Build the optimal binary search tree from this data:

0 10 5 1 20 10 2 30 2 3 40 3 4 50 4 Index # key frequenc y The number in parentheses is the index of the root 5 (0) 20 (1) 24 (1) 32 (1) 44 (1) 10 (1) 14 (1) 22(1) 34 (1) 2 (2) 7 (3) 15 (3) 3 (3) 10 (4) 4 (4)