May 2017
Intermediate to advanced
340 pages
8h 16m
English
Content preview from PHP 7 Data Structures and Algorithms
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0 - 1 knapsack
A knapsack is a bag with straps, usually carried by soldiers to help them take their necessary items or valuables during their journey. Each item has a value and definite weight attached to it. So, the soldier has to pick the most valuable items within their maximum weight limit as they cannot put everything in their bag. The word 0/1 means that either we can take it or leave it. We cannot take an item partially. This is known as the famous 0-1 knapsack problem. We will take the bottom-up approach for solving the 0-1 knapsack problem. Here is the pseudocode for the solution:
Procedure knapsack(n, W, w1,...,wN, v1,...,vN) for w = 0 to W M[0, w] = 0 for i = 1 to n for w = 0 to W if wi > w : M[i, w] = M[i-1, w] else : M[i, ...
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