Add space optimized 0/1 knapsack implementation (O(W) space)#14537
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nickzerjeski wants to merge 3 commits intoTheAlgorithms:masterfrom
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Add space optimized 0/1 knapsack implementation (O(W) space)#14537nickzerjeski wants to merge 3 commits intoTheAlgorithms:masterfrom
nickzerjeski wants to merge 3 commits intoTheAlgorithms:masterfrom
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Pull request overview
Adds a new space-optimized 0/1 knapsack solver to the existing dynamic programming implementations, reducing auxiliary memory from a 2D table to a single 1D DP array while keeping the same time complexity.
Changes:
- Added
knapsack_space_optimized(capacity, weights, values, num_items) -> intusing 1D DP with reverse-capacity iteration. - Added basic input validation for negative
capacity/num_itemsandnum_itemsbounds. - Added doctests for a few representative successful scenarios.
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| for item_index in range(num_items): | ||
| item_weight = weights[item_index] | ||
| item_value = values[item_index] | ||
| for current_capacity in range(capacity, item_weight - 1, -1): | ||
| dp[current_capacity] = max( | ||
| dp[current_capacity], item_value + dp[current_capacity - item_weight] | ||
| ) |
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| if num_items < 0: | ||
| raise ValueError("The number of items cannot be negative.") | ||
| if capacity < 0: | ||
| raise ValueError("The knapsack capacity cannot be negative.") | ||
| if num_items > len(weights) or num_items > len(values): | ||
| raise ValueError("The number of items exceeds the provided input lengths.") |
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Summary
This PR adds a space-optimized 0/1 knapsack implementation using a single 1D DP array, reducing auxiliary space from
O(n * W)toO(W)while preservingO(n * W)time complexity.What Changed
knapsack_space_optimized(capacity, weights, values, num_items) -> inttodynamic_programming/knapsack.py.num_itemsbounds.Issue Comments Review
I reviewed issue #14462 comments before implementation. There are currently no comments, so this follows the issue specification directly.
Validation
python -m doctest -v dynamic_programming/knapsack.py(pass)220.Issue
Closes #14462