Count Nonempty Binary Segments with an Exact Sum

### Problem Given binary array `nums` and `goal`, count the nonempty contiguous subarrays whose sum equals goal. Return the number of index intervals, including distinct intervals with identical values. ```cpp class Solution { public: int numSubarraysWithSum(vector<int>& nums, int goal); }; ``` ### Examples **Example 1:** ```text Input: nums = [0,1,0], goal = 1 Output: 4 Explanation: Qualifying zero-based intervals are[1,1],[0,1],[1,2],and[0,2]. ``` **Example 2:** ```text Input: nums = [0,0,1], goal = 0 Output: 3 Explanation: The first two zeros contribute two singleton intervals and their combined interval. ``` ### Constraints - `1 <= nums.length <= 3*10^4`. - Each value is0 or1. - `0 <= goal <= nums.length`. ### Contract considerations Contiguous index intervals are required; arbitrary subsequences are not counted. ```hint Read the boundary condition Two prefix sums form a valid interval exactly when their difference is goal. ``` ### Boundary reminders Contiguous index intervals are required; arbitrary subsequences are not counted.