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Problem 1 1. T(n) = 9T(n/3) + n + n 2 + 1 2. T(n) = 2T(2n/9) + √ n 3. T(n) = 2T(n/11) + p√ n 4. T(n) = T(n − 2) + O(1) 5. T(n) = 2T(n 1/4 ) + 1 6. T(n) = 2T(n) + n 2 Problem 2 You are climbing a stair case. It takes n steps to reach to the top. Each time you can either climb 1 or 2 steps. In how many distinct ways can you climb to the top? Problem 3 Given n, how many structurally unique binary search trees (BST’s) can you construct that store values 1 . . . n? For example, given n = 3, there are a total of 5 unique BST’s: Figure 1: All the unique BST’s given n = 3

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