Count Number of Homogenous Substrings

Count Number of Homogenous Substrings - Problem

Math String Medium

Given a string s, return the number of homogenous substrings of s. Since the answer may be too large, return it modulo 10⁹ + 7.

A string is homogenous if all the characters of the string are the same.

A substring is a contiguous sequence of characters within a string.

Input & Output

Example 1 — Basic Case

$ Input: s = "abbccc"

› Output: 10

💡 Note: Groups: "a"(1), "bb"(3), "ccc"(6). Homogenous substrings: "a", "b", "b", "bb", "c", "c", "c", "cc", "cc", "ccc". Total = 1+3+6 = 10

Example 2 — All Same Characters

$ Input: s = "aaaa"

› Output: 10

💡 Note: One group of 4 'a's. Using formula: 4*(4+1)/2 = 10 substrings: "a", "a", "a", "a", "aa", "aa", "aa", "aaa", "aaa", "aaaa"

Example 3 — All Different Characters

$ Input: s = "xy"

› Output: 2

💡 Note: Two groups each of size 1: "x"(1) and "y"(1). Total = 1+1 = 2 homogenous substrings

Constraints

1 ≤ s.length ≤ 10⁵
s consists of lowercase English letters

Visualization

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Asked in

f Facebook 25 a Amazon 20 G Google 15

The key insight is that for any group of n consecutive identical characters, there are exactly n*(n+1)/2 homogenous substrings. Best approach uses mathematical formula to count groups in one pass. Time: O(n), Space: O(1)

Common Approaches

✓ Brute Force - Check All Substrings

⏱️ Time: O(n³) Space: O(1)

For every starting position, try all possible ending positions and check if all characters in the substring are the same. Count valid homogenous substrings.

Mathematical Approach - Count Groups

⏱️ Time: O(n) Space: O(1)

Instead of checking all substrings, find groups of consecutive identical characters. For each group of length n, there are exactly n*(n+1)/2 homogenous substrings that can be formed.

Brute Force - Check All Substrings — Algorithm Steps

Step 1: For each starting index i, try all ending indices j >= i
Step 2: Check if substring s[i:j+1] has all same characters
Step 3: If homogenous, increment count

Visualization

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Step-by-Step Walkthrough

Generate Substrings

Try all i,j pairs

Check Homogenous

Verify all chars are same

Count Valid

Sum up homogenous substrings

Code -

solution.c — C

#include <stdio.h>
#include <string.h>

int solution(char* s) {
    const int MOD = 1000000007;
    int count = 0;
    int n = strlen(s);
    
    for (int i = 0; i < n; i++) {
        for (int j = i; j < n; j++) {
            // Check if substring s[i:j+1] is homogenous
            int isHomogenous = 1;
            for (int k = i + 1; k <= j; k++) {
                if (s[k] != s[i]) {
                    isHomogenous = 0;
                    break;
                }
            }
            if (isHomogenous) {
                count = (count + 1) % MOD;
            }
        }
    }
    
    return count;
}

int main() {
    char s[100001];
    fgets(s, sizeof(s), stdin);
    s[strcspn(s, "\n")] = 0;  // Remove newline
    printf("%d\n", solution(s));
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(n³)

Nested loops O(n²) to generate substrings, O(n) to check each substring

⚠ Quadratic Growth

Space Complexity

O(1)

Only using constant extra variables

✓ Linear Space

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Input & Output

Constraints

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Related Problems

Common Approaches

Brute Force - Check All Substrings — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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