Efficient algorithm to calculate the sum of all k-products

Question

Suppose you are given a list L of n numbers and an integer k. Is there an efficient way to calculate the sum of all products of

Answer 1

Algebraically, for k=2 just take the sum of the elements of L, square it, and subtract the sum of the squares of L. That is:

int sum = 0;
int sqSum = 0;
for (int i=0; i

In your example, what you are computing is this

(1 + 3 + 4 + 6)^2 - (1^2 + 3^2 + 4^2 + 6^2) = 1*3 + 1*4 + 1*6 + 3*4 + 3*6 + 4*6

This should give you a hint for how to proceed in general.