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Hw4Fl05Alg - Input(w p =(3 2(8 12(5 7 the knapsack-limit by...

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CSE 5211/4081 Algorithm Analysis HomeWork 4 Due: 11/3/05 Points: UG: 20/ Grad:20 .1. Write a recursive algorithm for the following formula. Input: a matrix of integers pij, 1<=i<=n, 1<=j<=n, for problem size n. C(i, j) = 0, for all 1<= i>j <=n. C(i, j) = min{ C(i+k1, j) + pij, C(i, j-k2) – pij | for all k1, k2 with 1<=k1<=n-i, 1<=k2<=j}, for all 1<= i<=j <=n .2. Write a dynamic programming algorithm for the above formula. Analyze the complexity for this algorithm. .3. Apply the dynamic programming algorithm for solving the following 0-1 Knapsack problem. Show the full matrix.
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Unformatted text preview: Input: (w, p) = ((3, 2), (8, 12), (5, 7)), the knapsack-limit by weight is M=7. GRAD 3b. Show how you would find the knapsack content from the matrix. [2] .4. Apply the dynamic programming algorithm for solving the following matrix chain-product problem. Show the full matrix and details of a sample calculation for each of the subproblem sizes >2. Input sequence of matrix-dimensions: (4x1)(1x5)(5x2)(2x3)(3x1) GRAD 4b. Keep track of the breakpoint data and recover the actual optimal order of matrix-chain multiplication in the above problem. [2]...
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