Editorial for A Knapsack Problem
Remember to use this editorial only when stuck, and not to copy-paste code from it. Please be respectful to the problem author and editorialist.
Submitting an official solution before solving the problem yourself is a bannable offence.
Submitting an official solution before solving the problem yourself is a bannable offence.
Author:
This is the classical 0-1 Knapsack dynamic programming problem. Some resources that may be useful in familiarizing with the solution can be found below:
Time complexity: .
Sample solution written in Python
N, W = map(int, input().split())
dp = [([0] * (W + 1)) for _ in range(N + 1)] # Empty 2D DP array
for i in range(1, N + 1):
w, v = map(int, input().split())
for j in range(W + 1):
if j - w >= 0: # Check if there is space to take this piece
# See if it is more optimal to take the piece of gold
dp[i][j] = max(dp[i - 1][j], dp[i - 1][j - w] + v)
else:
dp[i][j] = dp[i - 1][j] # If it doesn't fit, use previous answer
print(dp[N][W])
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