八数码（双向宽搜）

感受一下不同做法的时间
1.map+单向bfs 125ms
#include<iostream>
#include<cstdio>
#include<cstring>
#include<map>
#include<queue>
using namespace std;
string st,aim=" 123804765",s,si;
char x;
map<string,int>p;
queue<string>q;
queue<int>t;
int main()
{
    cin>>st;
    st=' '+st;
    q.push(st);
    p[st]=1;
    t.push(0);
    while(!q.empty())
      {
          s=q.front();
          int step=t.front();
          t.pop();q.pop();
          if(s==aim)
            {
                cout<<step<<endl;
                return 0;
          }
        si=s;
          int pi=si.find("0");
          if(pi+3<=9)
            {
                x=si[pi+3];si[pi+3]=si[pi];si[pi]=x;
                if(p[si]==0)
                  {
                      q.push(si);t.push(step+1);
                      p[si]=1;
              }
          }
        si=s;
        if(pi-3>=1)
          {
              x=si[pi-3];si[pi-3]=si[pi];si[pi]=x;
                if(p[si]==0)
                  {
                      q.push(si);t.push(step+1);
                      p[si]=1;
              }
          }
        si=s;
        if(pi+1<=9&&pi!=3&&pi!=6)
          {
              x=si[pi+1];si[pi+1]=si[pi];si[pi]=x;
                if(p[si]==0)
                  {
                      q.push(si);t.push(step+1);
                      p[si]=1;
              }
          }
        si=s;
        if(pi-1>=1&&pi!=7&&pi!=4)
          {
              x=si[pi-1];si[pi-1]=si[pi];si[pi]=x;
                if(p[si]==0)
                  {
                      q.push(si);t.push(step+1);
                      p[si]=1;
              }
          }
      }
}

2.康托展开+单向bfs 16ms
#include<iostream>
#include<cstdio>
#include<cstring>
#define maxn 1000100
#define maxx 50000100
#define modd 1000003
using namespace std;
int qi[maxn],head,tail,step[maxn],q[maxn];
int qg[maxn],sp=123804765;
bool f[maxx];
int KT(int sw)
{
    int g[10],i=9,sum=0;
    memset(g,0,sizeof(g));
    while(sw>0)
      {
          g[i]=sw%10;
          i--;
          sw=sw/10;
      }
    sum=g[9]*9*8*7*6*5*4*3*2+g[8]*8*7*6*5*4*3*2+g[7]*7*6*5*4*3*2+
    g[6]*6*5*4*3*2+g[5]*5*4*3*2+g[4]*4*3*2+g[3]*3*2+g[2]*2+g[1];
    return sum;
}
int sswap(int sw,int x,int y)
{
    int temp[10],i=9,tmp;
    memset(temp,0,sizeof(temp));
    while(sw>0)
      {
          temp[i]=sw%10;
          i--;
          sw=sw/10;
      }
    tmp=temp[x];
    temp[x]=temp[y];
    temp[y]=tmp;
    sw=0;
    for(i=1;i<=9;i++)
      sw=sw*10+temp[i];
    return sw;
}
int find(int s)
{
    int p=9,k;
    while(s>0)
      {
          k=s%10;
          if(k==0)return p;
          p--;
          s=s/10;
      }
}
int main()
{
    int s,ssi,ss,st;
    cin>>s;
    if(s==sp)
      {
          cout<<0;
          return 0;
      }
    int p=find(s);
    qg[++tail]=s;
    qi[tail]=p;
    while(head<tail)
      {
          p=qi[++head];
          ss=qg[head];
          //printf("%d\n",ss);
        if(p-1>=1&&p!=4&&p!=7)
          {
              ssi=ss;
              st=sswap(ssi,p,p-1);
              if(st==sp)
            {
                q[++tail]=head;
                cout<<step[head]+1<<"\n";
                return 0;
          }
              if(f[KT(st)]==0)
                {
                    f[KT(st)]=1;
                    qg[++tail]=st;
                    qi[tail]=p-1;
                    q[tail]=head;
                    step[tail]=step[head]+1;
              }
          }
        if(p-3>=1)
          {
              ssi=ss;
              st=sswap(ssi,p,p-3);
              if(st==sp)
            {
                q[++tail]=head;
                cout<<step[head]+1<<"\n";
                return 0;
          }
              if(f[KT(st)]==0)
                {
                    f[KT(st)]=1;
                    qg[++tail]=st;
                        q[tail]=head;
                qi[tail]=p-3;
                    step[tail]=step[head]+1;
              }
          }
        if(p+3<=9)
          {
              ssi=ss;
              st=sswap(ssi,p,p+3);
              if(st==sp)
            {
                q[++tail]=head;
                cout<<step[head]+1<<"\n";
                return 0;
          }
              if(f[KT(st)]==0)
                {
                    f[KT(st)]=1;
                    qg[++tail]=st;
                        q[tail]=head;
                    qi[tail]=p+3;
                    step[tail]=step[head]+1;
              }
          }
        if(p+1<=9&&p!=3&&p!=6)
          {
              ssi=ss;
              st=sswap(ssi,p,p+1);
              if(st==sp)
            {
                q[++tail]=head;
                cout<<step[head]+1<<"\n";
                return 0;
          }
              if(f[KT(st)]==0)
                {
                    f[KT(st)]=1;
                    qg[++tail]=st;
                        q[tail]=head;
                    qi[tail]=p+1;
                    step[tail]=step[head]+1;
              }
          }
      }
}

3.map+双向bfs 8ms
#include<iostream>
#include<cstdio>
#include<cstring>
#include<map>
#include<queue>
using namespace std;
map<string,int>f,step;
queue<string>q;
string s,t=" 123804765";
int Bfs()
{
    q.push(s);q.push(t);
    step[s]=0;step[t]=0;
    f[s]=1;f[t]=2;
    while(!q.empty())
      {
          string k=q.front();q.pop();
          int p=k.find('0');
        int ste=step[k];
          if(p<7)
            {
                string si=k;int pi=p+3;
                swap(si[p],si[pi]);
                if(f[si]==0){f[si]=f[k];q.push(si);step[si]=ste+1;}
                else if(f[si]!=f[k]){return step[si]+ste+1;}
          }
        if(p>3)
            {
                string si=k;int pi=p-3;
                swap(si[p],si[pi]);
                if(f[si]==0){f[si]=f[k];q.push(si);step[si]=ste+1;}
                else if(f[si]!=f[k]){return step[si]+ste+1;}
          }
        if(p!=1&&p!=4&&p!=7)
            {
                string si=k;int pi=p-1;
                swap(si[p],si[pi]);
                if(f[si]==0){f[si]=f[k];q.push(si);step[si]=ste+1;}
                else if(f[si]!=f[k]){return step[si]+ste+1;}
          }
        if(p!=3&&p!=6&&p!=9)
            {
                string si=k;int pi=p+1;
                swap(si[p],si[pi]);
                if(f[si]==0){f[si]=f[k];q.push(si);step[si]=ste+1;}
                else if(f[si]!=f[k]){return step[si]+ste+1;}
          }
      }
    return -1; 
}
int main()
{
    cin>>s;s=" "+s;
    if(s==t){cout<<0;return 0;}
    cout<<Bfs();
    return 0;
}