Expert · Dynamic programming · 213 of 264
Knapsack
Choose items to put in a bag without going over its capacity, making the total value as large as possible. Each item can be taken once.
Input: n and the capacity (up to 1000), then n lines "weight value". Output: the largest total value.
Examples
Input
3 50 10 60 20 100 30 120
Output
220
Input
1 5 6 10
Output
0
Input
4 7 1 1 3 4 4 5 5 7
Output
9
One more test checks other inputs when you press Check.
Stuck? The idea behind dynamic programming
Break the problem into smaller ones that repeat, and keep each answer in a table so it is worked out only once.
Decide what one cell of the table means ("the best total using the first i items"), how it follows from earlier cells, and where it starts.
n = 10
ways = [0] * (n + 1)
ways[0] = 1
for i in range(1, n + 1):
ways[i] = ways[i - 1] + (ways[i - 2] if i >= 2 else 0)
print(ways[n]) # climbing 10 stairs, 1 or 2 at a timeWatch for: Fill the table in an order where every cell it needs is already filled.