<p>Given a binary array <code>nums</code> and an integer <code>goal</code>, return <em>the number of non-empty <strong>subarrays</strong> with a sum</em> <code>goal</code>.</p>

<p>A <strong>subarray</strong> is a contiguous part of the array.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [1,0,1,0,1], goal = 2
<strong>Output:</strong> 4
<strong>Explanation:</strong> The 4 subarrays are bolded and underlined below:
[<u><strong>1,0,1</strong></u>,0,1]
[<u><strong>1,0,1,0</strong></u>,1]
[1,<u><strong>0,1,0,1</strong></u>]
[1,0,<u><strong>1,0,1</strong></u>]
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [0,0,0,0,0], goal = 0
<strong>Output:</strong> 15
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= nums.length &lt;= 3 * 10<sup>4</sup></code></li>
	<li><code>nums[i]</code> is either <code>0</code> or <code>1</code>.</li>
	<li><code>0 &lt;= goal &lt;= nums.length</code></li>
</ul>

class Solution {
public:

    int helper(vector<int> & v, int goal){
        int  n = v.size();
        int lo ,hi;
        lo = hi =0;
        int sum = 0;
        int  cnt =0;
        while(hi<n){
            sum += v[hi];
            while(sum > goal && lo<=hi){
                // cnt += hi-lo;
                sum -= v[lo];
                lo++;
            }
            hi++;
                cnt += (hi-lo);
        }
        // cnt += hi-lo;
        return cnt;
    }
    int helper2(vector<int> &v, int goal){
        int n = v.size();
        int sum = 0;
        int cnt = 0;
        int lo,hi;
        for(lo = 0, hi= 0; hi<n; hi++){
            sum += v[hi];
            while(sum > goal && lo<=hi){
                cnt += hi-lo;
                sum -= v[lo];
                lo++;
            }
        }
        cnt += (hi-lo)*(hi-lo+1)/2;
        return cnt;
    }
    int numSubarraysWithSum(vector<int>& v, int goal) {
        // no of subarrays with sum = goal
        // => no of subarrays with sum <= goal - no of subarrays with sum <= goal-1
        return helper2(v,goal)- helper2(v,goal-1);
    }
};
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