Give a dynamic-programming solution to the 0-1 knapsack problem that runs in O(nW) time, where n is the number of items and W is the maximum weight of items that the thief can put in his knapsack.
![[DP] The 0-1 knapsack problem](https://image.miaokee.com:8440/aHR0cDovL2ltYWdlcy5jbml0YmxvZy5jb20vaS8zNTg3MzAvMjAxNDA2LzE0MDUyMDEyNzAyMTMxOC5wbmc%3D.png?w=700&webp=1 "[DP] The 0-1 knapsack problem")
![[DP] The 0-1 knapsack problem](https://image.miaokee.com:8440/aHR0cDovL2ltYWdlcy5jbml0YmxvZy5jb20vaS8zNTg3MzAvMjAxNDA2LzE0MDUyMTQyODExMzMyMi5wbmc%3D.png?w=700&webp=1 "[DP] The 0-1 knapsack problem")
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