>Space Complexity<\/h2>\n    <li><p><strong>Space Complexity =  O(n * n!)<\/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<p><strong>Input:<\/strong> <code>digits = \"23\"<\/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);\">\nInitialize:\ndigits = \"23\"\nletters = { 2: \"abc\", 3: \"def\", 4: \"ghi\", 5: \"jkl\", 6: \"mno\", 7: \"pqrs\", 8: \"tuv\", 9: \"wxyz\" }\nresult = []\n\nCall backtrack([], 0)\nbacktrack([], 0):\nindex = 0 \u2192 digits[0] = '2' \u2192 choices = \"abc\"\n\nLoop i over \"abc\":\n  i = 0 \u2192 path = ['a']\n    \u2192 backtrack(['a'], 1)\n\n    backtrack(['a'], 1):\n    index = 1 \u2192 digits[1] = '3' \u2192 choices = \"def\"\n\n    Loop i over \"def\":\n      i = 0 \u2192 path = ['a','d']\n        \u2192 backtrack(['a','d'], 2)\n        index == digits.length \u2192 push \"ad\"\n        result = [\"ad\"]\n        path.pop() \u2192 ['a']\n\n      i = 1 \u2192 path = ['a','e']\n        \u2192 backtrack(['a','e'], 2)\n        push \"ae\"\n        result = [\"ad\",\"ae\"]\n        path.pop() \u2192 ['a']\n\n      i = 2 \u2192 path = ['a','f']\n        \u2192 backtrack(['a','f'], 2)\n        push \"af\"\n        result = [\"ad\",\"ae\",\"af\"]\n        path.pop() \u2192 ['a']\n\n    End of inner loop, path.pop() \u2192 []\n\ni = 1 \u2192 path = ['b']\n  \u2192 backtrack(['b'], 1)\n\n  index = 1 \u2192 digits[1] = '3' \u2192 choices = \"def\"\n\n  Loop:\n    'd' \u2192 push \"bd\"\n    'e' \u2192 push \"be\"\n    'f' \u2192 push \"bf\"\n\n  result = [\"ad\",\"ae\",\"af\",\"bd\",\"be\",\"bf\"]\n  path.pop() \u2192 []\n\ni = 2 \u2192 path = ['c']\n  \u2192 backtrack(['c'], 1)\n\n  digits[1] = '3' \u2192 choices = \"def\"\n\n  Loop:\n    'd' \u2192 push \"cd\"\n    'e' \u2192 push \"ce\"\n    'f' \u2192 push \"cf\"\n\n  result = [\"ad\",\"ae\",\"af\",\"bd\",\"be\",\"bf\",\"cd\",\"ce\",\"cf\"]\n  path.pop() \u2192 []\n\nAll recursive calls complete.\nReturn result = [\"ad\",\"ae\",\"af\",\"bd\",\"be\",\"bf\",\"cd\",\"ce\",\"cf\"]\n  <\/pre>\n\n  <p><strong>Output:<\/strong> <code>[\"ad\",\"ae\",\"af\",\"bd\",\"be\",\"bf\",\"cd\",\"ce\",\"cf\"]<\/code><\/p> \n  <p><strong>Explanation:<\/strong>\n  The algorithm uses backtracking:\n  <ul>\n    <li>For each digit, loop through the mapped letters.<\/li>\n    <li>Append a letter, recurse to the next digit, then pop (backtrack).<\/li>\n    <li>When <code>index === digits.length<\/code>, join the path and push to <code>result<\/code>.<\/li>\n  <\/ul>\n  <\/p>\n<\/div>\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 permuteUnique = function(arr) {\n    let result = [];\n    arr.sort((a,b) => (a-b));\n    let backtrack = (path, choices) => {\n        if(path.length === arr.length) {\n            result.push([...path]);\n            return;\n        }\n\n        for(let i=0; i<choices.length; i++){\n            if(i > 0 && choices[i] === choices[i-1])\n            continue;\n            path.push(choices[i]);\n            backtrack(path, [...choices.slice(0, i), ...choices.slice(i+1)]);\n            path.pop();\n        }\n    }\n    backtrack([], arr);\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 permuteUnique(nums):\n    result = []\n    nums.sort()\n    used = [False] * len(nums)\n\n    def backtrack(path):\n        if len(path) == len(nums):\n            result.append(path[:])\n            return\n        for i in range(len(nums)):\n            if used[i]:\n                continue\n            if i > 0 and nums[i] == nums[i-1] and not used[i-1]:\n                continue\n            used[i] = True\n            path.append(nums[i])\n            backtrack(path)\n            path.pop()\n            used[i] = False\n\n    backtrack([])\n    return result\n\n<\/code><\/pre>\n<\/div>\n\n<div class=\"wp_blog_code-tab-content\" data-lang=\"java\">\n<pre><code class=\"language-java\">\nimport java.util.*;\n\nclass Solution {\n    public List<List<Integer>> permuteUnique(int[] nums) {\n        List<List<Integer>> result = new ArrayList<>();\n        Arrays.sort(nums);\n        boolean[] used = new boolean[nums.length];\n        backtrack(nums, used, new ArrayList<>(), result);\n        return result;\n    }\n\n    private void backtrack(int[] nums, boolean[] used, List<Integer> path, List<List<Integer>> result) {\n        if (path.size() == nums.length) {\n            result.add(new ArrayList<>(path));\n            return;\n        }\n\n        for (int i = 0; i < nums.length; i++) {\n            if (used[i]) continue;\n            if (i > 0 && nums[i] == nums[i-1] && !used[i-1]) continue;\n\n            used[i] = true;\n            path.add(nums[i]);\n            backtrack(nums, used, path, result);\n            path.remove(path.size() - 1);\n            used[i] = false;\n        }\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\">\nclass Solution {\npublic:\n    vector<vector<int>> permuteUnique(vector<int>& nums) {\n        vector<vector<int>> result;\n        sort(nums.begin(), nums.end());\n        vector<int> path;\n        vector<bool> used(nums.size(), false);\n        backtrack(nums, used, path, result);\n        return result;\n    }\n\n    void backtrack(vector<int>& nums, vector<bool>& used, vector<int>& path, vector<vector<int>>& result) {\n        if (path.size() == nums.size()) {\n            result.push_back(path);\n            return;\n        }\n\n        for (int i = 0; i < nums.size(); i++) {\n            if (used[i]) continue;\n            if (i > 0 && nums[i] == nums[i-1] && !used[i-1]) continue;\n\n            used[i] = true;\n            path.push_back(nums[i]);\n            backtrack(nums, used, path, result);\n            path.pop_back();\n            used[i] = false;\n        }\n    }\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 size) {\n    for(int i = 0; i < size; i++) {\n        printf(\"%d \", path[i]);\n    }\n    printf(\"\\n\");\n}\n\nvoid backtrack(int* nums, int numsSize, bool* used, int* path, int depth) {\n    if (depth == numsSize) {\n        printPermutation(path, numsSize);\n        return;\n    }\n\n    for (int i = 0; i < numsSize; i++) {\n        if (used[i]) continue;\n        if (i > 0 && nums[i] == nums[i-1] && !used[i-1]) continue;\n\n        used[i] = true;\n        path[depth] = nums[i];\n        backtrack(nums, numsSize, used, path, depth + 1);\n        used[i] = false;\n    }\n}\n\nint cmp(const void* a, const void* b) {\n    return (*(int*)a - *(int*)b);\n}\n\nint main() {\n    int nums[] = {1, 1, 2};\n    int size = sizeof(nums) \/ sizeof(nums[0]);\n    qsort(nums, size, sizeof(int), cmp);\n\n    bool used[100] = {false};\n    int path[100];\n    backtrack(nums, size, used, path, 0);\n    return 0;\n}\n\n<\/code><\/pre>\n<\/div>\n\n<div class=\"wp_blog_code-tab-content\" data-lang=\"cs\">\n<pre><code class=\"language-csharp\">\nusing System;\nusing System.Collections.Generic;\n\npublic class Solution {\n    public IList<IList<int>> PermuteUnique(int[] nums) {\n        var result = new List<IList<int>>();\n        Array.Sort(nums);\n        bool[] used = new bool[nums.Length];\n        Backtrack(nums, used, new List<int>(), result);\n        return result;\n    }\n\n    private void Backtrack(int[] nums, bool[] used, List<int> path, IList<IList<int>> result) {\n        if (path.Count == nums.Length) {\n            result.Add(new List<int>(path));\n            return;\n        }\n\n        for (int i = 0; i < nums.Length; i++) {\n            if (used[i]) continue;\n            if (i > 0 && nums[i] == nums[i-1] && !used[i-1]) continue;\n\n            used[i] = true;\n            path.Add(nums[i]);\n            Backtrack(nums, used, path, result);\n            path.RemoveAt(path.Count - 1);\n            used[i] = false;\n        }\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 a collection of numbers, nums, that might contain duplicates, return all possible unique permutations in any order. Example 1: Input: nums = [1,1,2] Output: [[1,1,2], [1,2,1], [2,1,1]] Example 2: Input: nums = [1,2,3] Output: [[1,2,3],[1,3,2],[2,1,3],[2,3,1],[3,1,2],[3,2,1]] Constraints 1 0 &#038;&#038; nums[i] == nums[i-1] &#038;&#038; !used[i-1]) continue; used[i] = true; path.add(nums[i]); backtrack(nums, used,<\/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-9509","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\/9509","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=9509"}],"version-history":[{"count":4,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/9509\/revisions"}],"predecessor-version":[{"id":10260,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/9509\/revisions\/10260"}],"wp:attachment":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/media?parent=9509"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/categories?post=9509"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/tags?post=9509"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}