Unformatted text preview: A[0,w] = 0 ‐ When there are no items to be considered, there is no value A[i, 0] = 0 – When there is no weight remaining, there is no value A[i, w] = A[i ‐ 1,w ] ( if w i > w) – New item being considered weighs more than the current limit A[i, w] = max(A[i ‐ 1,w], m[i ‐ 1,w ‐ w i ]+v i ) (if w i ≤ w) Calculating A[N,W] given there are N items and a total Weight of W gets the optimal solution to the DP 4. MATLAB Code A Dynamic Programming Problem has been written in MATLAB and can be downloaded from: http://www.mathworks.com/matlabcentral/fileexchange/22783 ‐ ‐ 1 ‐ knapsack Download and look at the code to see the Dynamic Programming Algorithm at work. 5. Extension Study the MATLAB code for the Knapsack DP for next week’s lab....
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- Spring '11
- Dynamic Programming, WI, Knapsack problem