Determine a recurrence relation for the divide-and-conquer sum-computation algorithm. The problem is computing the sum of n numbers. This algorithm divides the problem into two instances of the same problem: to compute the sum of the first [n/2] numbers and compute the sum of the remaining [n/2] numbers. Once each of these two sums is computed by applying the same method recursively, we can add their values to get the sum in question.

Solve the recursion by substitution: T(n) = 3T(n/2)+ 5n where T(1)=1

Consider the following recursive algorithm Algorithm Q(n)// Input: a positive integer nif n == 1 return 1else return Q(n-1)+2*n-1 1) Set up a recurrence relation for this function’s value and solve it to determine what this algorithm computes. 2) Setup a recurrence relation for the number of multiplication made by this algorithm and solve it to find the total number of multiplications that are executed.

The recursive algorithm below takes as input an array A of distinct integers, indexed between s andf, and an integer k. The algorithm returns the index of the integer k in the array A, or ?1 if the integerk is not contained within A. Complete the missing portion of the algorithm in such a way that you makethree recursive calls to subarrays of approximately one third the size of A.• Write and justify a recurrence for the runtime T(n) of the above algorithm.• Use the recursion tree to show that the algorithm runs in time O(n).FindK(A,s,f,k)if s < fif f = s + 1if k = A[s] return sif k = A[f] return felseq1 = b(2s + f)=3cq2 = b(q1 + 1 + f)=2c... to be continued.else... to be continued.