class Solution {
public:
    int coinChange(vector<int>& coins, int amount) {
        // dp[j]: fewest number of coins to make amount=j
        // dp[j] = min(dp[j], dp[j - coins[i]] + 1)

        // max will be amount+1 because the min value of coin is 1
        // only possible amount of coins is amount
        vector<int> dp(amount+1, amount+1);
        dp[0] = 0;

        for(int coin : coins) {
            for(int j = coin; j <= amount; j++) {
                dp[j] = min(dp[j], dp[j - coin] + 1);
            }
        }

        if(dp[amount] > amount) return -1;
        return dp[amount];
    }
};