【启发式搜索】八数码问题

首先就是f(n)=g(n)+h(n)这个h(n)就是估价函数，然后每次更新一下g(n)然后用康托展开，搞一下判重就好了。

#include <cstdio>
#include <algorithm>
#include <cstring>
#include <iostream>
#include <queue>
using namespace std;
const int MAXVIS = 1000000;
struct State{
    int s[9];
    int step;
    int h, g;
    bool operator < (const State& s) const {
        return (g+h)>(s.g+s.h);
    }
    bool operator > (const State& s) const {
        return (g+h)<(s.g+s.h);
    }
}st, ed;
priority_queue<State> que;
int _pow[9]; pair<int, int> show[9];
int fx[4][2] = {{-1, 0}, {1, 0}, {0, -1}, {0, 1}};
bool vis[MAXVIS+5];
int hash(int s[]){
    int ret = 0, count =0 ;
    for(int i=0;i<9;i++){
        count = 0;
        for(int j=i+1;j<9;j++)
            count += int(s[j]<s[i]);
        ret += count * _pow[8-i];
    }
    return ret;
}
int _abs(int u){return u>0?u:-u;}
int _h(int s[]){
    int ret = 0;
    for(int i=0;i<9;i++) if(s[i])
        ret += _abs(i/3-show[s[i]].first) + _abs(i%3-show[s[i]].second);
    return ret;
}
bool check(State s){
    for(int i=0;i<9;i++)
        if(s.s[i] != ed.s[i])
            return false;
    return true;
}
bool check_pos(int a, int b){
    if(a > 2 || b > 2 || a < 0 || b < 0) 
        return false;
    return true;
}
void solve(){
    //printf("666");
    State tmp=st; State t2;
    int id=hash(st.s);
    vis[id] = true;
    tmp.h = _h(st.s); tmp.h = 0;
    que.push(tmp);
    while(!que.empty()){
        //printf("6");
        tmp = que.top(); que.pop();
        //printf("6");
        if(check(tmp)) break;
        int zx=0, zy=0, pos=0;
        while(tmp.s[pos]) pos++;
        zx = pos / 3; zy = pos % 3;
        for(int i=0;i<4;i++) {
            int nzx = zx + fx[i][0], nzy = zy + fx[i][1];
            //printf("6");
            if(check_pos(nzx, nzy)){
                t2 = tmp;
                swap(t2.s[pos], t2.s[nzx*3+nzy]);
                id = hash(t2.s);
                if(vis[id]) continue;
                vis[id] = true;
                t2.g++; t2.step++;
                t2.h = _h(t2.s);
                que.push(t2);
            }
        }
    }
    if(check(tmp)) printf("%d\n", tmp.step);
    else printf("-1\n");
}
int main(){
    _pow[0] = 1;
    for(int i=1;i<=8;i++) _pow[i] = _pow[i-1] * i;
    for(int i=0;i<9;i++) scanf("%d", &st.s[i]);
    for(int i=0;i<9;i++){
        scanf("%d", &ed.s[i]);
        show[ed.s[i]] = make_pair(i/3, i%3);
    }
    if(check(st)) printf("0\n");
    else solve();

    return 0;
}