【leetcode最短路】818. Race Car

https://leetcode.com/problems/race-car/description/

1. BFS剪枝 0<=current position<=2*target。为什么2*target有点不太明白

class Solution {
public:
    int dp[10002];
    struct Node{
        int pos;
        int speed;
        int step;
        Node(int p,int s,int ss){
            pos=p;
            speed=s;
            step=ss;
        }
    };
    int racecar(int target) {
        queue<Node> Q;
        set<pair<int,int> > vis;
        Q.push(Node(0,1,0));
        vis.insert({0,1});
        while(!Q.empty()){
            Node q=Q.front();
            Q.pop();
            if(q.pos==target) return q.step;
            if(vis.find({q.pos+q.speed,q.speed*2})==vis.end()&&q.pos+q.speed>=0&&q.pos+q.speed<=2*target){
                vis.insert({q.pos+q.speed,q.speed*2});
                Q.push(Node(q.pos+q.speed,q.speed*2,q.step+1));
            }
            if(vis.find({q.pos,q.speed>0?-1:1})==vis.end()){
                vis.insert({q.pos,q.speed>0?-1:1});
                Q.push(Node(q.pos,q.speed>0?-1:1,q.step+1));
            }
        }
        return -1;
    }
};

2. Dijkstra，官方题解，没太看懂

3. DP

class Solution {
public:
    int dp[10002];
    int racecar(int target) {
        if(dp[target]!=0) return dp[target];
        int bound;
        for(int i=0;i<32;i++){
            if((1<<i)-1==target) return dp[target]=i;
            if((1<<i)-1>target){
                bound=i;
                break;
            }
        }
        dp[target]=bound+1+racecar((1<<bound)-1-target);
        for(int i=0;i<bound-1;i++){
            dp[target]=min(dp[target],bound-1+1+i+1+racecar(target-(((1<<(bound-1))-1)-((1<<i)-1))));
        }
        return dp[target];
    }
};