It is a simple yet powerful technique that allows to perform fast calculation on the sum of elements in a given range (called contiguos segment of an array).
👉 Here A[i] = sum of all elements from 0 to i.
As mentioned above 👆 sum between range 0 to 4 : would be A[4] , which implies all elements between 0 to 4.
From the prefix sum array we only have following data:
prefix_sum[i] = Sum of all elements between 0 to i.
So we only have prefix sum data for a range where start range is always 0 and the end range can be any value < len(input array). So when we are given a range where start element is a non zero value , we should break the given range to a equation which can be represented with a range where start element can be 0.