Count Substrings Divisible By Last Digit

Count Substrings Divisible By Last Digit - Problem

You are given a string s consisting of digits. Return the number of substrings of s divisible by their non-zero last digit.

Note: A substring may contain leading zeros.

Input & Output

Example 1 — Basic Case

$ Input: s = "123"

› Output: 5

💡 Note: Valid substrings: "1" (1÷1=0), "2" (2÷2=0), "3" (3÷3=0), "12" (12÷2=0), "123" (123÷3=0). Total: 5.

Example 2 — With Zeros

$ Input: s = "1020"

› Output: 3

💡 Note: Valid substrings: "1" (1÷1=0), "2" (2÷2=0), "102" (102÷2=0). Substrings ending in 0 are skipped.

Example 3 — Single Digit

$ Input: s = "5"

› Output: 1

💡 Note: Only one substring "5", and 5÷5=0, so count is 1.

Constraints

1 ≤ s.length ≤ 10³
s consists of digits only

Visualization

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Asked in

G Google 25 M Microsoft 18 a Amazon 15

The key insight is to use modular arithmetic to avoid integer overflow when checking divisibility. We build the remainder incrementally using (remainder × 10 + digit) % last_digit. Best approach uses modular arithmetic with Time: O(n²), Space: O(1).

Common Approaches

✓ Brute Force

⏱️ Time: O(n³) Space: O(1)

For each possible substring, convert it to a number and check if it's divisible by its last digit. Skip substrings ending with zero.

Modular Arithmetic Optimization

⏱️ Time: O(n²) Space: O(1)

Instead of converting substrings to integers, build the number modulo the last digit incrementally. This avoids overflow and is more efficient.

Brute Force — Algorithm Steps

Generate all possible substrings
Convert each substring to integer
Check if divisible by last digit
Count valid substrings

Visualization

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Step-by-Step Walkthrough

Generate

Create all possible substrings

Convert

Convert each to integer

Check

Test divisibility by last digit

Code -

solution.c — C

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

int solution(char* s) {
    int count = 0;
    int n = strlen(s);
    
    for (int i = 0; i < n; i++) {
        for (int j = i; j < n; j++) {
            char substring[1001];
            strncpy(substring, s + i, j - i + 1);
            substring[j - i + 1] = '\0';
            
            int lastDigit = substring[strlen(substring) - 1] - '0';
            
            // Skip if last digit is 0
            if (lastDigit == 0) continue;
            
            // Convert substring to number and check divisibility
            long long num = atoll(substring);
            if (num % lastDigit == 0) {
                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 convert to integer

⚠ Quadratic Growth

Space Complexity

O(1)

Only using constant extra variables

✓ 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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