Count Substrings with Only One Distinct Letter

Count Substrings with Only One Distinct Letter - Problem

Math String Easy

Given a string s, return the number of substrings that have only one distinct letter.

A substring is a contiguous sequence of characters within a string. For example, in the string "aaaba", the substrings "aaa", "aa", and "a" all have only one distinct letter, but "ab" does not.

Input & Output

Example 1 — Mixed Characters

$ Input: s = "aaaba"

› Output: 10

💡 Note: Groups: "aaa"→6 substrings, "b"→1 substring, "a"→1 substring. Total: 6+1+1+1+1 = 10

Example 2 — All Same

$ Input: s = "aaaa"

› Output: 10

💡 Note: One group of 4 chars: 4*(4+1)/2 = 10 substrings ("a", "aa", "aaa", "aaaa", "a", "aa", "aaa", "a", "aa", "a")

Example 3 — All Different

$ Input: s = "abc"

› Output: 3

💡 Note: Each character forms its own group of length 1: 1*(1+1)/2 = 1 each. Total: 1+1+1 = 3

Constraints

1 ≤ s.length ≤ 1000
s consists of lowercase English letters only

Visualization

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Understanding the Visualization

Input String

Parse string into character groups

Count Groups

Apply n*(n+1)/2 formula to each group

Sum Results

Total count of valid substrings

Key Takeaway

🎯 Key Insight: Group consecutive identical characters and use the formula n*(n+1)/2 for efficient counting

Asked in

G Google 25 f Facebook 20 a Amazon 15

The key insight is that for any group of n consecutive identical characters, there are exactly n*(n+1)/2 possible substrings. The optimal approach groups consecutive characters and applies this mathematical formula. Time: O(n), Space: O(1)

Common Approaches

Approach	Time	Space	Notes
✓ Mathematical Optimization	O(n)	O(1)	Group consecutive same characters and use math formula for counting
Brute Force	O(n³)	O(1)	Check every possible substring to see if it has only one distinct character

Mathematical Optimization — Algorithm Steps

Scan string to find consecutive character groups
For each group of length n, add n*(n+1)/2 to result
Sum counts from all groups

Visualization

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Step-by-Step Walkthrough

Group Characters

Find consecutive same character segments

Apply Formula

For each group of length n: n*(n+1)/2 substrings

Sum Results

Add up counts from all groups

Code -

solution.c — C

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

int solution(char* s) {
    int len = strlen(s);
    if (len == 0) return 0;
    
    int totalCount = 0;
    int currentLength = 1;
    
    for (int i = 1; i < len; i++) {
        if (s[i] == s[i-1]) {
            currentLength++;
        } else {
            // End of current group, add its contribution
            totalCount += currentLength * (currentLength + 1) / 2;
            currentLength = 1;
        }
    }
    
    // Add the last group
    totalCount += currentLength * (currentLength + 1) / 2;
    
    return totalCount;
}

int main() {
    char s[1001];
    fgets(s, sizeof(s), stdin);
    s[strcspn(s, "\n")] = 0;
    int result = solution(s);
    printf("%d\n", result);
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(n)

Single pass through string to count consecutive groups

✓ Linear Growth

Space Complexity

O(1)

Only using constant extra variables for counting

✓ Linear Space

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Input & Output

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Related Problems

Common Approaches

Mathematical Optimization — Algorithm Steps

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Code -

Time & Space Complexity

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