{"id":10141,"date":"2025-09-27T16:03:08","date_gmt":"2025-09-27T10:33:08","guid":{"rendered":"https:\/\/namastedev.com\/blog\/?p=10141"},"modified":"2025-09-27T16:04:40","modified_gmt":"2025-09-27T10:34:40","slug":"palindromicsubstrings","status":"publish","type":"post","link":"https:\/\/namastedev.com\/blog\/palindromicsubstrings\/","title":{"rendered":"Palindromic Substrings"},"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; 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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 string <code>s<\/code>, return <strong><i>the number of palindromic substrings in it<\/i><\/strong>.\n    <\/p>\n\n    <p>\n        A string is a palindrome when it reads the same backward as forward.\n    <\/p>\n\n    <p>\n        A <strong>substring<\/strong> is a contiguous sequence of characters within the string.\n    <\/p>\n\n\n    <h3>Example 1:<\/h2>\n    <p><strong>Input:<\/strong> s = &#8220;abc&#8221;<\/p>\n    <p><strong>Output:<\/strong> 3<\/p>\n    <p><strong>Explanation:<\/strong> Three palindromic strings: &#8220;a&#8221;, &#8220;b&#8221;, &#8220;c&#8221;.<\/p>\n\n    <h3>Example 2:<\/h2>\n    <p><strong>Input:<\/strong> s = &#8220;aaa&#8221;<\/p>\n    <p><strong>Output:<\/strong> 6<\/p>\n    <p><strong>Explanation:<\/strong> Six palindromic strings: &#8220;a&#8221;, &#8220;a&#8221;, &#8220;a&#8221;, &#8220;aa&#8221;, &#8220;aa&#8221;, &#8220;aaa&#8221;.<\/p>\n\n    <h3>Constraints<\/h3>\n    <ul>\n       <li><code>1 <= s.length <= 1000<\/code><\/li>\n       <li><code>s<\/code> consists of lowercase English letters.<\/li>\n    <\/ul>\n    \n<h2>Approach:<\/h2>\n<ul>\n  <li>A 2D DP table <code>dp[i][j]<\/code> is used, where <code>dp[i][j] = true<\/code> if substring <strong>s[i..j] <\/strong>is a palindrome.<\/li>\n  <li>All single characters <code>(s[i])<\/code> are palindromes \u2192 <code>mark dp[i][i] = true.<\/code><\/li>\n  <li><strong>Check substrings of length 2 \u2192 <\/strong>if two consecutive characters are equal, mark them as palindromes.<\/li>\n  <li>For substrings of <code>length \u2265 3 \u2192 a substring s[i..j]<\/code> is palindrome if\n    <ul>\n      <li>The first and last characters match <code> (s[i] == s[j])<\/code>.<\/li>\n      <li>The inner substring <code>s[i+1..j-1]<\/code> is palindrome <code>(dp[i+1][j-1] = true)<\/code>.<\/li>\n    <\/ul>\n  <\/li>\n\n  <li>Count <strong>all palindromic substrings<\/strong> while filling the table.<\/li>\n  <li><strong>Return<\/strong> the <code>total count of palindromic substrings<\/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<sup>2<\/sup>)<\/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 = \"aaa\"<\/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);\">\n\nStep 0: Start Function countSubstrings(\"aaa\")\nn = 3\ndp = 3x3 matrix filled with null\nans = 0\n\nFirst loop (single characters):\ni = 0 \u2192 dp[0][0] = true \u2192 ans = 1\ni = 1 \u2192 dp[1][1] = true \u2192 ans = 2\ni = 2 \u2192 dp[2][2] = true \u2192 ans = 3\n\nAlso check for 2-length palindromes:\ni = 0 \u2192 s[0] == s[1] \u2192 \"aa\" \u2192 dp[0][1] = true \u2192 ans = 4\ni = 1 \u2192 s[1] == s[2] \u2192 \"aa\" \u2192 dp[1][2] = true \u2192 ans = 5\n\nNow:\ndp =\n[\n  [T, T, null],\n  [ , T, T   ],\n  [ ,  , T   ]\n]\n\nSecond loop (length >= 3):\n\nlen = 3:\ni = 0, j = 2\n- s[0] == s[2] ? \"a\" == \"a\" \u2714\n- dp[1][1] == true \u2714\n- So dp[0][2] = true, ans = 6\n\nLoop ends\n\nStep 3: End\nReturn ans = 6\n  <\/pre> \n  \n  <p><strong>Output:<\/strong> <code>6<\/code><\/p> \n<\/div>\n\n\n        <h2>Visualisation:<\/h2>\n        <img decoding=\"async\" src=\"https:\/\/namastedev.com\/blog\/wp-content\/uploads\/2025\/09\/Screenshot-2025-09-27-at-4.00.33\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 countSubstrings = function(s) {\n    let n = s.length; \n    let dp = Array.from({ length: n }, () => Array(n).fill(null));\n    let ans = 0;\n\n    for (let i = 0; i < n; i++) {\n        dp[i][i] = true;\n        ++ans;\n        if (i < n - 1 &#038;&#038; s[i] === s[i + 1]) {\n            dp[i][i + 1] = true;\n            ++ans;\n        }\n    }\n    for (let len = 3; len <= n; len++) {\n        for (let i = 0; i <= n - len; i++) {\n            let j = i + len - 1;\n            if (s[i] === s[j] &#038;&#038; dp[i + 1][j - 1]) {\n                dp[i][j] = true;\n                ++ans;\n            }\n        }\n    }\n    return ans;\n};\n\n<\/code><\/pre>\n    <\/div>\n    <div class=\"wp_blog_code-tab-content\" data-lang=\"py\">\n      <pre><code class=\"language-python\">\ndef countSubstrings(s):\n    n = len(s)\n    dp = [[None] * n for _ in range(n)]\n    ans = 0\n    for i in range(n):\n        dp[i][i] = True\n        ans += 1\n        if i < n - 1 and s[i] == s[i + 1]:\n            dp[i][i + 1] = True\n            ans += 1\n\n    for length in range(3, n + 1):\n        for i in range(0, n - length + 1):\n            j = i + length - 1\n            if s[i] == s[j] and dp[i + 1][j - 1]:\n                dp[i][j] = True\n                ans += 1\n    return ans\n      <\/code><\/pre>\n    <\/div>\n    <div class=\"wp_blog_code-tab-content\" data-lang=\"java\">\n      <pre><code class=\"language-java\">\n    public class Solution {\n    public int countSubstrings(String s) {\n        int n = s.length();\n        boolean[][] dp = new boolean[n][n];\n        int ans = 0;\n        for (int i = 0; i < n; i++) {\n            dp[i][i] = true;\n            ++ans;\n            if (i < n - 1 &#038;&#038; s.charAt(i) == s.charAt(i + 1)) {\n                dp[i][i + 1] = true;\n                ++ans;\n            }\n        }\n        for (int len = 3; len <= n; len++) {\n            for (int i = 0; i <= n - len; i++) {\n                int j = i + len - 1;\n                if (s.charAt(i) == s.charAt(j) &#038;&#038; dp[i + 1][j - 1]) {\n                    dp[i][j] = true;\n                    ++ans;\n                }\n            }\n        }\n        return ans;\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;vector&gt;\n#include &lt;string&gt;\n\nint countSubstrings(const std::string &s) {\n    int n = (int)s.length();\n    std::vector<std::vector<bool>> dp(n, std::vector<bool>(n, false));\n    int ans = 0;\n    for (int i = 0; i < n; i++) {\n        dp[i][i] = true;\n        ++ans;\n        if (i < n - 1 &#038;&#038; s[i] == s[i + 1]) {\n            dp[i][i + 1] = true;\n            ++ans;\n        }\n    }\n    for (int len = 3; len <= n; len++) {\n        for (int i = 0; i <= n - len; i++) {\n            int j = i + len - 1;\n            if (s[i] == s[j] &#038;&#038; dp[i + 1][j - 1]) {\n                dp[i][j] = true;\n                ++ans;\n            }\n        }\n    }\n    return ans;\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\nint countSubstrings(const char *s) {\n    int n = strlen(s);\n    if (n == 0) return 0;\n    char **dp = (char **)malloc(n * sizeof(char *));\n    for (int i = 0; i < n; i++) {\n        dp[i] = (char *)calloc(n, sizeof(char));\n    }\n    int ans = 0;\n    for (int i = 0; i < n; i++) {\n        dp[i][i] = 1;\n        ++ans;\n        if (i < n - 1 &#038;&#038; s[i] == s[i + 1]) {\n            dp[i][i + 1] = 1;\n            ++ans;\n        }\n    }\n    for (int len = 3; len <= n; len++) {\n        for (int i = 0; i <= n - len; i++) {\n            int j = i + len - 1;\n            if (s[i] == s[j] &#038;&#038; dp[i + 1][j - 1]) {\n                dp[i][j] = 1;\n                ++ans;\n            }\n        }\n    }\n    for (int i = 0; i < n; i++) free(dp[i]);\n    free(dp);\n\n    return ans;\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;\npublic class Solution {\n    public static int CountSubstrings(string s) {\n        int n = s.Length;\n        bool[,] dp = new bool[n, n];\n        int ans = 0;\n        for (int i = 0; i < n; i++) {\n            dp[i, i] = true;\n            ++ans;\n            if (i < n - 1 &#038;&#038; s[i] == s[i + 1]) {\n                dp[i, i + 1] = true;\n                ++ans;\n            }\n        }\n        for (int len = 3; len <= n; len++) {\n            for (int i = 0; i <= n - len; i++) {\n                int j = i + len - 1;\n                if (s[i] == s[j] &#038;&#038; dp[i + 1, j - 1]) {\n                    dp[i, j] = true;\n                    ++ans;\n                }\n            }\n        }\n        return ans;\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 a string s, return the number of palindromic substrings in it. A string is a palindrome when it reads the same backward as forward. A substring is a contiguous sequence of characters within the string. Example 1: Input: s = &#8220;abc&#8221; Output: 3 Explanation: Three palindromic strings: &#8220;a&#8221;, &#8220;b&#8221;, &#8220;c&#8221;. 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":[210,322,176,175,211,810,174,172,173],"tags":[],"class_list":["post-10141","post","type-post","status-publish","format-standard","category-algorithms","category-algorithms-and-data-structures","category-csharp","category-cplusplus","category-data-structures","category-dsa","category-java","category-javascript","category-python"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/10141","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=10141"}],"version-history":[{"count":2,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/10141\/revisions"}],"predecessor-version":[{"id":10143,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/10141\/revisions\/10143"}],"wp:attachment":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/media?parent=10141"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/categories?post=10141"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/tags?post=10141"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}