Finding an array after repeatedly applying prefix sum

Revision en1, by bihariforces, 2023-01-30 12:37:21

Suppose we're given an array of length N upto 1e6 and we apply prefix sum to the array in place, ie. [a, b, c] becomes [a, a + b, a + b + c], we repeat this K times where K can be upto 1e6.

Can we find the resulting array after K operations faster than O(N*K)?

I have observed each preceding element has some contribution for an element in resulting array, but the coefficient doesn't seem intuitive to derive, can someone help derive how to compute the resulting array?

Finding a particular element of the resulting array, for example, just last element in better than O(N*K) would also suffice, hope someone can help.

Tags math, prefix sum


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en1 English bihariforces 2023-01-30 12:37:21 697 Initial revision (published)