Question: Interview Question practice problem Suppose that you are given a sorted sequence of distinct integers {a1, a2, , an }. Design and analyze a divide-and-conquer

Interview Question practice problem

Suppose that you are given a sorted sequence of distinct integers {a1, a2, , an }. Design and analyze a divide-and-conquer algorithm to determine whether there exists an index i such at ai = i. For example, in {-10, -3, 3, 5, 7}, a3 = 3. In {2, 3, 4, 5, 6}, there is no such i.

Make sure to give the pseudocode for your algorithm and prove that it is correct. Give the recurrence relation for the running time for the algorithm and solve its recurrence relation.

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