Suppose that we are given a sequence A of n 32-bit integers (a, a, ... a.) to sort such that 0 < a < N. The objective of this exercise is to produce the most efficient strategy to use Bucket Sort to sort Sequence A. 1) (5 points) Propose a strategy to adapt Bucket Sort to sort the above Sequence A. The objective is to design the most efficient algorithm. We aim a linear running time for the worst case. 2) (25 points) Describe precisely the pseudocode of your modified Bucket Sort algorithm. 3) (5 points) Analyze the running time and space complexity of your algorithm. BUCKET-SORT(A) 1 let B[0..n-1] 2n = A.length for i for i=0 ton - 1 3 4 5 for i=1 to n 6 7 for i = 0 to n - 1 8 9 be a new array make B[i] an empty list insert A[i] into list B[[n A[i]]] sort list B[i] with insertion sort concatenate the lists B[0], B[1]...., B[n 1] together in order -