Rely methods to separate array into two equal sum subarrays by changing every array ingredient to Zero as soon as

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Given an array arr[] consisting of N integers, the duty is to depend the variety of methods to separate the array into two subarrays of equal sum after altering a single array ingredient to 0.

Enter: arr[] = {1, 2, -1, 3}
Output: 4
Clarification:
Changing arr[0] by 0, arr[] is modified to {0, 2, -1, 3}. Only one attainable break up is {0, 2} and {-1, 3}.
Changing arr[1] by 0, arr[] is modified to {1, 0, -1, 3}. No solution to break up the array.
Changing arr[2] by 0, arr[] is modified to {1, 2, 0, 3}. The two attainable splits are {1, 2, 0} and {3}, {1, 2} and {0, 3}.
Changing arr[3] by 0, arr[] is modified to {1, 2, -1, 0}. Only one attainable break up is {1} and {2, -1, 0}.
Due to this fact, the overall variety of methods to separate = 1 + 0 + 2 + 1 = 4.

Enter: arr[] = {1, 2, 1, 1, 3, 1}
Output: 6
Clarification:
Changing arr[0] by 0, arr[] is modified to {0, 2, 1, 1, 3, 1}. Only one attainable break up exists.
Changing arr[1] by 0, arr[] is modified to {1, 0, 1, 1, 3, 1}. No solution to break up the array.
Changing arr[2] by 0, arr[] is modified to {1, 2, 0, 1, 3, 1}. Only one attainable break up exists.
Changing arr[3] by 0, arr[] is modified to {1, 2, 1, 0, 3, 1}. Solely 2 attainable splits exist.
Changing arr[4] by 0, arr[] is modified to {1, 2, 1, 1, 0, 1}. Only one attainable break up exists.
Changing arr[5] by 0, arr[] is modified to {1, 2, 1, 1, 3, 0}. Only one attainable break up exists.
Whole variety of methods to separate is = 1 + 0 + 1 + 2 + 1 + 1 = 6.

Environment friendly Strategy: To optimize the above strategy, the concept relies on the next observations:

For each index within the vary [0, N – 1], the overall variety of methods may be obtained by contemplating the present index because the splitting level, by making any ingredient equal to 0 utilizing the method mentioned above. Observe the steps beneath to resolve the issue:

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