whag is loop variant and please answer only in pseudocode with explanation....

The following implementation of partition (the quicksort subroutine) is incorrect. def partition(A, i, j): 1 = i+1 r = j-1 p = A[i] # loop invariant: # |p|

=p | # # i i+1 1 r+1 j while 1 = p: r -= 1 else: A [1], A [r+1] = A [r+1], A [1] 1 + = 1 r -= 1 A [r], A [i] = A [i], A[r] return r (a) What happens if one runs this code on A = [1, 2, 3], i = 0, j = 3? (b) Modify this code to fix this problem while still maintaining the loop invariant described in the comments