Count Number of Homogenous Substrings - Practice Coding Problems

Count Number of Homogenous Substrings - Problem

Math String Medium

Count Number of Homogenous Substrings

Given a string s, you need to count all homogenous substrings within it. A homogenous substring is one where all characters are identical.

For example, in the string "abbcccaa", substrings like "a", "bb", "ccc", and "aa" are homogenous, but "ab" or "bcc" are not.

Your task: Return the total count of all possible homogenous substrings. Since this number can be very large, return the result modulo 10⁹ + 7.

Key insight: A contiguous sequence of n identical characters contributes n × (n + 1) / 2 homogenous substrings to the total count.

Input & Output

example_1.py — Basic Case

$ Input: s = "abbcccaa"

› Output: 13

💡 Note: Groups: 'a'(1), 'bb'(2), 'ccc'(3), 'aa'(2). Contributions: 1×2/2=1, 2×3/2=3, 3×4/2=6, 2×3/2=3. Total: 1+3+6+3=13

example_2.py — Single Character

$ Input: s = "xy"

› Output: 2

💡 Note: Each single character forms one homogenous substring: 'x' and 'y'. Total: 2

example_3.py — All Same Characters

$ Input: s = "zzzzz"

› Output: 15

💡 Note: All characters identical, so we have one group of size 5. Contribution: 5×6/2=15 homogenous substrings

Visualization

Tap to expand

Understanding the Visualization

Scan for Groups

Identify consecutive identical character sequences

Calculate Contributions

Apply mathematical formula to each group

Sum and Return

Add all contributions modulo 10^9+7

Key Takeaway

🎯 Key Insight: Transform O(n³) substring enumeration into O(n) group analysis using the mathematical property that n consecutive identical characters contribute exactly n×(n+1)/2 homogenous substrings

Time & Space Complexity

Time Complexity

⏱️

O(n)

Single pass through the string, each character processed exactly once

✓ Linear Growth

Space Complexity

O(1)

Only using a few variables to track current state, no additional data structures needed

✓ Linear Space

Constraints

1 ≤ s.length ≤ 10⁵
s consists of lowercase English letters only
Return result modulo 10⁹ + 7

Asked in

a Amazon 45 G Google 38 f Meta 32 ⊞ Microsoft 28

The optimal solution uses mathematical insight to solve this problem in O(n) time. Instead of checking all possible substrings, we identify groups of consecutive identical characters and apply the formula n×(n+1)/2 to calculate each group's contribution efficiently.

Common Approaches

Approach	Time	Space	Notes
✓ One-Pass Linear Scan (Optimal)	O(n)	O(1)	Count consecutive identical characters and use mathematical formula
Brute Force (Check All Substrings)	O(n³)	O(1)	Generate all possible substrings and count homogenous ones

One-Pass Linear Scan (Optimal) — Algorithm Steps

Initialize current character and count of consecutive occurrences
Iterate through the string once
When character changes, calculate contribution using formula count×(count+1)/2
Add contribution to total result
Reset count for new character group
Handle the last group after the loop

Visualization

Tap to expand

Step-by-Step Walkthrough

Identify Groups

Scan string to find consecutive identical character groups

Apply Formula

For each group of size n, calculate n×(n+1)/2 contributions

Sum Results

Add all group contributions to get final answer

Code -

solution.c — C

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

int countHomogenous(char* s) {
    const int MOD = 1000000007;
    long long result = 0;
    int count = 1;
    int n = strlen(s);
    
    for (int i = 1; i < n; i++) {
        if (s[i] == s[i-1]) {
            count++;
        } else {
            // Add contribution of current group
            result = (result + (long long)count * (count + 1) / 2) % MOD;
            count = 1;
        }
    }
    
    // Don't forget the last group
    result = (result + (long long)count * (count + 1) / 2) % MOD;
    
    return result;
}

int main() {
    char s[100001];
    scanf("%s", s);
    printf("%d\n", countHomogenous(s));
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(n)

Single pass through the string, each character processed exactly once

✓ Linear Growth

Space Complexity

O(1)

Only using a few variables to track current state, no additional data structures needed

✓ Linear Space

Constraints

1 ≤ s.length ≤ 10⁵
s consists of lowercase English letters only
Return result modulo 10⁹ + 7

42.3K Views

Medium Frequency

~15 min Avg. Time

1.8K Likes

Ln 1, Col 1

Smart Actions

💡 Explanation

AI Ready

💡 Suggestion Tab to accept Esc to dismiss

// Output will appear here after running code

Code Editor Closed

Click the red button to reopen

Input & Output

Visualization

Time & Space Complexity

Related Problems

Constraints

Common Approaches

One-Pass Linear Scan (Optimal) — Algorithm Steps

Visualization

Code -

Time & Space Complexity

Constraints

Select Compiler