Dynamic Programming Problems - 1

Coin Change

Leetcode: 322

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.

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

Example 1:

Input: coins = [1,2,5], amount = 11
Output: 3
Explanation: 11 = 5 + 5 + 1

Example 2:

Input: coins = [2], amount = 3
Output: -1

public int CoinChange(int[] coins, int amount)
{
    if (coins.Length == 0) return -1;
    Array.Sort(coins);
    int[] dp = new int[amount + 1];
    dp[0] = 0;

    for (int i = 1; i <= amount; i++)
    {
        dp[i] = Int32.MaxValue;
        
        // check for every coin
        for (int j = 0; j < coins.Length; j++)
        {
            //ignore coins which are greater than current amount
            if (coins[j] <= i &&
            dp[i - coins[j]] != Int32.MaxValue)
            {
                dp[i] = Math.Min(dp[i], dp[i - coins[j]] + 1);
            }
        }
    }
    return (dp[amount] > amount) ? -1 : dp[amount];
}