{"id":10197,"date":"2025-09-30T15:42:33","date_gmt":"2025-09-30T10:12:33","guid":{"rendered":"https:\/\/namastedev.com\/blog\/?p=10197"},"modified":"2025-09-30T15:50:03","modified_gmt":"2025-09-30T10:20:03","slug":"word-break","status":"publish","type":"post","link":"https:\/\/namastedev.com\/blog\/word-break\/","title":{"rendered":"Word Break"},"content":{"rendered":"\n<!-- PrismJS for Syntax Highlighting -->\n<link href=\"https:\/\/cdn.jsdelivr.net\/npm\/prismjs@1.29.0\/themes\/prism-tomorrow.min.css\" rel=\"stylesheet\">\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 integer array nums, find a subarray that has the largest product, and return <i> the product.<\/i>\n    <\/p>\n    <p>\n        The test cases are generated so that the answer will fit in a <strong>32-bit integer<\/strong>.\n    <\/p>\n    <h3>Example 1:<\/h2>\n    <p><strong>Input:<\/strong> nums = [2,3,-2,4]<\/p>\n    <p><strong>Output:<\/strong> 6<\/p>\n    <p><strong>Explanation:<\/strong> [2,3] has the largest product 6.<\/p>\n\n    <h3>Example 2:<\/h2>\n    <p><strong>Input:<\/strong> nums = [-2,0,-1]<\/p>\n    <p><strong>Output:<\/strong> 0<\/p>\n    <p><strong>Explanation:<\/strong> The result cannot be 2, because [-2,-1] is not a subarray.<\/p>\n\n    <h3>Constraints<\/h3>\n    <ul>\n       <li><code>1 <= nums.length <= 2 * 10<sup>4<\/sup><\/code><\/li>\n        <li><code>-10 <= nums[i] <= 10<\/code><\/li>\n        <li>The product of any subarray of <code>nums<\/code> is <strong>guaranteed<\/strong> to fit in a <strong>32-bit<\/strong> integer.<\/li>\n    <\/ul>\n    \n<h2>Approach:<\/h2>\n<ul>\n    <li>Use <code>recursion to try breaking the string s<\/code> into <strong>valid<\/strong> dictionary words.<\/li>\n    <li>At each step, <code>check all prefixes<\/code> of the remaining string.\n        <ul>\n            <li>If the <code>prefix is in wordDict<\/code>, recursively <strong>check the rest<\/strong> of the string.<\/li>\n        <\/ul>\n    <\/li>\n\n    <li>Use a <code>memoization map dp<\/code> to <strong>store results<\/strong> for substrings to <code>avoid repeated works<\/code>.<\/li>\n    <li>If any split leads to the entire string being segmented into <code>valid words, return true; otherwise return false<\/code>.<\/li>\n<\/ul>\n\n    <h2>Time & Space Complexity:<\/h2>\n    <p><strong>Time Complexity:<\/strong> <code>O(n<sup>2<\/sup>)<\/code><\/p>\n    <p><strong>Space Complexity:<\/strong> <code>O(n)<\/code><\/p>\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>s = \"leetcode\", wordDict = [\"leet\", \"code\"]<\/code><\/p>\n  <pre style=\"white-space: pre-wrap; background: var(--code-bg); padding: 1rem; border-radius: 8px; overflow-x: auto; color: var(--code-text);\">\nStart: wordBreak(\"leetcode\", [\"leet\",\"code\"])\ndp = {}\n\nCall fn(\"leetcode\"):\n remS = \"leetcode\", res = false\n i = 0 \u2192 substr = \"l\"   \u2192 not in dict\n i = 1 \u2192 substr = \"le\"  \u2192 not in dict\n i = 2 \u2192 substr = \"lee\" \u2192 not in dict\n i = 3 \u2192 substr = \"leet\" \u2192 in dict \u2192 call fn(\"code\")\n\n   Call fn(\"code\"):\n    remS = \"code\", res = false\n    i = 0 \u2192 substr = \"c\"   \u2192 not in dict\n    i = 1 \u2192 substr = \"co\"  \u2192 not in dict\n    i = 2 \u2192 substr = \"cod\" \u2192 not in dict\n    i = 3 \u2192 substr = \"code\" \u2192 in dict \u2192 call fn(\"\")\n\n      Call fn(\"\"):\n       remS = \"\" \u2192 base case \u2192 return true\n\n    fn(\"code\"): fn(\"\") returned true \u2192 res = true\n    dp[\"code\"] = true\n    return true\n\n fn(\"leetcode\"): fn(\"code\") returned true \u2192 res = true\n dp[\"leetcode\"] = true\n return true\n\nFinal dp: { \"code\": true, \"leetcode\": true }\nReturn: true\n  <\/pre>\n\n  <p><strong>Output:<\/strong> <code>true<\/code><\/p>\n<\/div>\n\n\n\n\n        <!-- <h2>Visualisation:<\/h2>\n        <img decoding=\"async\" src=\"https:\/\/namastedev.com\/blog\/wp-content\/uploads\/2025\/09\/Screenshot-2025-09-30-at-3.00.03\u202fPM.png\" alt=\"Stocks\" \/>\n    -->\n<\/div>\n\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 wordBreak = function(s, wordDict) {\n    let dp = {};\n    let fn = (remS) => {\n            if(remS === \"\") return true;\n            if(remS in dp) return dp[remS];\n            let res = false;\n            for(let i=0; i< remS.length; i++){\n                let substr = remS.substring(0, i+1);\n                if(wordDict.includes(substr) &#038;&#038; fn(remS.substring(i + 1))) {\n                res = true;\n            }\n        }\n        return dp[remS] = res;\n    }\n    return fn(s);\n};\n<\/code><\/pre>\n    <\/div>\n    <div class=\"wp_blog_code-tab-content\" data-lang=\"py\">\n      <pre><code class=\"language-python\">\ndef wordBreak(s, wordDict):\n    dp = {}\n    def fn(remS):\n        if remS == \"\":\n            return True\n        if remS in dp:\n            return dp[remS]\n        res = False\n        for i in range(len(remS)):\n            substr = remS[:i+1]\n            if substr in wordDict and fn(remS[i+1:]):\n                res = True\n                break\n        dp[remS] = res\n        return res\n    return fn(s)\n      <\/code><\/pre>\n    <\/div>\n    <div class=\"wp_blog_code-tab-content\" data-lang=\"java\">\n      <pre><code class=\"language-java\">\nimport java.util.*;\n\npublic class Solution {\n    public boolean wordBreak(String s, List<String> wordDict) {\n        Map<String, Boolean> dp = new HashMap<>();\n        return fn(s, wordDict, dp);\n    }\n\n    private boolean fn(String remS, List<String> wordDict, Map<String, Boolean> dp) {\n        if (remS.equals(\"\")) return true;\n        if (dp.containsKey(remS)) return dp.get(remS);\n        boolean res = false;\n        for (int i = 0; i < remS.length(); i++) {\n            String substr = remS.substring(0, i + 1);\n            if (wordDict.contains(substr) &#038;&#038; fn(remS.substring(i + 1), wordDict, dp)) {\n                res = true;\n                break;\n            }\n        }\n        dp.put(remS, res);\n        return res;\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\">\n#include &lt;bits\/stdc++.h&gt;     \nusing namespace std;\n\nbool fn(const string &remS, const vector<string> &wordDict, unordered_map<string,bool> &dp) {\n    if (remS == \"\") return true;\n    if (dp.find(remS) != dp.end()) return dp[remS];\n    bool res = false;\n    for (size_t i = 0; i < remS.size(); ++i) {\n        string substr = remS.substr(0, i+1);\n        if (find(wordDict.begin(), wordDict.end(), substr) != wordDict.end() &#038;&#038;\n            fn(remS.substr(i+1), wordDict, dp)) {\n            res = true;\n            break;\n        }\n    }\n    dp[remS] = res;\n    return res;\n}\nbool wordBreak(string s, vector<string>& wordDict) {\n    unordered_map<string,bool> dp;\n    return fn(s, wordDict, dp);\n}\n<\/code><\/pre>\n    <\/div>\n    <div class=\"wp_blog_code-tab-content\" data-lang=\"c\">\n      <pre><code class=\"language-c\">\n#include &lt;stdio.h&gt;\n#include &lt;stdlib.h&gt;\n#include &lt;string.h&gt;\n#include &lt;stdbool.h&gt;\n\n#define HASH_SIZE 10007\ntypedef struct Entry {\n    char *key;\n    int val; \/\/ 0 => false, 1 => true\n    struct Entry *next;\n} Entry;\n\nEntry* table[HASH_SIZE];\n\nunsigned long djb2(const char *str) {\n    unsigned long hash = 5381;\n    int c;\n    while ((c = *str++))\n        hash = ((hash << 5) + hash) + c;\n    return hash;\n}\nvoid dp_set(const char *key, int val) {\n    unsigned long h = djb2(key) % HASH_SIZE;\n    Entry *e = table[h];\n    while (e) {\n        if (strcmp(e->key, key) == 0) {\n            e->val = val;\n            return;\n        }\n        e = e->next;\n    }\n    Entry *ne = (Entry*)malloc(sizeof(Entry));\n    ne->key = strdup(key);\n    ne->val = val;\n    ne->next = table[h];\n    table[h] = ne;\n}\nint dp_get(const char *key, int *out) {\n    unsigned long h = djb2(key) % HASH_SIZE;\n    Entry *e = table[h];\n    while (e) {\n        if (strcmp(e->key, key) == 0) {\n            *out = e->val;\n            return 1;\n        }\n        e = e->next;\n    }\n    return 0;\n}\nbool fn(const char *remS, char **wordDict, int wordCount) {\n    if (remS[0] == '\\0') return true;\n    int cached;\n    if (dp_get(remS, &cached)) return cached ? true : false;\n    bool res = false;\n    size_t len = strlen(remS);\n    for (size_t i = 0; i < len; ++i) {\n        size_t prefixLen = i + 1;\n        char *substr = (char*)malloc(prefixLen + 1);\n        strncpy(substr, remS, prefixLen);\n        substr[prefixLen] = '\\0';\n\n        bool included = false;\n        for (int w = 0; w < wordCount; ++w) {\n            if (strcmp(wordDict[w], substr) == 0) {\n                included = true;\n                break;\n            }\n        }\n        if (included) {\n            const char *nextRem = remS + prefixLen;\n            if (fn(nextRem, wordDict, wordCount)) {\n                res = true;\n                free(substr);\n                break;\n            }\n        }\n        free(substr);\n    }\n    dp_set(remS, res ? 1 : 0);\n    return res;\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;\npublic class Solution {\n    public bool WordBreak(string s, IList<string> wordDict) {\n        var dp = new Dictionary<string, bool>();\n        return Fn(s, wordDict, dp);\n    }\n    private bool Fn(string remS, IList<string> wordDict, Dictionary<string,bool> dp) {\n        if (remS == \"\") return true;\n        if (dp.ContainsKey(remS)) return dp[remS];\n        bool res = false;\n        for (int i = 0; i < remS.Length; i++) {\n            string substr = remS.Substring(0, i + 1);\n            if (wordDict.Contains(substr) &#038;&#038; Fn(remS.Substring(i + 1), wordDict, dp)) {\n                res = true;\n                break;\n            }\n        }\n        dp[remS] = res;\n        return res;\n    }\n}\n      <\/code><\/pre>\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 an integer array nums, find a subarray that has the largest product, and return the product. The test cases are generated so that the answer will fit in a 32-bit integer. Example 1: Input: nums = [2,3,-2,4] Output: 6 Explanation: [2,3] has the largest product 6. Example 2: Input: nums =<\/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],"tags":[],"class_list":{"0":"post-10197","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"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/10197","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=10197"}],"version-history":[{"count":1,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/10197\/revisions"}],"predecessor-version":[{"id":10198,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/10197\/revisions\/10198"}],"wp:attachment":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/media?parent=10197"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/categories?post=10197"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/tags?post=10197"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}