Problem 5. Suppose that groups of 3 are used in the deterministic selection algorithm instead of groups of 5. (a) Suppose that the algorithm recurses on the high side H. Find a constant c such that H = cn + O(1) in the worst case. Explain why this is indeed the largest size of H. Is this constant the same for the low side? Write the recursion for the worst-case running time T(n). (b) Prove that T(n) = O(n lg n) and T(n) = N2n lgn). Problem 5. Suppose that groups of 3 are used in the deterministic selection algorithm instead of groups of 5. (a) Suppose that the algorithm recurses on the high side H. Find a constant c such that H = cn + O(1) in the worst case. Explain why this is indeed the largest size of H. Is this constant the same for the low side? Write the recursion for the worst-case running time T(n). (b) Prove that T(n) = O(n lg n) and T(n) = N2n lgn)