八数码问题使用HashTable优化查找后的版本

 

在《双向广度优先搜索算法框架及八数码问题例程》一文中，给出了使用双向广度优先搜索算法解决八数码问题的一个

简单版本，查找都是线性的，没有优化。这里给出使用HashTable优化后的版本！

/*
 * Author: puresky
 * Date: 2010.01.12
 * Purpose: solve EIGTH NUMBER problem!
 */

#include <stdio.h>
#include <stdlib.h>
#include <string.h>

#define MAXN 10000

#define SWAP(a, b) {char t = a; a = b; b = t;}

typedef struct _Node Node;

struct _Node
{
        char tile[10]; // represent the tile as a string ending with '\0'
        char pos;   // the position of 'x'
        char dir;  //the moving direction of 'x'
        int parent; //index of parent node
};

int head[2], tail[2];
Node queue[2][MAXN];// two queues for double directoin BFS

//shift of moving up, down, left ,right
int shift[4][2] = {{-1, 0}, {1, 0}, {0, -1}, {0, 1}};

//for output direction!
char dir[4][2] = {{'u', 'd'}, {'d', 'u'}, {'l', 'r'}, {'r', 'l'}};

//test case
char start[10] = "23415x768";
char end[10] = "12345678x";

/*=================hash table start=========================================*/

#define HASH_TABLE_MAX_SIZE 10000
typedef struct HashNode_Struct HashNode;

struct HashNode_Struct
{
        char* sKey;
        int nValue;
        HashNode* pNext;
};

HashNode* ht[2][HASH_TABLE_MAX_SIZE];//hash table data strcutrue

//initialize hash table
void hash_table_init(HashNode *hashTable[])
{
        memset(hashTable, 0, sizeof(HashNode*) * HASH_TABLE_MAX_SIZE);
}

//string hash function
unsigned int hash_table_hash_str(const char* skey)
{
        const signed char *p = (const signed char*)skey;
        unsigned int h = *p;
        if(h)
        {
                for(p += 1; *p != '\0'; ++p)
                        h = (h << 5) - h + *p;
        }
        return h;
}

//insert key-value into hash table
void hash_table_insert(HashNode *hashTable[], char* skey, int nvalue)
{

        unsigned int pos = hash_table_hash_str(skey) % HASH_TABLE_MAX_SIZE;

        HashNode* pHead =  hashTable[pos];
        while(pHead)
        {
                if(strcmp(pHead->sKey, skey) == 0)
                {
                        printf("%s already exists!\n", skey);
                        return ;
                }
                pHead = pHead->pNext;
        }

        HashNode* pNewNode = (HashNode*)malloc(sizeof(HashNode));
        memset(pNewNode, 0, sizeof(HashNode));
        pNewNode->sKey = skey;
        pNewNode->nValue = nvalue;

        pNewNode->pNext = hashTable[pos];
        hashTable[pos] = pNewNode;

}

//lookup a key in the hash table
HashNode* hash_table_lookup(HashNode *hashTable[], const char* skey)
{
        unsigned int pos = hash_table_hash_str(skey) % HASH_TABLE_MAX_SIZE;
        if(hashTable[pos])
        {
                HashNode* pHead = hashTable[pos];
                while(pHead)
                {
                        if(strcmp(skey, pHead->sKey) == 0)
                                return pHead;
                        pHead = pHead->pNext;
                }
        }
        return NULL;
}

//free the memory of the hash table
void hash_table_release(HashNode *hashTable[])
{
        int i;
        for(i = 0; i < HASH_TABLE_MAX_SIZE; ++i)
        {
                if(hashTable[i])
                {
                        HashNode* pHead = hashTable[i];
                        while(pHead)
                        {
                                HashNode* pTemp = pHead;
                                pHead = pHead->pNext;
                                if(pTemp)
                                {
                                        free(pTemp);
                                }

                        }
                }
        }
}

/* ===============================hash table end=========================*/

//read a tile 3 by 3
void readtile()
{
        int i;
        char temp[10];
        for(i = 0; i < 9; ++i)
        {
                scanf("%s", temp);
                start[i] = temp[0];
        }
        start[9] = '\0';
}

//print result
void print_backward(int i)
{
        if(queue[0][i].parent != -1)
        {
                print_backward(queue[0][i].parent);
                printf("%c", queue[0][i].dir);
        }
}
void print_forward(int j)
{
        if(queue[1][j].parent != -1)
        {
                printf("%c", queue[1][j].dir);
                print_forward(queue[1][j].parent);
        }
}
void print_result(int i, int j)
{
        //printf("%d,%d\n", i, j);
        print_backward(i);
        print_forward(j);
        printf("\n");
}

//init the queue
void init(int qi, const char* state)
{
        strcpy(queue[qi][0].tile, state);
        queue[qi][0].pos = strchr(state, 'x') - state;
        queue[qi][0].parent = -1;

        head[qi] = tail[qi]  = 0;
}

//check if there are duplicates in the queue
//time comlexity:O(n)
//We can optimise this function using HashTable
int isduplicate(int qi)
{
        if(hash_table_lookup(ht[qi], queue[qi][tail[qi]].tile))
        {
                return 1;
        }
        return 0;
}

//check if the current node is in another queue!
//time comlexity:O(n)
//We can optimise this function using HashTable
int isintersect(int qi)
{
        HashNode* hn = hash_table_lookup(ht[1 - qi], queue[qi][tail[qi]].tile);
        if(hn)
        {
                return hn->nValue;
        }
        return -1;
}

//expand nodes
int expand(int qi)
{
        int i, x, y, r;

        Node* p = &(queue[qi][head[qi]]);
        head[qi]++;

        for(i = 0; i < 4; ++i)
        {
                x = p->pos / 3 + shift[i][0];
                y = p->pos % 3 + shift[i][1];
                if(x >= 0 && x <= 2 && y >= 0 && y <= 2)
                {
                        tail[qi]++;
                        Node* pNew = &(queue[qi][tail[qi]]);
                        strcpy(pNew->tile, p->tile);
                        SWAP(pNew->tile[ 3 * x + y], pNew->tile[p->pos]);
                        pNew->pos = 3 * x + y;
                        pNew->parent = head[qi] - 1;
                        pNew->dir = dir[i][qi];
                        if(isduplicate(qi))
                        {
                                tail[qi]--;
                        }
                        else
                        {
                                if((r = isintersect(qi)) != -1)
                                {
                                        if(qi == 1)
                                        {
                                                print_result(r, tail[qi]);
                                        }
                                        else
                                        {
                                                print_result(tail[qi], r);
                                        }
                                        return 1;
                                }
                                hash_table_insert(ht[qi], pNew->tile, tail[qi]);
                        }
                }
        }
        return 0;
}

//call expand to generate queues
int solve()
{
        init(0, start);
        init(1, end);
       
        while(head[0] <= tail[0] && head[1] <= tail[1])
        {
                //expand the shorter queue firstly
                if(tail[0] - head[0] >= tail[1] - head[1])
                {
                        if(expand(1)) return 1;
                }
                else
                {
                        if(expand(0)) return 1;
                }
        }
       
        while(head[0] <= tail[0]) if(expand(0)) return 1;
        while(head[1] <= tail[1]) if(expand(1)) return 1;
        return 0;
}

int main(int argc, char** argv)
{
        hash_table_init(ht[0]);
        hash_table_init(ht[1]);
        readtile();
        if(!solve())
        {
                printf("unsolvable\n");
        }
        hash_table_release(ht[0]);
        hash_table_release(ht[1]);
        //system("pause"); //pause
        return 0;
}

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