322力扣：零钱兑换

DP：

class Solution {
public:
    int coinChange(vector<int>& coins, int amount) {
        int n=coins.size();
        vector<int> dp(amount+1,-1);
        dp[0]=0;
        for(int i=1;i<=amount;i++){
            for(int j=0;j<n;j++){
                if(i-coins[j]>=0 && dp[i-coins[j]]>=0){
                    int res=dp[i-coins[j]]+1;
                    if(dp[i]==-1 || dp[i]>res)
                    dp[i]=res;
                }
            }
        }
        return dp[amount];
    }
};

记忆化与回溯：

class Solution {
public:
    int coinChange(vector<int>& coins, int amount) {
        vector<int> count(amount+1,0);
        function<int(int)> dfs=[&](int amount){
            int Min=INT_MAX;
            if(amount==0) return 0;
            if(amount<0) return -1;
            if(count[amount]!=0) return count[amount];
            for(auto num:coins){
                if(dfs(amount-num)==-1) continue;
                if(dfs(amount-num)<Min)
                Min=dfs(amount-num)+1;
            }
            count[amount]=Min==INT_MAX?-1:Min;
            return count[amount];
        };
        return dfs(amount);;
    }
};