PROBLEM LINK:

Practice
Contest

Author:Lalit Kundu
Tester:Shang Jingbo and Gerald Agapov
Editorialist:Devendra Agarwal

DIFFICULTY:

Cakewalk

PREREQUISITES:

Adhoc

PROBLEM:

Given a string S consisting of only 1's and 0's, find the number of substrings which start and end both in 1.

Quick Explanation

You need to find number of pairs of 1.

Explanation

Find total number of 1's in the given string. Let suppose that the total number of 1's in the string is n , then the answer is (n*(n+1))/2.

Reason

Let's suppose that the n 1's in the string occur at x₁ , x₂, ... , x_n position in the string then all substring starting from x_i and ending at x_j are taken, so total possible ways in taking it is (n*(n+1))/2

Pseudo Code

solve(string s)
    int n = 0 
    for ( i = 0 ; i< s.size() ; i++)
        if s[i] == '1' 
            n++
    return (n*(n+1))/2

Complexity:

O(N), You just need a single pass of the string.

AUTHOR'S and TESTER'S SOLUTIONS:

Author's solution
Tester's solution