Imagine an infinitely large array A[0 ellipsis infinity]. In this array, A[0] = A[1] = ellipsis = A[n - 1] = 0, and A[n] = A[n + 1] = A[n + 2] = ellipsis = 1. That is, the first n elements of the array arc 0 and all subsequent elements arc 1. In constant time we can query the array to find the value of an array element A[i]. We do not know the value of n, the index of the first nonzero element. Describe an algorithm to find the value of n. This algorithm should make at mostO(log n) queries. Describe an algorithm for finding any index m, where A[m] = 1 and m 1. Show that this algorithm requires O(log log n) array queries. Describe an algorithm for finding any m, where A[m] = 1. How fast can you make thisalgorithm? Imagine an infinitely large array A[0 ellipsis infinity]. In this array, A[0] = A[1] = ellipsis = A[n - 1] = 0, and A[n] = A[n + 1] = A[n + 2] = ellipsis = 1. That is, the first n elements of the array arc 0 and all subsequent elements arc 1. In constant time we can query the array to find the value of an array element A[i]. We do not know the value of n, the index of the first nonzero element. Describe an algorithm to find the value of n. This algorithm should make at mostO(log n) queries. Describe an algorithm for finding any index m, where A[m] = 1 and m 1. Show that this algorithm requires O(log log n) array queries. Describe an algorithm for finding any m, where A[m] = 1. How fast can you make thisalgorithm