{"id":9447,"date":"2025-08-18T20:42:43","date_gmt":"2025-08-18T15:12:43","guid":{"rendered":"https:\/\/namastedev.com\/blog\/?p=9447"},"modified":"2025-10-13T16:23:01","modified_gmt":"2025-10-13T10:53:01","slug":"letter-combinations-of-a-phone-number","status":"publish","type":"post","link":"https:\/\/namastedev.com\/blog\/letter-combinations-of-a-phone-number\/","title":{"rendered":"Letter Combinations of a Phone Number"},"content":{"rendered":"\n<!-- Letter Combination_9 -->\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<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 string containing digits from <code>2-9<\/code> inclusive, return all possible letter combinations that the number could represent. Return the answer in any order.\n    <\/p>\n\n    <p>\n        A mapping of digits to letters (just like on the telephone buttons) is given below. Note that 1 does not map to any letters.\n    <\/p>\n    <img decoding=\"async\" src=\"https:\/\/namastedev.com\/blog\/wp-content\/uploads\/2025\/08\/Screenshot-2025-08-18-at-8.40.40\u202fPM.png\" alt=\"\">\n    <p>\n        <i>source: leetcode image<\/i>\n    <\/p>\n    <p><strong>Example 1:<\/strong><\/p>\n    <p><strong>Input:<\/strong> digits = &#8220;23&#8221;<\/p>\n    <p><strong>Output:<\/strong><code> [\"ad\",\"ae\",\"af\",\"bd\",\"be\",\"bf\",\"cd\",\"ce\",\"cf\"]<\/code><\/p>\n\n    <p><strong>Example 2:<\/strong><\/p>\n    <p><strong>Input:<\/strong> digits = &#8220;&#8221;<\/p>\n    <p><strong>Output:<\/strong><code> []<\/code><\/p>\n\n    <p><strong>Example 3:<\/strong><\/p>\n    <p><strong>Input:<\/strong> digits = &#8220;2&#8221;<\/p>\n    <p><strong>Output:<\/strong><code> [\"a\",\"b\",\"c\"]<\/code><\/p>\n\n    <h2>Constraints<\/h2>\n    <ul>\n        <li><code>0 <= digits.length <= 4<\/code><\/li>\n        <li><code>digits[i]<\/code> is a digit in the range <code>['2', '9']<\/code>.<\/li>\n    <\/ul>\n\n    <h2>Approach<\/h2>\n    <ul>\n        <li><strong>Mapping digits<\/strong> \u2192 letters (like on a phone keypad).<\/li>\n        <li><strong>Use backtracking<\/strong> to build all possible strings:\n            <ul>\n                <li><code>At each digit<\/code>, try every possible letter.<\/li>\n                <li><code>Add the letter<\/code> to the current path, recurse for the next digit.<\/li>\n                <li>When the <code>path length<\/code> equals the number of digits \u2192 <strong>add to result<\/strong>.<\/li>\n            <\/ul>\n        <\/li>\n        <li><strong>Return<\/strong> the collected <code>results<\/code>.<\/li>\n    <\/ul>\n\n    <h2>Time Complexity<\/h2>\n    <li><p><strong>Time Complexity = O(3<sup>N<\/sup> * 4<sup>M<\/sup>)<\/strong><\/p><\/li> \n    <h2>Space Complexity<\/h2>\n    <li><p><strong>Space Complexity =  O(N)<\/strong> (output) + O(n) (stack)<\/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><\/p> <pre> k = 3, n = 7 <\/pre> <p><strong>State Transitions:<\/strong><\/p> <pre> Initialize: result = []\n  <pre style=\"white-space: pre-wrap; background: var(--code-bg); padding: 1rem; border-radius: 8px; overflow-x: auto; color: var(--code-text);\">\n\n\nCall backtrack(7, [], 1)\nLoop i = 1\npath.push(1) \u2192 path = [1]\nCall backtrack(6, [1], 2)\nLoop i = 2\n  path.push(2) \u2192 path = [1, 2]\n  Call backtrack(4, [1, 2], 3)\n\n    Loop i = 3\n      path.push(3) \u2192 path = [1, 2, 3]\n      Call backtrack(1, [1, 2, 3], 4)\n        path.length == 3 but remainingSum = 1 \u2260 0 \u2192 return\n      path.pop() \u2192 path = [1, 2]\n\n    Loop i = 4\n      path.push(4) \u2192 path = [1, 2, 4]\n      Call backtrack(0, [1, 2, 4], 5)\n        path.length == 3 and remainingSum == 0 \u2192 result.push([1, 2, 4])\n      path.pop() \u2192 path = [1, 2]\n\n    Loop i = 5 \u2192 path would be length 3 but remainingSum < 0 \u2192 return\n    ...\n    End inner loop\n  path.pop() \u2192 path = [1]\n\nLoop i = 3\n  path.push(3) \u2192 path = [1, 3]\n  Call backtrack(3, [1, 3], 4)\n\n    Loop i = 4\n      path.push(4) \u2192 path = [1, 3, 4]\n      Call backtrack(-1, [1, 3, 4], 5)\n        remainingSum < 0 \u2192 return\n      path.pop() \u2192 path = [1, 3]\n    End\n  path.pop() \u2192 path = [1]\n\nLoop i = 4\n  path.push(4) \u2192 path = [1, 4]\n  Call backtrack(2, [1, 4], 5)\n\n    Loop i = 5\n      path.push(5) \u2192 path = [1, 4, 5]\n      Call backtrack(-3, [1, 4, 5], 6) \u2192 return\n      path.pop()\n    End\n  path.pop() \u2192 path = [1]\n\n... continue similarly\npath.pop() \u2192 path = []\nLoop i = 2\npath.push(2) \u2192 path = [2]\nCall backtrack(5, [2], 3)\nLoop i = 3\n  path.push(3) \u2192 path = [2, 3]\n  Call backtrack(2, [2, 3], 4)\n\n    Loop i = 4\n      path.push(4) \u2192 path = [2, 3, 4]\n      Call backtrack(-2, [2, 3, 4], 5)\n        remainingSum < 0 \u2192 return\n      path.pop()\n    End\n  path.pop() \u2192 path = [2]\n\nLoop i = 4\n  path.push(4) \u2192 path = [2, 4]\n  Call backtrack(1, [2, 4], 5)\n\n    Loop i = 5\n      path.push(5) \u2192 path = [2, 4, 5]\n      Call backtrack(-4, [2, 4, 5], 6) \u2192 return\n      path.pop()\n    End\n  path.pop()\nEnd\npath.pop() \u2192 path = []\nLoop i = 3, 4, 5... \u2192 no valid 3-number combos left within sum = 7\n<\/pre>\n<p><strong>Final Output:<\/strong> \n    <code>[[1, 2, 4]]<\/code><\/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 letterCombinations = function(digits) {\n    if(!digits.length) return [];\n    let letters = {\n        2: \"abc\",\n        3: \"def\", \n        4: \"ghi\", \n        5: \"jkl\",\n        6: \"mno\",\n        7: \"pqrs\", \n        8: \"tuv\",\n        9: \"wxyz\",\n    };\n    let result = [];\n    let backtrack = (path, index) => {\n        if(index === digits.length) {\n            result.push(path.join(\"\"));\n            return;\n        }\n        let choices = letters[digits[index]];\n        for(let i=0; i < choices.length; i++){\n            path.push(choices[i]);\n            backtrack(path, index + 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 letterCombinations(digits: str):\n    if not digits:\n        return []\n    letters = {\n        \"2\":\"abc\", \"3\":\"def\", \"4\":\"ghi\", \"5\":\"jkl\",\n        \"6\":\"mno\", \"7\":\"pqrs\", \"8\":\"tuv\", \"9\":\"wxyz\"\n    }\n    result = []\n    def backtrack(path, index):\n        if index == len(digits):\n            result.append(\"\".join(path))\n            return\n        for ch in letters[digits[index]]:\n            path.append(ch)\n            backtrack(path, index+1)\n            path.pop()\n    backtrack([], 0)\n    return result\nprint(letterCombinations(\"23\"))\nprint(sol.combinationSum3(3, 7))\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.*;\nclass Solution {\n    Map<Character, String> letters = new HashMap<>() {{\n        put('2',\"abc\"); put('3',\"def\"); put('4',\"ghi\"); put('5',\"jkl\");\n        put('6',\"mno\"); put('7',\"pqrs\"); put('8',\"tuv\"); put('9',\"wxyz\");\n    }};\n    public List<String> letterCombinations(String digits) {\n        List<String> result = new ArrayList<>();\n        if(digits.isEmpty()) return result;\n        \n        backtrack(new StringBuilder(), 0, digits, result);\n        return result;\n    }\n    private void backtrack(StringBuilder path, int index, String digits, List<String> result) {\n        if(index == digits.length()) {\n            result.add(path.toString());\n            return;\n        }\n        String choices = letters.get(digits.charAt(index));\n        for(char c : choices.toCharArray()) {\n            path.append(c);\n            backtrack(path, index+1, digits, result);\n            path.deleteCharAt(path.length()-1);\n        }\n    }   \n    public static void main(String[] args) {\n        Solution sol = new Solution();\n        System.out.println(sol.letterCombinations(\"23\"));\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<string> letterCombinations(string digits) {\n        if(digits.empty()) return {};\n        unordered_map<char, string> letters = {\n            {'2',\"abc\"}, {'3',\"def\"}, {'4',\"ghi\"}, {'5',\"jkl\"},\n            {'6',\"mno\"}, {'7',\"pqrs\"}, {'8',\"tuv\"}, {'9',\"wxyz\"}\n        };\n        vector<string> result;\n        string path;\n        function<void(int)> backtrack = [&](int index) {\n            if(index == digits.size()) {\n                result.push_back(path);\n                return;\n            }\n            string choices = letters[digits[index]];\n            for(char ch : choices) {\n                path.push_back(ch);\n                backtrack(index+1);\n                path.pop_back();\n            }\n        };\n        backtrack(0);\n        return result;\n    }\n};\n\nint main() {\n    Solution sol;\n    vector<string> res = sol.letterCombinations(\"23\");\n    for(string s : res) cout << s << \" \";\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\">\nchar *letters[] = {\n    \"\", \"\", \"abc\", \"def\", \"ghi\", \"jkl\", \"mno\", \"pqrs\", \"tuv\", \"wxyz\"\n};\nvoid backtrack(char *digits, int index, char *path, int pathLen) {\n    if(digits[index] == '\\0') {\n        path[pathLen] = '\\0';\n        printf(\"%s\\n\", path);\n        return;\n    }\n    char *choices = letters[digits[index]-'0'];\n    for(int i=0; choices[i]; i++) {\n        path[pathLen] = choices[i];\n        backtrack(digits, index+1, path, pathLen+1);\n    }\n}\nint main() {\n    char digits[] = \"23\";\n    char path[100];\n    if(strlen(digits) > 0) backtrack(digits, 0, path, 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\">\nclass Solution {\n    Dictionary<char, string> letters = new Dictionary<char, string>() {\n        {'2',\"abc\"}, {'3',\"def\"}, {'4',\"ghi\"}, {'5',\"jkl\"},\n        {'6',\"mno\"}, {'7',\"pqrs\"}, {'8',\"tuv\"}, {'9',\"wxyz\"}\n    };\n    public IList<string> LetterCombinations(string digits) {\n        List<string> result = new List<string>();\n        if(digits.Length == 0) return result;\n        void Backtrack(int index, List<char> path) {\n            if(index == digits.Length) {\n                result.Add(new string(path.ToArray()));\n                return;\n            }\n            string choices = letters[digits[index]];\n            foreach(char c in choices) {\n                path.Add(c);\n                Backtrack(index+1, path);\n                path.RemoveAt(path.Count-1);\n            }\n        }   \n        Backtrack(0, new List<char>());\n        return result;\n    }\n    static void Main() {\n        Solution sol = new Solution();\n        var res = sol.LetterCombinations(\"23\");\n        foreach(var s in res) Console.Write(s + \" \");\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\n","protected":false},"excerpt":{"rendered":"<p>\ud83c\udf19 Problem Statement Given a string containing digits from 2-9 inclusive, return all possible letter combinations that the number could represent. Return the answer in any order. A mapping of digits to letters (just like on the telephone buttons) is given below. Note that 1 does not map to any letters. source: leetcode image Example<\/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-9447","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\/9447","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=9447"}],"version-history":[{"count":2,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/9447\/revisions"}],"predecessor-version":[{"id":10262,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/9447\/revisions\/10262"}],"wp:attachment":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/media?parent=9447"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/categories?post=9447"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/tags?post=9447"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}