LeetCode 638 Shopping Offers

题目链接：

LeetCode 638 Shopping Offers

题解

dynamic programing
需要用到进制转换来表示状态，或者可以直接用一个vector来保存状态。

代码

1、未优化，超时代码：

class Solution {
public:
    int max(int x,int y){ return x>y?x:y; }
    int min(int x,int y){ return x>y?y:x; }

    int dfs(vector<int>& price,vector<vector<int> >& special, map<vector<int>,int>& dp,vector<int> cur){
        if(dp.count(cur)) return dp[cur];
        int &res=dp[cur]=INF;

        for(int i=0;i<special.size();i++){
            bool flag=true;
            vector<int> nex;
            for(int j=0;j<price.size();j++){
                int tmp=cur[j]-special[i][j];
                if(tmp<0){
                    flag=false; break;
                }
                nex.push_back(tmp);
            }
            if(flag){
                res=min(res,dfs(price,special,dp,nex)+special[i][special[i].size()-1]);
            }
        }
		
		//这里可以优化，能优化的原因是因为转移顺序是可调整的
        for(int i=0;i<price.size();i++){
            vector<int> nex(cur);
            if(nex[i]>0){
                nex[i]--;
                res=min(res,dfs(price,special,dp,nex)+price[i]);
            }
        }

        return res;
    }

    int shoppingOffers(vector<int>& price, vector<vector<int> >& special, vector<int>& needs) {
        map<vector<int>,int> dp;
        vector<int> start;
        for(int i=0;i<price.size();i++){
            start.push_back(0);
        }
        dp[start]=0;
        vector<int> cur(needs);
        return dfs(price,special,dp,cur);
    }

private:
    const static int INF=0x3f3f3f3f;

};

2、优化之后的代码

class Solution {
public:
    int max(int x,int y){ return x>y?x:y; }
    int min(int x,int y){ return x>y?y:x; }

    int dfs(vector<int>& price,vector<vector<int> >& special, map<vector<int>,int>& dp,vector<int> cur){
        if(dp.count(cur)) return dp[cur];
        int res=INF;

        for(int i=0;i<special.size();i++){
            bool flag=true;
            vector<int> nex;
            for(int j=0;j<price.size();j++){
                int tmp=cur[j]-special[i][j];
                if(tmp<0){
                    flag=false; break;
                }
                nex.push_back(tmp);
            }
            if(flag){
                res=min(res,dfs(price,special,dp,nex)+special[i][special[i].size()-1]);
            }
        }
		
		//这里进行了优化
        int noSpecial=0;
        for(int i=0;i<cur.size();i++){
            noSpecial+=cur[i]*price[i];
        }

        res=min(res,noSpecial);
        return dp[cur]=res;
    }

    int shoppingOffers(vector<int>& price, vector<vector<int> >& special, vector<int>& needs) {
        map<vector<int>,int> dp;
        vector<int> start;
        for(int i=0;i<price.size();i++){
            start.push_back(0);
        }
        dp[start]=0;
        vector<int> cur(needs);
        return dfs(price,special,dp,cur);
    }

private:
    const static int INF=0x3f3f3f3f;

};