# Binary Subarrays With Sum Problem

## Description

LeetCode Problem 930.

Given a binary array nums and an integer goal, return the number of non-empty subarrays with a sum goal.

A subarray is a contiguous part of the array.

Example 1:

``````1
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Input: nums = [1,0,1,0,1], goal = 2
Output: 4
Explanation: The 4 subarrays are bolded and underlined below:
[1,0,1,0,1]
[1,0,1,0,1]
[1,0,1,0,1]
[1,0,1,0,1]
``````

Example 2:

``````1
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Input: nums = [0,0,0,0,0], goal = 0
Output: 15
``````

Constraints:

• 1 <= nums.length <= 3 * 10^4
• nums[i] is either 0 or 1.
• 0 <= goal <= nums.length

## Sample C++ Code

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class Solution {
public:
int numSubarraysWithSum(vector<int>& A, int S) {
int left, right, sum, count;
int last_left, next_left, right_start;

count = 0;
sum = 0;
left = 0;
right_start = 0;

if (S == 0) {
while ((A[right_start] == 1) && (right_start < A.size()))
right_start ++;
}

last_left = right_start;
next_left = right_start;

for (right = right_start; right < A.size(); right++) {
sum += A[right];
if (sum == S) {
break;
}
}
if (sum < S)
return 0;

for (; right < A.size(); right++) {
if (A[right] == 1) {
last_left = next_left;
}
for (left = last_left; left < A.size(); left ++) {
if (A[left] == 1) {
next_left = left + 1;
break;
}
}
for (left = last_left; left <= right; left ++) {
count ++;
if (A[left] == 1) {
break;
}
}

}

return count;
}
};
``````