I am trying to solve this problem from SPOJ, it's a dynamic programming problem, but I'm having trouble visualizing the recursive step. I believe it's similar to a knapsack, but here there are two constraints of Oxygen and Nitrogen.
Here is the link: http://www.spoj.pl/problems/SCUBADIV/
This should work I think:
dp[i, j] = minimum weight needed such that we have i litres of oxygen and j litres of nitrogen dp[0, 0] = 0 and inf everywhere else for each read cylinder k do for i = maxTotalOxygen down to oxygen[k] do for j = maxTotalNitrogen down to nitrogen[k] do dp[i, j] = min(dp[i, j], <- do not take cylinder k dp[i - oxygen[k], j - nitrogen[k]] + weight[k]) <- take cylinder k Answer is the minimum dp[i, j] such that i >= RequiredOxygen and j >= RequiredNitrogen.
Note that the
for loops must go from the max down to the values of the current cylinder, otherwise you allow a cylinder to be used more than once.
The problem constraints are very small and I think this should work.