1513. Number of Substrings With Only 1s -----M

Given a binary string s (a string consisting only of '0' and '1's).

Return the number of substrings with all characters 1's.

Since the answer may be too large, return it modulo 10^9 + 7.

 

Example 1:

Input: s = "0110111"
Output: 9
Explanation: There are 9 substring in total with only 1's characters.
"1" -> 5 times.
"11" -> 3 times.
"111" -> 1 time.

Example 2:

Input: s = "101"
Output: 2
Explanation: Substring "1" is shown 2 times in s.

Example 3:

Input: s = "111111"
Output: 21
Explanation: Each substring contains only 1's characters.

Example 4:

Input: s = "000"
Output: 0

 

Constraints:

• s[i] == '0' or s[i] == '1'
• 1 <= s.length <= 10^5

 

A:

class Solution {
public:
    int numSub(string s) {
        int n = s.length();
        int start = 0;
        vector<long> count(n+1,0);
        for(int i=1;i<=n;i++){
            count[i] = i + count[i-1];
        }
        
        int res = 0;
        while(start<n){
            while(start<n && s[start]=='0'){
                start++;
            }
            int end = start;
            while(end<n && s[end]=='1'){
                end++;
            }
            int len = end - start;
            res =  (res + count[len]) % 1000000007;
            start = end;
        }
        return res;
    }
};

核心是 f( i 个连续1 的子集数) = f(i-1) + i;