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SPOJ-PIGBANK | Unbounded Knapsack ( Minimization)

Unbounded Knapsack: Given a knapsack weight W and a set of N items with certain value Vi and weight Wi, we need to calculate minimum amount that could make up this quantity exactly. To have a more clear understanding of this problem, see SPOJ-PIGBANK

 Sample Problem: We're given a box which can hold maximum W weight. There are N various coins each of value Vi and Weight Wi. We need to fill the box with total W weight with any number of coins of any value. Note that coins are unlimited. 


100 ----- W 
2 ------- N
1 1 ----- vi,wi    
30 50 --- vi,wi

Answer of the problem above is, 60. If we take 2 coins of value 30, weight 50, we'll get exactly weight 100 with a minimum value of 60.

 Algorithm: This is a DP solution. To get the solution for W=100, we'll solve subproblems first. Let dp[W+1]  be an array which will store the subproblems solutions. In the end, dp[W] will give us the minimum amount. Subproblems soultion will be the minimum of taking the coin Vk + solution for dp[ weight left after taking that coin ] or not taking that coin; where k ranges from 1 to N; meaning loop will run for all types of coins.

Here's a solution for SPOJ-PIGBANK:

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