Count Substrings Starting and Ending with Given Character

Count Substrings Starting and Ending with Given Character - Problem

You are given a string s and a character c. Return the total number of substrings of s that start and end with c.

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

Input & Output

Example 1 — Basic Case

$ Input: s = "abaca", c = "a"

› Output: 6

💡 Note: The substrings starting and ending with 'a' are: "a" (position 0), "a" (position 2), "a" (position 4), "aba", "abaca", and "aca". Total count is 6.

Example 2 — No Matches

$ Input: s = "abc", c = "z"

› Output: 0

💡 Note: Character 'z' doesn't appear in string "abc", so no substrings can start and end with 'z'.

Example 3 — Single Character

$ Input: s = "a", c = "a"

› Output: 1

💡 Note: Only one substring "a" exists, and it starts and ends with 'a'.

Constraints

1 ≤ s.length ≤ 10⁵
c is a single lowercase English letter
s consists of lowercase English letters only

Visualization

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Asked in

G Google 15 M Microsoft 12 a Amazon 8

The key insight is that if character c appears n times in the string, we can form exactly n*(n+1)/2 valid substrings. This includes each single occurrence plus all possible combinations between any two positions. Best approach is the mathematical formula with Time: O(n), Space: O(1).

Common Approaches

✓ Brute Force

⏱️ Time: O(n³) Space: O(1)

Generate every possible substring and check if both the first and last characters match the given character c. This involves nested loops to create all substrings.

Mathematical Formula

⏱️ Time: O(n) Space: O(1)

First count how many times character c appears in the string. If there are n occurrences, any two positions can form a valid substring, including single characters. Use the mathematical formula n*(n+1)/2 to calculate total combinations.

Brute Force — Algorithm Steps

Generate all possible substrings using nested loops
For each substring, check if first and last characters equal c
Count valid substrings

Visualization

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Step-by-Step Walkthrough

Generate Substrings

Use nested loops to create all possible substrings

Check Ends

For each substring, verify first and last characters

Count Matches

Increment counter when both ends match character c

Code -

solution.c — C

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

int solution(char* s, char c) {
    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 starts and ends with c
            if (s[i] == c && s[j] == c) {
                count++;
            }
        }
    }
    
    return count;
}

int main() {
    char s[100001], c[2];
    fgets(s, sizeof(s), stdin);
    s[strcspn(s, "\n")] = 0;
    fgets(c, sizeof(c), stdin);
    c[strcspn(c, "\n")] = 0;
    
    int result = solution(s, c[0]);
    printf("%d\n", result);
    
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(n³)

Two nested loops to generate O(n²) substrings, plus O(n) to check each substring

✓ Linear Growth

Space Complexity

O(1)

Only using a few variables for counting

✓ Linear Space

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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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