Question

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/

Answer 1

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.