1. Consider the following algorithm. ALGORITHM Mystery (A[0..n-1, 0..n-1], B[0..n-1, 0..n-1] //Input: Two n-by-n matrices A and B for i0 ton - 1 do for j-0 ton-1 do C[i, j] +0.0 for k0 to n 1 do return C C[i, j]C[i, j]+ A[i, k] B[k, j] What does this algorithm compute? What is its basic operation? What is the input size of this algorithm? What is the time complexity of this algorithm?

Assume that you are given an array containing n integer numbers from the set {0, 1, . . . , k} for some k ≤ n. Design an algorithm to produce a sorted array containing those n numbers in non-decreasing order in time O(n). Present the pseudocode for the algorithm and provide a justification for its running time.

Question 1. The input is an array a[1],. ,..., a[n] of size n containing natural numbers between 1 and n. Describe an O(n) algorithm that determines if the array contains 2 consecutive integers.

The Bubble Sort procedure bubblesort(a1,a2,...,an: real numbers with n>1) for i:=1 to n-1 for j:=1 to n-i   if aj>aj+1 then interchange aj and aj+1 _____________________________________________ Show how this algorithm works on the input sequence 3, 6, 1, 4, 2. What sequence do we have after the first pass (with i=1)? Make sure that you give the current state of the sequence after every pass.