Knapsack.py

"""
@author Anirudh Sharma

You are given weights and values of N items, put these items in a knapsack of capacity W
to get the maximum total value in the knapsack. Note that we have only one quantity of each item.

In other words, given two integer arrays val[0..N-1] and wt[0..N-1] which represent
values and weights associated with N items respectively. Also given an integer W
which represents knapsack capacity, find out the maximum value subset of val[]
such that sum of the weights of this subset is smaller than or equal to W.

You cannot break an item, either pick the complete item, or don’t pick it (0-1 property).

Constraints:
1 ≤ N ≤ 1000
1 ≤ W ≤ 1000
1 ≤ wt[i] ≤ 1000
1 ≤ v[i] ≤ 1000
"""


def knapSack(W, weights, values):
    # DP array to store the weight-values combination
    dp = [[0 for x in range(W + 1)] for y in range(len(weights) + 1)]
    # Loop for all the combinations
    for i in range(len(weights) + 1):
        for j in range(W + 1):
            # For zero weight
                if i == 0 or j == 0:
                    dp[i][j] = 0
                    continue
                # If the total weight is less than the
                # current weight we are considering
                # i.e W < weights[i]
                if j < weights[i - 1]:
                    dp[i][j] = dp[i - 1][j]
                else:
                    dp[i][j] = max(values[i - 1] + dp[i - 1][j - weights[i - 1]], dp[i - 1][j])
    return dp[len(weights)][W]


if __name__ == "__main__":
    weights = [4, 5, 1]
    values = [1, 2, 3]
    W = 4
    print(knapSack(W, weights, values))

    weights = [4, 5, 6]
    values = [1, 2, 3]
    W = 3
    print(knapSack(W, weights, values))