【qbxt day2(1)】 搜索

使用BFS的必要条件：1.求一个状态到另一个状态的最小步数（但是不考虑代价）

                                    2.状态可压缩，内存可以全部存下

三类搜索问题：1.最优解   2.可行解 3.解的数量

剪枝：三类通用 减掉不可能的情况

最优解特有最优性剪枝

靶形数独:)

#include<iostream>
#include<cstring>
#include<cstdio>
#include<algorithm> 
using namespace std;
bool h[10][10],l[10][10],q[10][10]; 

int num[10][10];

int re=-1;

void dfs(int cnt,bool first); 

int go[10][10]={{0,0,0,0,0,0,0,0,0,0},
                {0,1,1,1,2,2,2,3,3,3},
                {0,1,1,1,2,2,2,3,3,3},
                {0,1,1,1,2,2,2,3,3,3},
                {0,4,4,4,5,5,5,6,6,6},
                {0,4,4,4,5,5,5,6,6,6},
                {0,4,4,4,5,5,5,6,6,6},
                {0,7,7,7,8,8,8,9,9,9},
                {0,7,7,7,8,8,8,9,9,9},
                {0,7,7,7,8,8,8,9,9,9},
               };
int sc[10][10]={{0,0,0,0,0,0,0,0,0,0},
                {0,6,6,6,6,6,6,6,6,6},
                {0,6,7,7,7,7,7,7,7,6},
                {0,6,7,8,8,8,8,8,7,6},
                {0,6,7,8,9,9,9,8,7,6},
                {0,6,7,8,9,10,9,8,7,6},
                {0,6,7,8,9,9,9,8,7,6},
                {0,6,7,8,8,8,8,8,7,6},
                {0,6,7,7,7,7,7,7,7,6},
                {0,6,6,6,6,6,6,6,6,6}
}; 

void dfs(int cnt,bool first=true){
    int aa=9;
    int w,e,r;
    if(cnt<81){
        for(int i=1;i<=9;i++){ 
        for(int j=1;j<=9;j++){
            if(num[i][j]==0){
                int minn=0,ga=0,qu=go[i][j];
                for(int a=1;a<=9;a++){
                    if(!l[j][a] && !h[i][a] && !q[qu][a]){
                        minn++;
                        ga=a;
                    }
                }
                    if(minn==1 && first){
                        l[j][ga]=true;
                        h[i][ga]=true;
                        q[qu][ga]=true;
                        num[i][j]=ga;
                        dfs(cnt+1,true);
                    } 
                    if(minn<=aa){
                        aa=minn;
                        w=i;
                        e=j;
                        r=qu;
                    }
            }
        }
        } 
        for(int i=1;i<=9;i++){
        if(!h[w][i] && !l[e][i] && !q[r][i]){
            h[w][i]=true;
            l[e][i]=true;
            q[r][i]=true;
            num[w][e]=i;
            dfs(cnt+1,false);
            h[w][i]=false;
            l[e][i]=false;
            q[r][i]=false;
            num[w][e]=0;
        }
      } 
    }
    
    else{
            int ans=0;
            for(int i=1;i<=9;i++){ 
            for(int j=1;j<=9;j++){
                ans+=num[i][j]*sc[i][j];
              }
            } 
            if(re<ans||re==-1){
                re=ans;
            }
        }
}

int main(){
    memset(h,false,sizeof(h));
    memset(l,false,sizeof(l));
    memset(q,false,sizeof(q));
    int cnt=0;
    for(int i=1;i<=9;i++){ 
    for(int j=1;j<=9;j++){
        cin>>num[i][j];
        if(num[i][j]!=0) 
        {
            h[i][num[i][j]]=true;
            l[j][num[i][j]]=true;
            int qu=go[i][j];
            q[qu][num[i][j]]=true;
            cnt++;
        }
      }
    } 
    dfs(cnt,true);
    cout<<re;
    return 0;
}