322. Coin Change

You are given coins of different denominations and a total amount of money amount. Write a function to compute the fewest number of coins that you need to make up that amount. If that amount of money cannot be made up by any combination of the coins, return -1.

Example 1:
coins = [1, 2, 5], amount = 11
return 3 (11 = 5 + 5 + 1)

Example 2:
coins = [2], amount = 3
return -1.

Note:
You may assume that you have an infinite number of each kind of coin.

Solution:

The problem asks the minimum number of coins that can form the target amount.

We create an DP array int[] ways = new int[amount + 1].

ways[i] denotes the minimum number of coins that can form amount i.

Therefore the transaction function is:

ways[i] = min(ways[i], ways[i - coin] + 1) for all coin <= i.

A detailed video of numbers of combinations of coins (similar to this problem).



Code:

public class Solution {
    public int coinChange(int[] coins, int amount) {
        int[] ways = new int[amount + 1];
        Arrays.fill(ways, amount + 1);
        ways[0] = 0;
        for (int i = 1; i <= amount; i++) {
            for (int coin : coins) {
                if (i >= coin) {
                    ways[i] = Math.min(ways[i], ways[i - coin] + 1);
                }
            }
        }
        return ways[amount] > amount ? -1 : ways[amount];
    }
}