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: 8

💡 Note: Groups: "aaa"→6 substrings, "b"→1 substring, "a"→1 substring. Total: 6+1+1 = 8

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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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

✓ Brute Force

⏱️ Time: O(n³) Space: O(1)

Generate all possible substrings and check each one to see if all characters in it are the same. This requires examining every substring individually.

Mathematical Optimization

⏱️ Time: O(n) Space: O(1)

Instead of checking every substring, group consecutive identical characters and use the formula n*(n+1)/2 to count all possible substrings within each group.

Brute Force — Algorithm Steps

Generate all possible substrings
For each substring, check if all characters are identical
Count valid substrings

Visualization

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Step-by-Step Walkthrough

Generate Substrings

Create all possible contiguous substrings

Check Each One

Verify if all characters in substring are same

Count Valid

Sum up substrings with one distinct letter

Code -

solution.c — C

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

int solution(char* s) {
    int count = 0;
    int n = strlen(s);
    
    // Check all possible substrings
    for (int i = 0; i < n; i++) {
        for (int j = i; j < n; j++) {
            // Check if substring s[i:j+1] has only one distinct character
            char firstChar = s[i];
            bool isUniform = true;
            for (int k = i; k <= j; k++) {
                if (s[k] != firstChar) {
                    isUniform = false;
                    break;
                }
            }
            if (isUniform) {
                count++;
            }
        }
    }
    
    return count;
}

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(n³)

O(n²) substrings, each taking O(n) time to verify

⚠ Quadratic Growth

Space Complexity

O(1)

Only using constant extra variables

✓ Linear Space

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Medium Frequency

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Smart Actions

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Input & Output

Constraints

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Related Problems

Common Approaches

Brute Force — Algorithm Steps

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Code -

Time & Space Complexity

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