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6. [Total 6 pts] Given a one-dimensional array A[1..n] (n ? 2), we consider the problem of finding number of pairs (i, j), such that: 1 ? i < j ? n, and A[i] > 3* A[j]. Use the following array as an example, the respective solution for this problem should be 7 and the corresponding pairs are: (1, 6), (2, 6), (3, 5), (3, 6), (4, 5), (4, 6), (4, 8) 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 --|---|---|---|---|---|---|-- 4 | 5 | 8 | 10| 2 | 1 | 7 | 3 Question #1 [4 pts]: Let us use Pairs(A, 1, n) to represent the solution, apply the divide-and-conquer technique to design an algorithm which solves the problem. Clearly write your algorithm in pseudo-code similar as those in your textbook and feel free to add additional return values if needed. Question #2 [2 pts]: Let T(n) be the running time of Pairs(A, 1, n) in question #1. Write the recurrence expressing T(n) in terms of T(k) for some k < n. Solve it to determine the upper bound of T(n).

          6. [Total 6 pts] Given a one-dimensional array A[1..n] (n ? 2), we consider the problem of finding
number of pairs (i, j), such that: 1 ? i < j ? n, and A[i] > 3* A[j]. Use the following array as an
example, the respective solution for this problem should be 7 and the corresponding pairs are:
(1, 6), (2, 6), (3, 5), (3, 6), (4, 5), (4, 6), (4, 8)

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8
--|---|---|---|---|---|---|--
4 | 5 | 8 | 10| 2 | 1 | 7 | 3

Question #1 [4 pts]: Let us use Pairs(A, 1, n) to represent the solution, apply the divide-and-conquer technique to design an algorithm which solves the problem. Clearly write your algorithm in pseudo-code similar as those in your textbook and feel free to add additional return values if needed.

Question #2 [2 pts]: Let T(n) be the running time of Pairs(A, 1, n) in question #1. Write the recurrence expressing T(n) in terms of T(k) for some k < n. Solve it to determine the upper bound of T(n).

6. [Total 6 pts] Given a one-dimensional array A[1..n] (n ? 2), we consider the problem of finding
number of pairs (i, j), such that: 1 ? i < j ? n, and A[i] > 3* A[j]. Use the following array as an
example, the respective solution for this problem should be 7 and the corresponding pairs are:
(1, 6), (2, 6), (3, 5), (3, 6), (4, 5), (4, 6), (4, 8)

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8
–|—|—|—|—|—|—|–
4 | 5 | 8 | 10| 2 | 1 | 7 | 3

Question #1 [4 pts]: Let us use Pairs(A, 1, n) to represent the solution, apply the divide-and-conquer technique to design an algorithm which solves the problem. Clearly write your algorithm in pseudo-code similar as those in your textbook and feel free to add additional return values if needed.

Question #2 [2 pts]: Let T(n) be the running time of Pairs(A, 1, n) in question #1. Write the recurrence expressing T(n) in terms of T(k) for some k < n. Solve it to determine the upper bound of T(n).

Added by Ver-Nica M.

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