Number of Substrings With Only 1s

Number of Substrings With Only 1s - Problem

Math String Medium

Given a binary string s, return the number of substrings with all characters 1's.

Since the answer may be too large, return it modulo 10⁹ + 7.

Example: For string "111", the substrings are: "1" (3 times), "11" (2 times), "111" (1 time), totaling 6 substrings.

Input & Output

Example 1 — Basic Consecutive 1's

$ Input: s = "111"

› Output: 6

💡 Note: Substrings with only 1's: "1" (at positions 0,1,2), "11" (at positions 0-1,1-2), "111" (at position 0-2). Total: 3+2+1 = 6

Example 2 — Mixed String

$ Input: s = "0"

› Output: 0

💡 Note: No substrings contain only 1's, so the count is 0

Example 3 — Multiple Segments

$ Input: s = "1101"

› Output: 4

💡 Note: Segment "11" contributes 2*(2+1)/2 = 3 substrings: "1" (pos 0), "1" (pos 1), "11" (pos 0-1). Segment "1" contributes 1*(1+1)/2 = 1 substring: "1" (pos 3). Total = 3 + 1 = 4

Constraints

1 ≤ s.length ≤ 10⁵
s[i] is either '0' or '1'

Visualization

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Asked in

f Facebook 15 a Amazon 12

The key insight is that for any consecutive sequence of n ones, there are exactly n×(n+1)/2 possible substrings. The optimal approach identifies all consecutive segments and applies this mathematical formula. Time: O(n), Space: O(1)

Common Approaches

✓ Brute Force - Check All Substrings

⏱️ Time: O(n³) Space: O(1)

For each starting position, check all substrings beginning at that position. Count those containing only 1's. This approach examines every possible substring individually.

Mathematical Formula

⏱️ Time: O(n) Space: O(1)

Identify all consecutive segments of 1's in the string. For each segment of length n, the number of substrings is n*(n+1)/2. Sum these values for all segments.

Brute Force - Check All Substrings — Algorithm Steps

Step 1: For each starting index i, check all substrings s[i:j]
Step 2: Count substrings that contain only '1' characters
Step 3: Return count modulo 10^9 + 7

Visualization

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Step-by-Step Walkthrough

Generate Substrings

Create all possible substrings

Check Each One

Verify if substring contains only 1's

Count Valid

Sum up all valid substrings

Code -

solution.c — C

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

int solution(char* s) {
    const int MOD = 1000000007;
    int count = 0;
    int n = strlen(s);
    
    for (int i = 0; i < n; i++) {
        for (int j = i; j < n; j++) {
            int allOnes = 1;
            for (int k = i; k <= j; k++) {
                if (s[k] != '1') {
                    allOnes = 0;
                    break;
                }
            }
            if (allOnes) {
                count = (count + 1) % MOD;
            }
        }
    }
    
    return count;
}

int main() {
    char s[100001];
    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)

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

⚠ Quadratic Growth

Space Complexity

O(1)

Only using a few variables to track count and indices

✓ 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 - Check All Substrings — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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