Task 2. [ 70 Points ] Rank Sort The RANK-SORT algorithm given in Figure 1 accepts an array of distinct numbers, and rearranges the numbers in the array in increasing order of value. RANK-SORT (A) 1. 2. j = 1 while i S A. length k = 0 3. 4. 5. 6. 7. for i = 1 to A. length if A[i] = A[j] then k = k + 1 1/ swap Ali and A[k] A[k] A[] if k = j then j = i + 1 8. 9. 10. Figure 1: The RANK-SORT algorithm: input is an array A[1: n) of n distinct numbers (i.e., no two numbers in A are equal), and the output is A with its items sorted in increasing order of value. (a) [ 5 Points ] Describe in words (using only one sentence) as accurately as possible what the j-th iteration of the outer loop (in lines 2-10) is trying to do. meaning no two numbers in the array are equal (b) [ 5 Points ] Describe in words (using only one sentence) as accurately as possible what the inner loop (in lines 46) is trying to do in the j-th iteration of the outer loop (in lines 2-10). (c) ( 20 Points ] Using the example we used in the class to show how INSERTION-SORT and SELECTION-SORT work, show step-by-step how RANK-SORT works (i.e., sorts the numbers in that example) (d) ( 20 + 20 Points ) Analyze the worst-case and the best-case running times of RANK-SORT