【POJ2286】The Rotation Game

Solution

由于搜索量较大，我们采用IDA*算法求解。

按照迭代加深搜索的基本方法，我们限制搜索深度，然后寻找在当前限制下是否存在解。

为了提高算法效率，我们设计A*函数作为估价，返回目标位置与实际不同的个数即可。

在搜索时我们不妨记录上一步搜索的分支，以免执行上一次操作的逆操作。

本题难点主要在于对读入数据的处理和执行旋转操作。

Code

#include <cstdio>
#include <iostream>
inline int read() {
    int ret = 0, op = 1;
    char c = getchar();
    while (!isdigit(c)) {
        if (c == '-') op = -1; 
        c = getchar();
    }
    while (isdigit(c)) {
        ret = ret * 10 + c - '0';
        c = getchar();
    }
    return ret * op;
}
const int center[10] = {6, 7, 8, 11, 12, 15, 16, 17};
const int all[80][70] = {
    {0, 2, 6, 11, 15, 20, 22}, //  A
    {1, 3, 8, 12, 17, 21, 23}, //  B
    {10, 9, 8, 7, 6, 5, 4},   // C
    {19, 18, 17, 16, 15, 14, 13},   //  D
    {23, 21, 17, 12, 8, 3, 1},   //  E 
    {22, 20, 15, 11, 6, 2, 0},   //  F
    {13, 14, 15, 16, 17, 18, 19},   //  G
    {4, 5, 6, 7, 8, 9, 10}   //  H
};
int a[50];
char ans[100];
inline int check() {
    for (register int i = 1; i < 8; ++i) 
        if (a[center[i]] != a[center[0]]) return 0;
    return 1;
}
inline int A_star() {
    int ret = 100;
    for (register int i = 1; i < 4; ++i) {
        int sum = 0;
        for (register int j = 0; j < 8; ++j)
            if (i != a[center[j]]) sum++;
        ret = std :: min(ret, sum);
    }
    return ret;
}
inline void rotate(int op) {
    int fir = a[all[op][0]];
    for (register int i = 0; i < 6; ++i) a[all[op][i]] = a[all[op][i + 1]];
    a[all[op][6]] = fir;
}
int dfs(int now, int maxdep, int last) {
    if (now == maxdep) return check();
    if (now + A_star() > maxdep) return 0;
    for (register int i = 0; i < 8; ++i) {
        if (last == -1);
        else if (last % 2 == 1 && i == (last + 3) % 8) continue ;
        else if (last % 2 == 0 && i == (last + 5) % 8) continue ;
        ans[now] = i + 'A';
        rotate(i);
        if (dfs(now + 1, maxdep, i)) return 1;
        if (i & 1) rotate((i + 3) % 8);
        else rotate((i + 5) % 8);
    }
    return 0;
}
int main() {
    while (1) {
        a[0] = read();
        if (!a[0]) return 0;
        for (register int i = 1; i < 24; ++i) a[i] = read();
        if (check()) {
            puts("No moves needed");
            printf("%d
", a[center[0]]);
            continue ;
        }
        register int i;
        for (i = 0; !dfs(0, i, -1); ++i);
        ans[i] = '';
        printf("%s
", ans);
        printf("%d
", a[center[0]]);
    }
    return 0;
}