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.

coinChange.cpp

/* Dynamic programming solution:
1. Let dp[i] where i is between [0..amount+1] represents the minimum amount of coins needed for i.
2. dynamic programming solution gives:
for each coin in coins and foreach amount i: dp[i] = min(dp[i], dp[i - coins[j]] + 1);
*/
int coinChange(vector<int>& coins, int amount) {
    int Max = amount + 1;
    vector<int> dp(amount + 1, Max);
    dp[0] = 0;
    for (int i = 1; i <= amount; i++) {
        for (int j = 0; j < coins.size(); j++) {
            if (coins[j] <= i) {
                dp[i] = min(dp[i], dp[i - coins[j]] + 1);
            }
        }
    }
    return dp[amount] > amount ? -1 : dp[amount];
}