{"id":12203,"date":"2026-04-15T00:02:01","date_gmt":"2026-04-14T18:32:01","guid":{"rendered":"https:\/\/namastedev.com\/blog\/?p=12203"},"modified":"2026-04-15T11:55:01","modified_gmt":"2026-04-15T06:25:01","slug":"sum-of-beauty-of-all-substrings","status":"publish","type":"post","link":"https:\/\/namastedev.com\/blog\/sum-of-beauty-of-all-substrings\/","title":{"rendered":"Sum of Beauty of all Substrings"},"content":{"rendered":"\n\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    <div class=\"wp_blog_explanation\">\n        <h2>Problem Statement:<\/h2>\n        <p>\n            The beauty of a string is the difference in frequencies between the most frequent and least frequent characters.\n        <\/p>\n\n        <ul>\n            <li><strong>For example<\/strong>, the beauty of <code>\"abaacc\" is 3 - 1 = 2<\/code>.<\/li>\n        <\/ul>\n\n        <p>Given a <i>string s<\/i>, return the sum of beauty of all of its substrings.<\/p>\n\n\n                <h2>Examples:<\/h2>\n\n                <h3>Example 1:<\/h3>\n                <p><strong>Input:<\/strong> s = &#8220;aabcb&#8221;\n                <\/p>\n                <p><strong>Output:<\/strong> 5<\/p>\n                <p>\n                  <code>Explanation:<\/code>\n                  The substrings with non-zero beauty are [&#8220;aab&#8221;,&#8221;aabc&#8221;,&#8221;aabcb&#8221;,&#8221;abcb&#8221;,&#8221;bcb&#8221;], each with beauty equal to 1.\n                <\/p>\n\n\n                <h3>Example 2:<\/h3>\n                <p><strong>Input:<\/strong> s = &#8220;aabcbaa&#8221;<\/p>\n\n                <p><strong>Output:<\/strong> 17<\/p>\n                <!-- <p><strong>Explanation:<\/strong> Your reversed string should not contain leading or trailing spaces.<\/p> -->\n\n                <!-- <h3>Example 3:<\/h3>\n                <p><strong>Input:<\/strong> s = \"a good   example\"<\/p>\n\n                <p><strong>Output:<\/strong> \"example good a\"<\/p> \n                <p><strong>Explanation:<\/strong> You need to reduce multiple spaces between two words to a single space in the reversed string.<\/p> -->\n        \n\n                <!-- <h5>Example 3:<\/h5>\n                <p><strong>Input:<\/strong>\n                <\/p>\n                <p>\n                    nums1 = [0], m = 0\n                    nums2 = [1], n = 1\n                <\/p>    \n                <p><strong>Output:<\/strong>[1]<\/p>\n                  <p>\n                  <code>Explanation:<\/code>\n                 The arrays we are merging are [] and [1].\n                    The result of the merge is [1].\n                    Note that because m = 0, there are no elements in nums1. \n                    The 0 is only there to ensure the merge result can fit in nums1.\n                <\/p> -->\n\n                <h2>Constraints<\/h2>\n                <p><code>1 <= s.length <= 500<\/code><\/p>\n                <p><code>\n                  <code>s<\/code> consists of only lowercase English letters..\n                <\/code><\/p>\n                <p>There is at least one word in <code>s<\/code>.<\/p>\n\n                    <h2>Time Complexity:<\/h2>\n                    <li>\n                      <p><strong>Time Complexity = O(n<sup>2<\/sup>)<\/strong>\n                      <\/li>\n                    <h2>Space Complexity:<\/h2>\n                    <li>\n                      <p><strong>Space Complexity = O(1)<\/strong><\/p>\n                    <\/li>\n\n<h2>Approach<\/h2>\n<ul>\n    <li>\n        <code>Iterate<\/code> over all <strong>possible substrings using two loops<\/strong> \u2192\n        Use an outer loop to fix the starting index and an inner loop to expand the substring one character at a time.\n    <\/li>\n\n    <li>\n        <strong>Initialize a frequency array<\/strong> \u2192\n        For each starting index, create a frequency array of size <code>26<\/code> (for lowercase English letters) initialized with <code>0<\/code>.\n    <\/li>\n\n    <li>\n        <strong>Expand the substring<\/strong> \u2192\n        As the inner loop progresses, include one character at a time in the substring and update its frequency in the array.\n    <\/li>\n\n    <li>\n        For every substring:\n        <ul>\n            <li>\n                <strong>Update frequency<\/strong> \u2192 Increment the count of the current character in the frequency array.\n            <\/li>\n            <li>\n                <strong>Find maximum and minimum frequency<\/strong> \u2192\n                Traverse the frequency array to determine:\n                <ul>\n                    <li><code>max<\/code> \u2192 highest frequency of any character.<\/li>\n                    <li><code>min<\/code> \u2192 lowest frequency excluding <code>0<\/code> (ignore characters not present in the substring).<\/li>\n                <\/ul>\n            <\/li>\n            <li>\n                <strong>Calculate beauty<\/strong> \u2192 Add <code>(max - min)<\/code> to the result for the current substring.\n            <\/li>\n        <\/ul>\n    <\/li>\n\n    <li>\n        <strong>Accumulate result<\/strong> \u2192 Keep adding the beauty value of each substring to a running total.\n    <\/li>\n\n    <li>\n        <strong>Return the final sum<\/strong> \u2192 After processing all substrings, return the accumulated result.\n    <\/li>\n<\/ul>\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 = \"aab\"<\/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);\">\nInitial:\n   beautySum = 0\n\nOuter Loop i = 0:\n   freq = [0...0] (size 26)\n\n   j = 0 \u2192 substring = \"a\"\n      freq['a'] = 1\n      max = 1, min = 1\n      beauty = max - min = 0\n      beautySum = 0\n\n   j = 1 \u2192 substring = \"aa\"\n      freq['a'] = 2\n      max = 2, min = 2\n      beauty = 0\n      beautySum = 0\n\n   j = 2 \u2192 substring = \"aab\"\n      freq['a'] = 2, freq['b'] = 1\n      max = 2, min = 1\n      beauty = 1\n      beautySum = 1\n\nOuter Loop i = 1:\n   freq = [0...0]\n\n   j = 1 \u2192 substring = \"a\"\n      freq['a'] = 1\n      max = 1, min = 1\n      beauty = 0\n      beautySum = 1\n\n   j = 2 \u2192 substring = \"ab\"\n      freq['a'] = 1, freq['b'] = 1\n      max = 1, min = 1\n      beauty = 0\n      beautySum = 1\n\nOuter Loop i = 2:\n   freq = [0...0]\n\n   j = 2 \u2192 substring = \"b\"\n      freq['b'] = 1\n      max = 1, min = 1\n      beauty = 0\n      beautySum = 1\n\nFinal:\n   beautySum = 1\n  <\/pre> \n  \n  <p><strong>Output:<\/strong> <code>1<\/code><\/p> \n<\/div>\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\">\n            JavaScript\n        <\/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\">\n\nvar beautySum = function(s) {\n    let beautySum = 0;\n\n    for (let i = 0; i < s.length; i++) {\n        let freq = new Array(26).fill(0);\n\n        for (let j = i; j < s.length; j++) {\n            let index = s.charCodeAt(j) - \"a\".charCodeAt(0);\n            freq[index]++;\n\n            let max = 0;\n            let min = Infinity;\n\n            for (let k = 0; k < 26; k++) {\n                if (freq[k] > 0) {\n                    max = Math.max(max, freq[k]);\n                    min = Math.min(min, freq[k]);\n                }\n            }\n\n            beautySum += (max - min);\n        }\n    }\n\n    return beautySum;\n};\n    <\/code><\/pre>\n    <\/div>\n    <div class=\"wp_blog_code-tab-content\" data-lang=\"py\">\n        <pre><code class=\"language-python\">\ndef beautySum(s: str) -> int:\n    beauty_sum = 0\n\n    for i in range(len(s)):\n        freq = [0] * 26\n\n        for j in range(i, len(s)):\n            index = ord(s[j]) - ord('a')\n            freq[index] += 1\n\n            max_freq = 0\n            min_freq = float('inf')\n\n            for f in freq:\n                if f > 0:\n                    max_freq = max(max_freq, f)\n                    min_freq = min(min_freq, f)\n\n            beauty_sum += (max_freq - min_freq)\n\n    return beauty_sum\n    <\/code><\/pre>\n    <\/div>\n    <div class=\"wp_blog_code-tab-content\" data-lang=\"java\">\n        <pre><code class=\"language-java\">\nclass Solution {\n    public int beautySum(String s) {\n        int beautySum = 0;\n\n        for (int i = 0; i < s.length(); i++) {\n            int[] freq = new int[26];\n\n            for (int j = i; j < s.length(); j++) {\n                int index = s.charAt(j) - 'a';\n                freq[index]++;\n\n                int max = 0;\n                int min = Integer.MAX_VALUE;\n\n                for (int k = 0; k < 26; k++) {\n                    if (freq[k] > 0) {\n                        max = Math.max(max, freq[k]);\n                        min = Math.min(min, freq[k]);\n                    }\n                }\n\n                beautySum += (max - min);\n            }\n        }\n\n        return beautySum;\n    }\n}\n<\/code><\/pre>\n    <\/div>\n    <div class=\"wp_blog_code-tab-content\" data-lang=\"cpp\">\n        <pre><code class=\"language-cpp\">\nclass Solution {\npublic:\n    int beautySum(string s) {\n        int beautySum = 0;\n\n        for (int i = 0; i < s.length(); i++) {\n            vector<int> freq(26, 0);\n\n            for (int j = i; j < s.length(); j++) {\n                int index = s[j] - 'a';\n                freq[index]++;\n\n                int maxFreq = 0;\n                int minFreq = INT_MAX;\n\n                for (int k = 0; k < 26; k++) {\n                    if (freq[k] > 0) {\n                        maxFreq = max(maxFreq, freq[k]);\n                        minFreq = min(minFreq, freq[k]);\n                    }\n                }\n\n                beautySum += (maxFreq - minFreq);\n            }\n        }\n\n        return beautySum;\n    }\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;limits.h&gt;\n#include &lt;string.h&gt;\n\nint beautySum(char* s) {\n    int beautySum = 0;\n    int n = strlen(s);\n\n    for (int i = 0; i < n; i++) {\n        int freq[26] = {0};\n\n        for (int j = i; j < n; j++) {\n            int index = s[j] - 'a';\n            freq[index]++;\n\n            int max = 0;\n            int min = INT_MAX;\n\n            for (int k = 0; k < 26; k++) {\n                if (freq[k] > 0) {\n                    if (freq[k] > max) max = freq[k];\n                    if (freq[k] < min) min = freq[k];\n                }\n            }\n\n            beautySum += (max - min);\n        }\n    }\n\n    return beautySum;\n}\n   <\/code><\/pre>\n    <\/div>\n    <div class=\"wp_blog_code-tab-content\" data-lang=\"cs\">\n        <pre><code class=\"language-csharp\">\npublic class Solution {\n    public int BeautySum(string s) {\n        int beautySum = 0;\n\n        for (int i = 0; i < s.Length; i++) {\n            int[] freq = new int[26];\n\n            for (int j = i; j < s.Length; j++) {\n                int index = s[j] - 'a';\n                freq[index]++;\n\n                int max = 0;\n                int min = int.MaxValue;\n\n                for (int k = 0; k < 26; k++) {\n                    if (freq[k] > 0) {\n                        max = Math.Max(max, freq[k]);\n                        min = Math.Min(min, freq[k]);\n                    }\n                }\n\n                beautySum += (max - min);\n            }\n        }\n\n        return beautySum;\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\n","protected":false},"excerpt":{"rendered":"<p>\ud83c\udf19 Problem Statement: The beauty of a string is the difference in frequencies between the most frequent and least frequent characters. For example, the beauty of &#8220;abaacc&#8221; is 3 &#8211; 1 = 2. Given a string s, return the sum of beauty of all of its substrings. Examples: Example 1: Input: s = &#8220;aabcb&#8221; Output:<\/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-12203","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\/12203","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=12203"}],"version-history":[{"count":2,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/12203\/revisions"}],"predecessor-version":[{"id":12205,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/posts\/12203\/revisions\/12205"}],"wp:attachment":[{"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/media?parent=12203"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/categories?post=12203"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/namastedev.com\/blog\/wp-json\/wp\/v2\/tags?post=12203"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}