Tree-Minimum(x)

1 While x.left != NIL

2 x = x.left

3 return x

The TreeSuccessor algorithm returns the successor of node x function TreeSuccessor (x) if x. right ! = NIL return TreeMinimum (x.right)//TreeMinimum is on page 291 y = x.p//parent while y! -NIL and x --y.right x = y y = y.p return y Explain why this algorithm works, assuming all keys are distinct. In your explanation, give an argument as to why, in the case where the while loop is entered, the successor of x is the lowest ancestor of x whose left child is also an ancestor of x. (In the definition of "ancestor", a node is an ancestor of itself.)