HDU3567
Eight II
Time Limit: 4000/2000 MS (Java/Others) Memory Limit: 130000/65536 K (Java/Others)
Total Submission(s): 3449 Accepted Submission(s): 753
Problem Description
Eight-puzzle, which is also called "Nine grids", comes from an old game.
In this game, you are given a 3 by 3 board and 8 tiles. The tiles are numbered from 1 to 8 and each covers a grid. As you see, there is a blank grid which can be represented as an 'X'. Tiles in grids having a common edge with the blank grid can be moved into that blank grid. This operation leads to an exchange of 'X' with one tile.
We use the symbol 'r' to represent exchanging 'X' with the tile on its right side, and 'l' for the left side, 'u' for the one above it, 'd' for the one below it.
![](http://acm.hdu.edu.cn/data/images/C301-1004-1.jpg)
A state of the board can be represented by a string S using the rule showed below.
![](http://acm.hdu.edu.cn/data/images/C301-1004-2.jpg)
The problem is to operate an operation list of 'r', 'u', 'l', 'd' to turn the state of the board from state A to state B. You are required to find the result which meets the following constrains:
1. It is of minimum length among all possible solutions.
2. It is the lexicographically smallest one of all solutions of minimum length.
In this game, you are given a 3 by 3 board and 8 tiles. The tiles are numbered from 1 to 8 and each covers a grid. As you see, there is a blank grid which can be represented as an 'X'. Tiles in grids having a common edge with the blank grid can be moved into that blank grid. This operation leads to an exchange of 'X' with one tile.
We use the symbol 'r' to represent exchanging 'X' with the tile on its right side, and 'l' for the left side, 'u' for the one above it, 'd' for the one below it.
![](http://acm.hdu.edu.cn/data/images/C301-1004-1.jpg)
A state of the board can be represented by a string S using the rule showed below.
![](http://acm.hdu.edu.cn/data/images/C301-1004-2.jpg)
The problem is to operate an operation list of 'r', 'u', 'l', 'd' to turn the state of the board from state A to state B. You are required to find the result which meets the following constrains:
1. It is of minimum length among all possible solutions.
2. It is the lexicographically smallest one of all solutions of minimum length.
Input
The first line is T (T <= 200), which means the number of test cases of this problem.
The input of each test case consists of two lines with state A occupying the first line and state B on the second line.
It is guaranteed that there is an available solution from state A to B.
The input of each test case consists of two lines with state A occupying the first line and state B on the second line.
It is guaranteed that there is an available solution from state A to B.
Output
For each test case two lines are expected.
The first line is in the format of "Case x: d", in which x is the case number counted from one, d is the minimum length of operation list you need to turn A to B.
S is the operation list meeting the constraints and it should be showed on the second line.
The first line is in the format of "Case x: d", in which x is the case number counted from one, d is the minimum length of operation list you need to turn A to B.
S is the operation list meeting the constraints and it should be showed on the second line.
Sample Input
2
12X453786
12345678X
564178X23
7568X4123
Sample Output
Case 1: 2
dd
Case 2: 8
urrulldr
Author
zhymaoiing
Source
1 //2017-09-23 2 #include <iostream> 3 #include <cstdio> 4 #include <algorithm> 5 #include <cmath> 6 #include <map> 7 8 using namespace std; 9 10 const int INF = 0x3f3f3f3f; 11 int a[10][10], target, postion[10], b[10], d[10000], sx, sy, deep; 12 bool ok; 13 map<int, bool> vis; 14 char dir[4] = {'d', 'l', 'r', 'u'}; 15 int dx[4] = {1, 0, 0, -1};//分别对应上下左右四个方向 16 int dy[4] = {0, -1, 1, 0}; 17 int kase; 18 19 int Astar() 20 { 21 int h = 0; 22 for(int i = 1; i <= 3; i++) 23 for(int j = 1; j <= 3; j++) 24 if(a[i][j]!=0) 25 { 26 int num = a[i][j]; 27 int nx = (postion[num]-1)/3; 28 int ny = (postion[num]-1)%3; 29 h += (abs(i-nx-1)+abs(j-ny-1)); 30 } 31 return h; 32 } 33 34 int toInt()//把矩阵转换为int型数字 35 { 36 int res = 0; 37 for(int i = 1; i <= 3; i++) 38 for(int j = 1; j <= 3; j++) 39 res = res*10+a[i][j]; 40 return res; 41 } 42 43 void IDAstar(int x, int y, int pre, int step) 44 { 45 if(ok)return ; 46 int h = Astar(); 47 if(!h && toInt()==target)//找到答案 48 { 49 printf("Case %d: %d\n", ++kase, step); 50 for(int i = 0; i < step; i++) 51 printf("%c", dir[d[i]]); 52 printf("\n"); 53 ok = 1; 54 return ; 55 } 56 if(step+h>deep)return ;//现实+理想<现状,则返回,IDA*最重要的剪枝 57 int now = toInt(); 58 //if(vis[now])return ;//如果状态已经搜过了,剪枝,避免重复搜索 59 //vis[now] = true; 60 for(int i = 0; i < 4; i++) 61 { 62 if(i+pre == 3)continue; 63 int nx = x+dx[i]; 64 int ny = y+dy[i]; 65 if(nx>=1&&nx<=3&&ny>=1&&ny<=3) 66 { 67 d[step] = i; 68 swap(a[x][y], a[nx][ny]); 69 IDAstar(nx, ny, i, step+1); 70 swap(a[x][y], a[nx][ny]); 71 d[step] = 0; 72 } 73 } 74 return; 75 } 76 77 char str1[20], str2[20]; 78 79 int main() 80 { 81 int T; 82 scanf("%d", &T); 83 char ch; 84 kase = 0; 85 while(T--) 86 { 87 ok = false; 88 deep = 0; 89 int cnt = 0; 90 scanf("%s%s", str1, str2); 91 for(int i = 1; i <= 3; i++) 92 { 93 for(int j = 1; j <= 3; j++) 94 { 95 ch = str1[(i-1)*3+j-1]; 96 if(ch == 'X') 97 { 98 a[i][j] = 0; 99 sx = i; 100 sy = j; 101 }else 102 a[i][j] = ch - '0'; 103 b[cnt++] = a[i][j]; 104 } 105 } 106 target = 0; 107 getchar(); 108 for(int i = 1; i <= 9; i++){ 109 target *= 10; 110 ch = str2[i-1]; 111 if(ch == 'X') 112 target += 0; 113 else{ 114 target += ch-'0'; 115 postion[ch-'0'] = i; 116 } 117 } 118 while(!ok) 119 { 120 vis.clear(); 121 IDAstar(sx, sy, INF, 0); 122 deep++;//一层一层增加搜索的深度 123 } 124 } 125 126 return 0; 127 }