状态记录

人工智能 - 马少平 - 朱小燕 - 编著 - 清华大学出版社

P55  第一章  习题1.2

积木原始状态 BBBWWWE  其中 E 表示空格，W表示白块，B表示黑块。

题目要求将所有白块都处于黑块的左侧，空格块可任意位置。

建模：将B看成1，将W看成0，而E看成-1,检测是否满足条件时，将-1除开，要求序列非递减。

对于滑动积木的状态记录问题思考：

记录方法：

1. 七维数组记录,   record[3][3][3][3][3][3][3];  空间3^7 = 2187   有再多黑白块或空格，这种方法不适用。

注：此时将B看成2，W可看成1，E看成0，为了能直接在数组中引用。

2. map键值映射，map<string,bool>。

3. vector、set导入，vecotr<string>, set<string>,检查子集判断是否存在过状态。

4. 将B,W映射成不同的数值，如BBBWWW -> 654321,将各个值计算后，进行比较得出是否存在。空间  7! = 5040。

获得解值(极粗糙版)：

#include"SlideBlockGame.h"
#include<iostream>
#include<cstdio>
using namespace std;

//To record the arising block' status.
int record_status[3][3][3][3][3][3][3];

//To record success
int flag;

//Copy the block
void copy(int temp_block[], int b[])
{
	for (int i = 0;i < 7;++i)
		temp_block[i] = b[i];
}

//Display the block'status.
void showVarystatus(int block[])
{
	for (int i = 0;i < 7;++i)
		cout << block[i] << ' ';
	cout << endl;
}

//Judge the block'status whether satisfying the goal or not.
bool isGoalstatus(int block[])
{
	int numi = 0,numj;
	for (int i = 0;i < 4;++i)
	{
		numj = 0;             
		if (block[i] == 1)
		{
			numi++;
			for (int j = i + 1;j < 7;++j)
				if (block[j] == 2)
					numj++;
			if (numj < 3)
				return false;
		}	
	}
	if (numi == 3)
	{
		flag = 1;
		cout << "satisfy.....";
		showVarystatus(block);
		return true;
	}
	return false;
}

void modifystatus(int b[],int able_shift)
{
	if (flag)
		return;
	/* 
	isGoalstatus had return a result: false
	if (isGoalstatus(b) || flag)        
		return true;
	*/
	isGoalstatus(b);

	if (flag) //success
		return;
	
	if (record_status[b[0]][b[1]][b[2]][b[3]][b[4]][b[5]][b[6]]) //this status had arisen
		return;

	showVarystatus(b);

	int index[6] = { -3,-2,-1,+1,+2,+3 };   //modify factors

	record_status[b[0]][b[1]][b[2]][b[3]][b[4]][b[5]][b[6]] = 1;  //make a record

	for (int i = 0;i < 6;++i)
	{
		int temp = able_shift + index[i];
		if (temp <= 6 && temp >= 0)
		{
			//has to create a new array
			int temp_block[7];
			copy(temp_block, b);
			//exchange the locations.
			int s = temp_block[temp];
			temp_block[temp] = 0;
			temp_block[able_shift] = s;

			modifystatus(temp_block, temp);
		}
	}
}

int main()
{
	int block[7] = { 2,2,2,1,1,1,0 };  //Initial status.
									  
	memset(record_status,0,sizeof(record_status));
	flag = 0;

	modifystatus(block, 6);   //Modify the block'status to satisfy the goal.

	if(flag)
		cout << "satisfy the rule" << endl;
	system("pause");
}

其中isGoalStatue()，错误想法

1.前四个位置有出现过3个1即可，错误：1121022

2.数列非递减,错误：1220112,1122201,由于空格（0）存在，特判后失败。

最后实现isGoalStatue：

检查到每一个白格，检查其后是否存在3个黑格。

深搜路径版

#include"SlideBlockGame.h"
#include<iostream>
#include<cstdio>
using namespace std;

//To record the arising block' Status.
int record_status[3][3][3][3][3][3][3];

//To record success
int flag;

//Copy the block
void copy(int temp_block[], int b[])
{
	for (int i = 0;i < 7;++i)
		temp_block[i] = b[i];
}

//Display the block'Status.
void showVaryStatus(blockstatus* block)
{
	/*
	for (int i = 0;i < 7;++i)
	cout << block->blocks[i] << ' ';
	cout << endl;
	*/

	blockstatus* pre1, *pre2;
	pre1 = block->link_pre_node;
	pre2 = pre1->link_pre_node;
	block->link_pre_node = NULL;

	while (pre2)
	{
		pre1->link_pre_node = block;
		block = pre1;
		pre1 = pre2;
		pre2 = pre2->link_pre_node;
	}
	pre1->link_pre_node = block;
//	pre2->link_pre_node = pre1;

	while (pre1)
	{
		for (int i = 0;i < 7;++i)
			cout << pre1->blocks[i] << ' ';
		cout << endl;
		pre1 = pre1->link_pre_node;
	}
}

//Judge the block'Status whether satisfying the goal or not.
bool isGoalStatus(blockstatus* block)
{
	int b[7];
	copy(b, block->blocks);
	int num;
	for (int i = 0;i < 7;++i)
	{
		num = 0;             
		if (b[i] == 1)
		{
			for (int j = i + 1;j < 7;++j)
				if (b[j] == 2)
					num++;
			if (num < 3)
				return false;
		}	
	}

	flag = 1;
	cout << "satisfy....."<<endl;
	showVaryStatus(block);
	return true;
}

void modifyStatus(blockstatus* fatherblock,int able_shift)
{
	if (flag)
		return;
	/* 
	isGoalStatus had return a result: false
	if (isGoalStatus(b) || flag)        
		return true;
	*/
	isGoalStatus(fatherblock);

	if (flag) //success
		return;

	int b[7];
	copy(b, fatherblock->blocks);
	
	if (record_status[b[0]][b[1]][b[2]][b[3]][b[4]][b[5]][b[6]]) //this Status had arisen
		return;

	int index[6] = { -3,-2,-1,+1,+2,+3 };   //modify factors

	record_status[b[0]][b[1]][b[2]][b[3]][b[4]][b[5]][b[6]] = 1;  //make a record

	for (int i = 0;i < 6;++i)
	{
		int new_shift = able_shift + index[i];
		if (new_shift <= 6 && new_shift >= 0)
		{
			//has to create a new blockstatus
			blockstatus* newblock;
			newblock = new blockstatus;
			copy(newblock->blocks, b);

			//exchange the locations.
			int s = newblock->blocks[new_shift];
			newblock->blocks[new_shift] = 0;
			newblock->blocks[able_shift] = s;

			newblock->link_pre_node = fatherblock;

			modifyStatus(newblock, new_shift);
		}
	}
}

void initBlockStatus(blockstatus* block)
{
	for (int i = 0;i < 3;++i)
		block->blocks[i] = 2;
	for (int i = 3;i < 6;++i)
		block->blocks[i] = 1;
	block->blocks[6] = 0;

	block->link_pre_node = NULL;
}

int main()
{
	blockstatus* block;

	block = new blockstatus; //Initial Status.
									  
	initBlockStatus(block);

	/*
	for (int i = 0;i < 7;++i)
	cout << block->blocks[i] << ' ';
	cout << endl;
	*/
	
	memset(record_status,0,sizeof(record_status));
	flag = 0;

	modifyStatus(block, 6);   //Modify the block'Status to satisfy the goal.

	if(flag)
		cout << "satisfy the rule" << endl;
	system("pause");
}