{"id":9352,"date":"2025-08-15T17:34:22","date_gmt":"2025-08-15T12:04:22","guid":{"rendered":"https:\/\/namastedev.com\/blog\/?p=9352"},"modified":"2025-10-15T14:08:38","modified_gmt":"2025-10-15T08:38:38","slug":"subsets-the-power-set","status":"publish","type":"post","link":"https:\/\/namastedev.com\/blog\/subsets-the-power-set\/","title":{"rendered":"Subsets The Power Set"},"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>Given an integer array <code>nums<\/code> of <strong>unique<\/strong> elements, return <i>all possible subsets (the power set)<\/i>.<\/p>\n    <p>The solution set <strong>must not<\/strong> contain duplicate subsets. Return the solution in <strong>any order<\/strong>.<\/p>\n    \n    \n    <p><strong>Example 1:<\/strong>\n    <p><strong>Input:<\/strong> nums = [1,2,3]<\/p>\n    <p><strong>Output:<\/strong><code>[[],[1],[2],[1,2],[3],[1,3],[2,3],[1,2,3]]<\/code><\/p>\n\n    <p><strong>Example 2:<\/strong>\n    <p><strong>Input:<\/strong> nums = [0]<\/p>\n    <p><strong>Output:<\/strong><code>[[],[0]]<\/code><\/p>\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 numbers of <code>nums<\/code> are <strong>unique<\/strong>.<\/li>\n    <\/ul>\n\n    <h2>Approach:<\/h2>\n   <ul>\n        <li><strong>Start<\/strong> with an empty subset <code>(path)<\/code>.<\/li>\n        <li><strong>At each step<\/strong>, add the <code>current subset<\/code> to the result.<\/li>\n        <li><strong>Iterate from the current start<\/strong> index to the end of the array: \n            <ul>\n                <li><code>Include the element<\/code> in the <code>subset<\/code>.<\/li>\n                <li><strong>Recurse to build<\/strong> further subsets from the next index.<\/li>\n                <li>Backtrack by removing the <code>last element<\/code> to explore other possibilities.<\/li> \n            <\/ul>\n        <\/li>\n        <li><code>Continue<\/code> until all combinations are generated.<\/li>\n    <\/ul> \n\n    <h2>Time Complexity:<\/h2>\n    <li><p><strong>Time Complexity = O(2<sup>n<\/sup>)<\/strong><\/p><\/li> \n    <h2>Space Complexity:<\/h2>\n    <li><p><strong>Space Complexity = O(2<sup>n<\/sup>)<\/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\nresult = []\npath = []\n\nCall backtrack([], 0)\n\u2192 Push [] \u2192 result = [[]]\n\nFirst loop:\ni = 0 \u2192 arr[0] = 1\npath.push(1) \u2192 path = [1]\nCall backtrack([1], 1)\n\u2192 Push [1] \u2192 result = [[], [1]]\n\nLoop i = 1 \u2192 arr[1] = 2\npath.push(2) \u2192 path = [1, 2]\nCall backtrack([1, 2], 2)\n\u2192 Push [1, 2] \u2192 result = [[], [1], [1, 2]]\n\nLoop i = 2 \u2192 arr[2] = 3\npath.push(3) \u2192 path = [1, 2, 3]\nCall backtrack([1, 2, 3], 3)\n\u2192 Push [1, 2, 3] \u2192 result = [[], [1], [1, 2], [1, 2, 3]]\nLoop ends (start = 3 >= arr.length)\npath.pop() \u2192 path = [1, 2]\nLoop ends\npath.pop() \u2192 path = [1]\n\nLoop i = 2 \u2192 arr[2] = 3\npath.push(3) \u2192 path = [1, 3]\nCall backtrack([1, 3], 3)\n\u2192 Push [1, 3] \u2192 result = [[], [1], [1, 2], [1, 2, 3], [1, 3]]\nLoop ends\npath.pop() \u2192 path = [1]\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\nLoop i = 2 \u2192 arr[2] = 3\npath.push(3) \u2192 path = [2, 3]\nCall backtrack([2, 3], 3)\n\u2192 Push [2, 3] \u2192 result = [..., [2, 3]]\nLoop ends\npath.pop() \u2192 path = [2]\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 = []\nLoop ends\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<\/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 subsets = function(arr) { \n    let result = []; \n    let backtrack = (path, start) => { \n        result.push([...path]); \n        for(let i = start; i < arr.length; i++){ \n            path.push(arr[i]); \n            backtrack(path, i+1); \n            path.pop(); \n        } \n    } \n    backtrack([], 0); \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 subsets(arr):\n    result = []\n    def backtrack(path, start):\n        result.append(list(path))\n        for i in range(start, len(arr)):\n            path.append(arr[i])\n            backtrack(path, i + 1)\n            path.pop()\n\n    backtrack([], 0)\n    return result\n\n# Example\narr = [1, 2, 3]\nprint(subsets(arr))\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\npublic class Main {\n    static void backtrack(int[] arr, List<Integer> path, int start, List<List<Integer>> result) {\n        result.add(new ArrayList<>(path));\n        for (int i = start; i < arr.length; i++) {\n            path.add(arr[i]);\n            backtrack(arr, path, i + 1, result);\n            path.remove(path.size() - 1);\n        }\n    }\n    static List<List<Integer>> subsets(int[] arr) {\n        List<List<Integer>> result = new ArrayList<>();\n        backtrack(arr, new ArrayList<>(), 0, result);\n        return result;\n    }\n    public static void main(String[] args) {\n        int[] arr = {1, 2, 3};\n        List<List<Integer>> res = subsets(arr);\n        for (List<Integer> subset : res) {\n            System.out.println(subset);\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, int start, vector<vector<int>>& result) {\n    result.push_back(path);\n    for (int i = start; i < arr.size(); i++) {\n        path.push_back(arr[i]);\n        backtrack(arr, path, i + 1, result);\n        path.pop_back();\n    }\n}\nvector<vector<int>> subsets(vector<int>& arr) {\n    vector<vector<int>> result;\n    vector<int> path;\n    backtrack(arr, path, 0, result);\n    return result;\n}\nint main() {\n    vector<int> arr = {1, 2, 3};\n    vector<vector<int>> res = subsets(arr);\n    for (auto& subset : res) {\n        cout << \"{ \";\n        for (int num : subset) cout << num << \" \";\n        cout << \"}\" << endl;\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 backtrack(int arr[], int n, int path[], int pathLen, int start) {\n    printf(\"{ \");\n    for (int i = 0; i < pathLen; i++) printf(\"%d \", path[i]);\n    printf(\"}\\n\");\n\n    for (int i = start; i < n; i++) {\n        path[pathLen] = arr[i];\n        backtrack(arr, n, path, pathLen + 1, i + 1);\n    }\n}\nint main() {\n    int arr[] = {1, 2, 3};\n    int n = sizeof(arr) \/ sizeof(arr[0]);\n    int path[100];\n    backtrack(arr, n, path, 0, 0);\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\">\nusing System;\nusing System.Collections.Generic;\n\nclass Program {\n    static void Backtrack(List<int> arr, List<int> path, int start, List<List<int>> result) {\n        result.Add(new List<int>(path));\n        for (int i = start; i < arr.Count; i++) {\n            path.Add(arr[i]);\n            Backtrack(arr, path, i + 1, result);\n            path.RemoveAt(path.Count - 1);\n        }\n    }\n\n    static List<List<int>> Subsets(List<int> arr) {\n        var result = new List<List<int>>();\n        Backtrack(arr, new List<int>(), 0, result);\n        return result;\n    }\n\n    static void Main() {\n        var arr = new List<int> {1, 2, 3};\n        var res = Subsets(arr);\n        foreach (var subset in res) {\n            Console.Write(\"{ \");\n            foreach (var num in subset) Console.Write(num + \" \");\n            Console.WriteLine(\"}\");\n        }\n    }\n}\n\n<\/code><\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n\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\n","protected":false},"excerpt":{"rendered":"<p>\ud83c\udf19 Problem Statement: Given an integer array nums of unique elements, return all possible subsets (the power set). The solution set must not contain duplicate subsets. Return the solution in any order. Example 1: Input: nums = [1,2,3] Output:[[],[1],[2],[1,2],[3],[1,3],[2,3],[1,2,3]] Example 2: Input: nums = [0] Output:[[],[0]] 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":{"0":"post-9352","1":"post","2":"type-post","3":"status-publish","4":"format-standard","6":"category-algorithms","7":"category-algorithms-and-data-structures","8":"category-c-c-plus-plus","9":"category-csharp","10":"category-cplusplus","11":"category-data-structures","12":"category-data-structures-and-algorithms","13":"category-dsa","14":"category-java","15":"category-javascript","16":"category-python"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/9352","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=9352"}],"version-history":[{"count":2,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/9352\/revisions"}],"predecessor-version":[{"id":10320,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/9352\/revisions\/10320"}],"wp:attachment":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/media?parent=9352"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/categories?post=9352"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/tags?post=9352"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}