True or False. Write T (for True) or F (for False) in front of each statement.

[ ] For any binary search tree, it will be a valid Red-Black tree if we color all nodes black.

[ ] In matrix-chain multiplication, if the minimum number of scalar multiplications needed to compute the product Ai Ai+1 . Aj-1 Aj is N, then the minimum number of scalar multiplications needed to compute the product Ai Ai+1 . Aj-2Aj-1 cannot exceed N.

[ ] In disjoint set forest representation, Union by rank makes a tree with more nodes point to a tree with fewer nodes.

[ ] In matrix-chain multiplication, if all the matrices are square matrices, any parenthesization will require the same total number of scalar multiplications.

[ ] If a node in a binary search tree has two children, its successor cannot have left child.

[ ] The height of any binary search tree with n nodes is O(logn).

[ ] The 5-step algorithm SELECT(A, k) for determining the kth smallest element of array A of size n has an O(n) complexity when the group size is 3. [ ] In Open Addressing, the loading factor is always 1.

[ ] The only value A that works for the hash function h(k) = m (kA mod 1 ) is A = (5 1)/2