Number of Substrings Containing All Three Characters

Number of Substrings Containing All Three Characters - Problem

Given a string s consisting only of characters a, b and c.

Return the number of substrings containing at least one occurrence of all these characters a, b and c.

Input & Output

Example 1 — Basic Case

$ Input: s = "abcabc"

› Output: 10

💡 Note: Substrings containing all three: "abc", "abca", "abcab", "abcabc", "bca", "bcab", "bcabc", "cab", "cabc", "abc" (from position 3-5)

Example 2 — Minimum Valid

$ Input: s = "aaacb"

› Output: 3

💡 Note: After seeing all three chars at position 4, substrings "aaacb", "aacb", "acb" contain a, b, and c

Example 3 — No Valid Substrings

$ Input: s = "abc"

› Output: 1

💡 Note: Only one substring "abc" contains all three characters

Constraints

3 ≤ s.length ≤ 5 × 10⁴
s only consists of 'a', 'b' or 'c' characters.

Visualization

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Asked in

a Amazon 15 M Microsoft 8

The key insight is to track the last positions of characters 'a', 'b', and 'c'. Once all three characters are seen, we can count valid substrings efficiently. Best approach is sliding window with Time: O(n), Space: O(1)

Common Approaches

✓ Brute Force - Check All Substrings

⏱️ Time: O(n³) Space: O(1)

Generate all possible substrings and check each one to see if it contains at least one 'a', one 'b', and one 'c'. Count those that satisfy the condition.

Sliding Window Optimization

⏱️ Time: O(n) Space: O(1)

Track the last seen positions of characters a, b, and c. For each position, if we've seen all three characters, count how many valid substrings end at this position.

Brute Force - Check All Substrings — Algorithm Steps

Generate all possible substrings
For each substring, check if it contains a, b, and c
Count valid substrings

Visualization

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Step-by-Step Walkthrough

Generate Substrings

Create all possible substrings from the input string

Check Each Substring

Verify if substring contains a, b, and c

Count Valid

Count substrings that contain all three characters

Code -

solution.c — C

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

bool hasAllThree(char* s, int start, int end) {
    bool hasA = false, hasB = false, hasC = false;
    for (int i = start; i <= end; i++) {
        if (s[i] == 'a') hasA = true;
        if (s[i] == 'b') hasB = true;
        if (s[i] == 'c') hasC = true;
    }
    return hasA && hasB && hasC;
}

int solution(char* s) {
    int n = strlen(s);
    int count = 0;
    
    for (int i = 0; i < n; i++) {
        for (int j = i; j < n; j++) {
            if (hasAllThree(s, i, j)) {
                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 check for all three characters

✓ Linear Growth

Space Complexity

O(1)

Only using constant extra space for counters

✓ Linear Space

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Common Approaches

Brute Force - Check All Substrings — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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