Parameter-passing costs
Throughout this book, we assume that parameter passing during procedure calls takes constant time, even if an N-element array is being passed. This assumption is valid in most systems because a pointer to the array is passed, not the array itself. This problem examines the implications of three parameter-passing strategies:
1. An array is passed by pointer. Time = Θ(1).
2. An array is passed by copying. Time = Θ(N), where N is the size of the array.
3. An array is passed by copying.only the subrange that might be accessed by the called procedure. Time = Θ(q - p + 1) if the subarray A[p..q] is passed.
a. Consider the recursive binary search algorithm for finding a number in a sorted array (see Exercise 2.3-5). Give recurrences for the worst-case running times of binary search when arrays are passed using each of the three methods above, and give good upper bounds on the solutions of the recurrences. Let N be the size of the original problem and n be the size of a subproblem.
b. Redo part (a) for the MERGE-SORT algorithm from Section 2.3.1.
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