Question 4 (10 points) From Algorithms ISBN: 9780073523408 Given two strings z = zi,Z2 Zn and y = nW2 Um, we wish to find the length of their longest common substring, that is, the largest k for which there are indices i and j with zizi+1 . . .Xi+k-1 = yjUj+1 yitk-1. Show how to do this in time 0(mm). Question 5 (10 points) From Algorithms ISBN: 9780073523408 Counting Heads. Given integers n and k, along with Plu ,Pn E 10, 1], you want to determine the probability of obtaining exactly k heads when n biased coins are tossed independently at random, where pi is the probability that the ith coin comes up heads. Give an O (n2) algorithm for this task. Assume you can multiply and add two numbers in [0, 1 in O(1) time. An O (n log n) time algorithm is possible