Sample Solutions to Homework # 3
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چکیده
“FIBONACCI” directly implements the recurrence relation of the Fibonacci sequence. Each number in the sequence is the sum of the two previous numbers in the sequence. The running time is clearly O(n). The subproblem graph consists of n+ 1 vertices, v0, v1, ..., vn. For i = 2, 3, ..., n, vertex i has two leaving edges: to vertex vi−1 and to vertex vi−2. No edges leave vertices v0 or v1. Thus, the subproblem graph has 2n− 2 edges. 2. (15) (a) The m and s tables computed by MATRIX-CHAIN-ORDER for n = 6 and the sequence of dimensions < 5, 10, 3, 12, 5, 50, 6 > are shown in Figure 1. The minimum number of scalar multiplications to multiply the six matrices is m[1, 6] = 2010 and its corresponding parenthesization is ((A1A2)((A3A4)(A5A6))). s m
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