简单八数码问题深搜实现

                            2 8 3         1 2 3

  编写程序输出由  1 0 4 变为  8 0 4 的最短路径

                            7 6 5         7 6 5

一.简单深搜寻找最短步骤：

/* 一般用广搜寻着最短路径，因为他是按照层次来的（设置一个visit记录访问过的点），
只要找到最先到达目标的就行。
如果用深搜着最短路径，你就需要找一个最深搜到哪里，或者题目自带到哪里不可以再
搜的条件否则你就需要设置一个每条路径的最大深度，同时最后要寻找这些你找到的长
度里面那个最小，最小的为输出长度。*/
#include <iostream>
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <algorithm>
using namespace std;
int s[10][10];
int MIN = 1000;

bool Check()
{
int k = 1;
for(int i = 0; i<3; i++)
{
if(s[0][i] != k++)
{
return 0;
}
}
k = 3;
for(int i = 0; i<3; i++)
{
if(s[i][2] != k++)
{
return 0;
}
}
k = 7;
for(int i = 0; i<3; i++)
{
if(s[2][i] != k--)
{
return 0;
}
}
if(s[1][0] != 8)
return 0;
return 1;
}

void Change(int x, int y, int z)//z 1234 is left up right down
{
if(z == 1)//和左交换
{
int i  = s[x][y-1];
s[x][y-1] = s[x][y];
s[x][y] = i;
}
else if(z == 2)//和上交换
{
int i = s[x-1][y];
s[x-1][y] = s[x][y];
s[x][y] = i;
}
else if(z == 3)//和右交换
{
int i = s[x][y+1];
s[x][y+1] = s[x][y];
s[x][y] = i;
}
else if(z == 4)//和下交换
{
int i = s[x+1][y];
s[x+1][y] = s[x][y];
s[x][y] = i;
}
}

void DFS(int x, int y, int step)//寻找最短路径要用广搜， 这是给定寻找方向来搜可以用深搜
{
if(Check())//finished
{
if(step<MIN)
MIN = step;
return;
}
if(step>10)
return ;
else
{
if(y-1>-1)//左
{
Change(x, y, 1);
DFS(x, y-1, step+1);
Change(x, y, 1);//回溯 思想 没有找到就退回来
}
if(x-1>-1)//上
{
Change(x, y, 2);
DFS(x-1, y, step+1);
Change(x, y, 2);//回溯
}
if(y+1<3)//右
{
Change(x, y, 3);
DFS(x, y+1, step+1);
Change(x, y, 3);//回溯
}
if(x+1<3)//下
{
Change(x, y, 4);
DFS(x+1, y, step+1);
Change(x, y, 4);//回溯
}
}
}

int main()
{
int x, y;
for(int i = 0; i<3; i++)
{
for(int j = 0; j<3; j++)
{
scanf("%d", &s[i][j]);
if(s[i][j] == 0)
{
x = i;
y = j;
}
}
}
DFS(x, y, 0);
printf("%d\n", MIN);
return 0;
}

二.用栈实现输出路径

#include <iostream>
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <algorithm>
using namespace std;
int s[10][10];
int MIN = 1000;

typedef struct Outstack//用链表实现栈
{
int x, y;
struct Outstack *next;
}OStack, *OSt;

typedef struct stack//操作栈
{
int x, y;
struct stack *next;
}Stack, *St;

OSt baseout;//输出栈
OSt topout;
St base;//操作栈
St top;

bool Check()
{
int k = 1;
for(int i = 0; i<3; i++)
{
if(s[0][i] != k++)
{
return 0;
}
}
k = 3;
for(int i = 0; i<3; i++)
{
if(s[i][2] != k++)
{
return 0;
}
}
k = 7;
for(int i = 0; i<3; i++)
{
if(s[2][i] != k--)
{
return 0;
}
}
if(s[1][0] != 8)
return 0;
return 1;
}

void Change(int x, int y, int z)//z 1234 is left up right down
{
if(z == 1)//和左交换
{
int i = s[x][y-1];
s[x][y-1] = s[x][y];
s[x][y] = i;
}
else if(z == 2)//和上交换
{
int i = s[x-1][y];
s[x-1][y] = s[x][y];
s[x][y] = i;
}
else if(z == 3)//和右交换
{
int i = s[x][y+1];
s[x][y+1] = s[x][y];
s[x][y] = i;
}
else if(z == 4)//和下交换
{
int i = s[x+1][y];
s[x+1][y] = s[x][y];
s[x][y] = i;
}
}

OSt opush(int x, int y, OSt topout)
{
OSt p;
p = (OSt)malloc(sizeof(OStack));
topout->x = x;
topout->y = y;
p->next = topout;
return p;
}

St push(int x, int y, St top)
{
St p;
p = (St)malloc(sizeof(Stack));
top->x = x;
top->y = y;
p->next = top;
return p;
}

void DFS(int x, int y, int step)
{
if(step == 0)//等于零建立操作栈
{
base = (St)malloc(sizeof(Stack));
base->next = NULL;
top = base;
}
if(Check())
{
if(step<MIN)
{
MIN = step;
topout = baseout;
St p = (St)malloc(sizeof(Stack));
p = top->next;
while(p != NULL)
{
topout = opush(p->x, p->y, topout);
p = p->next;
}
return;
}
}
if(step>10)
return;
else
{
if(y-1>-1)
{
Change(x, y, 1);
top = push(x, y-1, top);//压栈
DFS(x, y-1, step+1);
top = top->next;//回溯出栈
Change(x, y, 1);
}
if(x-1>-1)
{
Change(x, y, 2);
top = push(x-1, y, top);
DFS(x-1, y, step+1);
top = top->next;
Change(x, y, 2);
}
if(y+1<3)
{
Change(x, y
9f6d
, 3);
top = push(x, y+1, top);
DFS(x, y+1, step+1);
top = top->next;
Change(x, y, 3);
}
if(x+1<3)
{
Change(x, y, 4);
top = push(x+1, y, top);
DFS(x+1, y, step+1);
top = top->next;
Change(x, y, 4);
}
}
}

int main()
{
int x, y;
for(int i = 0; i<3; i++)
{
for(int j = 0; j<3; j++)
{
scanf("%d", &s[i][j]);
if(s[i][j] == 0)
{
x = i;
y = j;
}
}
}
baseout = (OSt)malloc(sizeof(OStack));
baseout->next = NULL;
topout = baseout;
DFS(x, y, 0);
printf("%d\n", MIN);
topout = topout->next;
while(topout!=NULL)
{
printf("%d, %d\n", topout->x, topout->y);
topout = topout->next;
}
return 0;
}