Sub array that produces a given sum and product

Question

Given an array of length N. How will you find the minimum length contiguous sub-array of whose sum is S and whose product is P. For eg 5 6 1 4 6 2 9 7 fo

Answer 1

Put two indices on the array. Lets call them i and j. Initially j = 1 and i =0. If the product between i and j is less than P, increment j. If it is greater than P, increment i. If we get something equal to p, sum up the elements (instead of summing up everytime, maintain an array where S(i) is the sum of everything to the left of it. Compute sum from i to j as S(i) - S(j)) and see whether you get S. Stop when j falls out of the array length.

This is O(n).