搜索 问题 D: 神奇密码锁

这道题个人认为隐含着状态转换，所以想到的还是BFS，将其中一位数加一或减一或交换临近两位，进入下一状态，使用一个大小为10000的bool数组判重，由于BFS的特性，得到的一定是最小步数；

普通BFS代码如下：

#include<iostream>
#include<cstdio>
#include<cstring>
#include<set>
using namespace std;
const int MaxSize = 1e5;
typedef struct node{
    int a[4];
    int step;
}Node;

Node Q[MaxSize];

bool visit[10005];

bool search_table(int *a){
    int tmp=0;
    tmp = a[0]*1000+a[1]*100+a[2]*10+a[3];
    if(visit[tmp])return false;
    visit[tmp] = true;
    return true;
}

int BFS(int *start,int *goal){
    int head=0,tail=1,tmp;
    memset(visit,0,sizeof(visit));
    Node t,s;
    memcpy(t.a,start,4*sizeof(int));
    t.step = 0;
    Q[head] = t;
    while(head!=tail){
        t = Q[head];
        if(!memcmp(t.a,goal,4*sizeof(int))) return t.step;
        for(int i=0;i<4;i++){
            s = t;
            s.a[i]++;
            s.step++;
            if(s.a[i]>9) s.a[i]=1;
            if(search_table(s.a)) {
                    Q[tail]=s;
            tail=(tail+1)%MaxSize;
            }
        }
        for(int i=0;i<4;i++){
            s = t;
            s.a[i]--;
            s.step++;
            if(s.a[i]<1) s.a[i]=9;
            if(search_table(s.a)) {
                    Q[tail]=s;
            tail=(tail+1)%MaxSize;
            }
        }
        for(int i=0;i<3;i++){
            s = t;
            tmp = s.a[i],s.a[i] = s.a[i+1],s.a[i+1] = tmp;
            s.step++;
            if(search_table(s.a)) {
                    Q[tail]=s;
            tail=(tail+1)%MaxSize;
            }
        }
        head=(head+1)%MaxSize;
    }
    return -1;
}

void Input_data(int *start,int *goal){
    char c[5];
    scanf("%s",c);
    for(int i=0;i<4;i++) start[i] = c[i]-'0';
    scanf("%s",c);
    for(int i=0;i<4;i++) goal[i] = c[i]-'0';
}

int main(){
    int T,start[4],goal[4];
    scanf("%d",&T);
    while(T--){
        Input_data(start,goal);
        printf("%d\n",BFS(start,goal));
    }
}

双向BFS：

#include<iostream>
#include<cstdio>
#include<cstring>

using namespace std;

int visit[10005];
const int MaxSize = 1e5;
typedef struct node{
    int a[4],step;
}Node;
Node start,goal;
int trans(Node x){
    int tmp = 0;
    for(int i=0;i<4;i++) tmp = tmp*10+x.a[i];
    //printf("%d\n",tmp);
    return tmp;
}

Node Q1[MaxSize],Q2[MaxSize];

int BFS(){
    memset(visit,0,sizeof(visit));
    //queue<Node> Q1,Q2;

    Node t,s;
    int step1=0,step2=0,ans,cnt;
    int head1=0,head2=0,tail1=1,tail2=1;
    start.step = 0;
    goal.step = 0;
    Q1[head1] = start;
    Q2[head2] = goal;
    visit[trans(start)]=1;
    visit[trans(goal)]=2;
    while(true){
            cnt = (tail1-head1+MaxSize)%MaxSize;
            while(cnt--){
                t = Q1[head1];
                if(!memcmp(t.a,goal.a,sizeof(goal.a))) return t.step;
                step1 = t.step + 1;
                for(int i=0;i<4;i++){
                    s = t;
                    s.a[i]++;
                    if(s.a[i]>9) s.a[i]=1;
                    ans = trans(s);
                    if(visit[ans]==2) return step1+step2;
                    if(!visit[ans]){
                        visit[ans] = 1;
                        s.step = step1;
                        Q1[tail1]=s;
                        tail1=(tail1+1)%MaxSize;
                    }
                }
                 for(int i=0;i<4;i++){
                    s = t;
                    s.a[i]--;
                    if(s.a[i]<1) s.a[i]=9;
                    ans = trans(s);
                    if(visit[ans]==2) return step1+step2;
                    if(!visit[ans]){
                        visit[ans] = 1;
                        s.step = step1;
                        Q1[tail1]=s;
                        tail1=(tail1+1)%MaxSize;
                    }
                }
                for(int i=0;i<3;i++){
                    s = t;
                    swap(s.a[i],s.a[i+1]);
                    ans = trans(s);
                    if(visit[ans]==2) return step1+step2;
                    if(!visit[ans]){
                        visit[ans] = 1;
                        s.step = step1;
                        Q1[tail1]=s;
                        tail1=(tail1+1)%MaxSize;
                    }
                }
                head1=(head1+1)%MaxSize;
            }
            cnt = (tail2-head2+MaxSize)%MaxSize;
            while(cnt--){
                 t = Q2[head2];
                if(!memcmp(t.a,start.a,sizeof(start.a))) return t.step;
                step2 = t.step + 1;
                for(int i=0;i<4;i++){
                    s = t;
                    s.a[i]++;
                    if(s.a[i]>9) s.a[i]=1;
                    ans = trans(s);
                    if(visit[ans]==1) return step1+step2;
                    if(!visit[ans]){
                        visit[ans] = 2;
                        s.step = step2;
                        Q2[tail2]=s;
                        tail2=(tail2+1)%MaxSize;
                    }
                }
                 for(int i=0;i<4;i++){
                    s = t;
                    s.a[i]--;
                    if(s.a[i]<1) s.a[i]=9;
                    ans = trans(s);
                    if(visit[ans]==1) return step1+step2;
                    if(!visit[ans]){
                        visit[ans] = 2;
                        s.step = step2;
                        Q2[tail2]=s;
                        tail2=(tail2+1)%MaxSize;
                    }
                }
                for(int i=0;i<3;i++){
                    s = t;
                    swap(s.a[i],s.a[i+1]);
                    ans = trans(s);
                    if(visit[ans]==1) return step1+step2;
                    if(!visit[ans]){
                        visit[ans] = 2;
                        s.step = step2;
                        Q2[tail2]=s;
                        tail2=(tail2+1)%MaxSize;
                    }
                }
                head2 = (head2+1)%MaxSize;
            }
    }
}
void Input_and_solve(){
    char ch[5];
    scanf("%s",ch);
    for(int i=0;i<4;i++) start.a[i] = ch[i]-'0';
    scanf("%s",ch);
    for(int i=0;i<4;i++) goal.a[i] = ch[i]-'0';
    printf("%d\n",BFS());
}
int main(){
    int T;
    scanf("%d",&T);
    while(T--){
        Input_and_solve();
    }
}
//如有错误，还请留言指出