bhakti-thakur
32 lines
969 B
Python
32 lines
969 B
Python
# 0/1 Knapsack Problem using Dynamic Programming
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def knapsack_01(values, weights, capacity):
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n = len(values)
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# Create DP table: (n+1) x (capacity+1)
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dp = [[0 for _ in range(capacity + 1)] for _ in range(n + 1)]
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# Build table bottom-up
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for i in range(1, n + 1):
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for w in range(1, capacity + 1):
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if weights[i - 1] <= w:
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# Option 1: include the item
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include = values[i - 1] + dp[i - 1][w - weights[i - 1]]
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# Option 2: exclude the item
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exclude = dp[i - 1][w]
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dp[i][w] = max(include, exclude)
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else:
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dp[i][w] = dp[i - 1][w]
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# The last cell contains the maximum value
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return dp[n][capacity]
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# Example usage
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if __name__ == "__main__":
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values = [60, 100, 120]
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weights = [10, 20, 30]
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capacity = 50
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max_value = knapsack_01(values, weights, capacity)
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print("Maximum value in Knapsack =", max_value)
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