[HDOJ1043]Eight（康托展开 BFS 打表）

题目链接：http://acm.hdu.edu.cn/showproblem.php?pid=1043

　　八数码问题，因为固定了位置所以以目标位置开始搜索，把所有情况（相当于一个排列）都记录下来，用康托展开来完成序列的记录问题开始BFS。打好表后按给出序列的康托数确定开始位置，逆向查找。

#include <algorithm>
#include <iostream>
#include <iomanip>
#include <cstring>
#include <climits>
#include <complex>
#include <fstream>
#include <cassert>
#include <cstdio>
#include <bitset>
#include <vector>
#include <deque>
#include <queue>
#include <stack>
#include <ctime>
#include <set>
#include <map>
#include <cmath>

using namespace std;

typedef struct Node1 {
    char s;
    int pre;
    Node1() { pre = -1; }
}Node1;
typedef struct Node2 {
    int status[11];
    int n, son;
}Node2;

Node1 path[666666];
int dx[4] = {1, -1, 0, 0};
int dy[4] = {0, 0, 1, -1};
int fac[11];

void init() {
    fac[0] = fac[1] = 1;
    for(int i = 2; i <= 10; i++) {
        fac[i] = fac[i-1] * i;
    }
}

int ecantor(int* s, int n = 9) {
    int num = 0;
    for(int i = 0; i < n; i++) {
        int tmp = 0;
        for(int j = i + 1; j < n; j++) {
            if(s[j] < s[i]) {
                tmp++;
            }
        }
        num += fac[n-1-i] * tmp;
    }
    return num;
}

void bfs() {
    queue<Node2> q;
    Node2 a, b;
    int t = 0;
    for(int i = 0; i < 9; i++) {
        a.status[i] = i + 1;
    }
    a.n = 8; a.son = 0;
    path[a.son].pre = 0;
    q.push(a);
    while(!q.empty()) {
        a = q.front(); q.pop();
        for(int i = 0; i < 4; i++) {
            b = a;
            int xx = a.n % 3 + dx[i];
            int yy = a.n / 3 + dy[i];
            if(!(xx >= 0 && xx < 3 && yy >= 0 && yy < 3)) continue;
            b.n = yy * 3 + xx;
            swap(b.status[b.n], b.status[a.n]);
            b.son = ecantor(b.status);
            if(path[b.son].pre == -1) {
                path[b.son].pre = a.son;
                if(i == 0) path[b.son].s = 'l';
                if(i == 1) path[b.son].s = 'r';
                if(i == 2) path[b.son].s = 'u';
                if(i == 3) path[b.son].s = 'd';
                q.push(b);
            }
        }
    }
}

int main() {
    // freopen("in", "r", stdin);
    init();
    int s, ss[11];
    char ch[55];
    bfs();
    while(gets(ch)) {
        int cnt = 0;
        for(int i = 0; ch[i]; i++) {
            if(ch[i] == 'x') {
                ss[cnt++] = 9;
            }
            else if(ch[i] >= '0' && ch[i] <= '9') {
                ss[cnt++] = ch[i] - '0';
            }
        }
        s = ecantor(ss);
        if(path[s].pre == -1) {
            printf("unsolvable
");
            continue;
        }
        while(s != 0) {
            printf("%c", path[s].s);
            s = path[s].pre;
        }
        printf("
");
    }
    return 0;
}