POJ1077&HDU1043 Eight 八数码第七境界 AStar hash 康托展开 最小堆优化 奇偶剪枝

Description
The 15-puzzle has been around for over 100 years; even if you don't know it by that name, you've seen it. It is constructed with 15 sliding tiles, each with a number from 1 to 15 on it, and all packed into a 4 by 4 frame with one tile missing. Let's call the missing tile 'x'; the object of the puzzle is to arrange the tiles so that they are ordered as: 
 1  2  3  4 

 5  6  7  8 

 9 10 11 12 

13 14 15  x 

where the only legal operation is to exchange 'x' with one of the tiles with which it shares an edge. As an example, the following sequence of moves solves a slightly scrambled puzzle: 
 1  2  3  4    1  2  3  4    1  2  3  4    1  2  3  4 

 5  6  7  8    5  6  7  8    5  6  7  8    5  6  7  8 

 9  x 10 12    9 10  x 12    9 10 11 12    9 10 11 12 

13 14 11 15   13 14 11 15   13 14  x 15   13 14 15  x 

           r->           d->           r-> 

The letters in the previous row indicate which neighbor of the 'x' tile is swapped with the 'x' tile at each step; legal values are 'r','l','u' and 'd', for right, left, up, and down, respectively. 

Not all puzzles can be solved; in 1870, a man named Sam Loyd was famous for distributing an unsolvable version of the puzzle, and 
frustrating many people. In fact, all you have to do to make a regular puzzle into an unsolvable one is to swap two tiles (not counting the missing 'x' tile, of course). 

In this problem, you will write a program for solving the less well-known 8-puzzle, composed of tiles on a three by three 
arrangement. 

Input

You will receive a description of a configuration of the 8 puzzle. The description is just a list of the tiles in their initial positions, with the rows listed from top to bottom, and the tiles listed from left to right within a row, where the tiles are represented by numbers 1 to 8, plus 'x'. For example, this puzzle 
 1  2  3 

 x  4  6 

 7  5  8 

is described by this list: 
 1 2 3 x 4 6 7 5 8 

Output

You will print to standard output either the word ``unsolvable'', if the puzzle has no solution, or a string consisting entirely of the letters 'r', 'l', 'u' and 'd' that describes a series of moves that produce a solution. The string should include no spaces and start at the beginning of the line.

Sample Input

 2  3  4  1  5  x  7  6  8 

Sample Output

ullddrurdllurdruldr

HDU 跑了1600ms+,应该以STL性能不足

#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
using namespace std;
const int MAXN = 2 * 3 * 4 * 5 * 6 * 7 * 8 * 9 + 10;

struct Node {
    int hash, index;
    int g, h;

    Node(int hash = 0, int index = 0, int g = 0, int h = 0) {
        this->hash = hash, this->index = index;
        this->g = g, this->h = h;
    }

    bool operator<(const Node& n) const {
        return g + h > n.g + n.h;
    }
};

struct Path {
    char dir;
    int pre;
    Path(char dir = 0, int pre = 0) {
        this->dir = dir;
        this->pre = pre;
    }
} path[MAXN];

int jie[10] = {1, 1};
int dirx[] = {-1, 1, 0, 0};
int diry[] = {0, 0, -1, 1};
char dir[] = "udlr";
bool vis[MAXN];

string Tidy(char* s) {
    int len = strlen(s);
    string ans = "";
    for (int i = 0; i < len; ++i) {
        if (s[i] == 'x') s[i] = '9';
        if (s[i] != ' ') ans += s[i];
    }
    return ans;
}

int IndexOfX(string s) {
    for (int i = 0; i < s.size(); ++i) {
        if (s[i] == '9') return i;
    }
    return -1;
}

bool InRange(int x, int y) {
    return x >= 0 && x < 3 && y >= 0 && y < 3;
}

int Hash(string s) {
    int ans = 0;
    for (int i = 0; i < 9; ++i) {
        int  rev = 0;
        for (int j = i + 1; j < 9; ++j) {
            if (s[i] > s[j]) ++rev;
        }
        ans += rev * jie[8 - i];
    }
    return ans;
}

string RevHash(int val) {
    string ans = "";
    bool tag[10] = {};
    for (int i = 0; i < 9; ++i) {
        int tNum = val / jie[8 - i] + 1;
        for (int j = 1; j <= tNum; ++j) {
            if (tag[j]) ++tNum;
        }
        val %= jie[8 - i];
        ans += tNum + '0';
        tag[tNum] = true;
    }
    return ans;
}

int H(string s) {
    int h = 0;
    int index = 0;
    for (int i = 0; i < 3; ++i) {
        for (int j = 0; j < 3; ++j) {
            int num = s[index++] - '1';
            if (num == 8) continue;
            int dx = abs(num / 3 - i);
            int dy = abs(num % 3 - j);
            h += dx + dy;
        }
    }
    return h;
}

void PutPath(int i) {
    if (path[i].pre == -1) return;
    PutPath(path[i].pre);
    putchar(path[i].dir);
}

bool AStar(string st) {
    memset(vis, 0, sizeof(vis));
    priority_queue que;
    int stHash = Hash(st);
    que.push(Node(stHash, IndexOfX(st)));
    path[stHash] = Path(0, -1);
    vis[stHash] = true;

    while (!que.empty()) {
        Node h = que.top();
        que.pop();

        int x = h.index / 3;
        int y = h.index % 3;

        for (int i = 0; i < 4; ++i) {
            int nx = x + dirx[i];
            int ny = y + diry[i];
            int nindex = nx * 3 + ny;

            if (InRange(nx, ny)) {
                string ns = RevHash(h.hash);
                swap(ns[nindex], ns[h.index]);
                int nhash = Hash(ns);

                if (!vis[nhash]) {
                    vis[nhash] = true;
                    path[nhash] = Path(dir[i], h.hash);
                    que.push(Node(nhash, nindex, h.g + 1, H(ns)));

                    if (nhash == 0) {
                        PutPath(nhash);
                        putchar('\n');
                        return true;
                    }
                }
            }
        }
    }
    return false;
}

int main() {
#ifdef NIGHT_13
    freopen("in.txt", "r", stdin);
#endif
    for (int i = 1; i < 10; ++i) {
        jie[i] = jie[i - 1] * i;
    }

    char s[100];
    while (gets_s(s) != NULL) {
        string ma = Tidy(s);

        int rev = 0;
        for (int i = 0; i < 9; ++i) {
            if (ma[i] == '9') continue;
            for (int j = i + 1; j < 9; ++j) {
                if (ma[i] > ma[j]) ++rev;
            }
        }

        if (rev & 1) puts("unsolvable");
        else if (ma == "123456789") puts("lr"); 
        else AStar(ma);
    }
    return 0;
}



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