322. Coin Change

class Solution {
public:
    int coinChange(vector<int>& coins, int amount) {
        vector<int> dp(amount + 1, amount + 1);
        dp[0] = 0;
        for (int i = 1; i <= amount; i++) {
            for (const auto& coin : coins) {
                if (coin <= i) {
                    dp[i] = min(dp[i], dp[i - coin] + 1);
                }
            }
        }
        return dp[amount] == amount + 1 ? -1 : dp[amount];
    }
};

• T: $O(S \cdot N)$
• S: $O(S)$

class Solution {
public:
    int coinChange(vector<int>& coins, int amount)
    {
        vector<int> dp(amount + 1, amount + 1);

        dp[0] = 0;
        for (auto& coin : coins)
        {
            for (int i = coin; i <= amount; i++)
            {
                dp[i] = min(dp[i], dp[i - coin] + 1);
            }
        }
        return dp[amount] == amount + 1 ? -1 : dp[amount];
    }
};

• T: $O(S \cdot N)$
• S: $O(S)$