UVa 11517 - Exact Change

Summary
Given n bills (or coins) of certain values. Select a subset of them so that the total value is at least P and is minimum.

Explanation
Use Dynamic Programming to determine whether there is a way to make a value V from the n bills.

Let dp[X] be the number of bills needed to make a value of X.

To fill in this DP table, first set dp[0] = 0 and set the rest to INFINITY.

For each bill with value C, update dp[v+C] = min(dp[v+C], dp[v]+1) for all value v where dp[v] is not INFINITY.

The answer is X and dp[X], where X >= P and dp[X] is not INFINITY and X is minimum. To find such X, a simple iteration will do.

Implementations
int dp[30001];

dp[0] = 0; for (int i=1; i<=30000; i++) dp[i] = INFINITE;

for each coin C do   for (int v = 30001 - C - 1; v >= 0; v--) if (dp[v] < INFINITE) dp[v+C] = min(dp[v+C], dp[v]+1);

Input
9 1400 3 500 1000 2000 12 5 1 2 2 2 5 4 4 2 1 1 1 20 4 4 4 5 10 1 2 1 1 2 1 3 1000 10 10 900 20 200 300 400 10 10 20 20 13 5 9 5 2 3 3 10000 5 10000 10000 10000 10000 10000

Output
1500 2 12 5 4 3 23 4 1 1 3 1 1100 2 13 4 10000 1

Category
Dynamic Programming Coin Change