8Puzzle问题算法使用A*算法，数据结构主要是优先队列。
评分系统错误修复记录
Board类toString实现丢失部分打印
解决方案，添加即可：
1
2
3
4
5
6
7
8
9
10
11
|
public String toString() {
StringBuilder sb = new StringBuilder();
sb.append(blocks.length).append("\n");
for (int[] block : blocks) {
for (int j = 0; j < blocks.length; j++) {
sb.append(" ").append(block[j]);
}
sb.append("\n");
}
return sb.toString();
}
|
添加对对象的类的判断，添加后即可：
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
|
public boolean equals(Object other) {
if (other == null) {
return false;
}
if (other == this) {
return true;
}
if (other.getClass() != this.getClass()) {
return false;
}
if (other instanceof Board) {
Board that = (Board) other;
if (that.blocks.length != this.blocks.length) {
return false;
}
for (int i = 0; i < this.blocks.length; i++) {
for (int j = 0; j < this.blocks.length; j++) {
if (this.blocks[i][j] != that.blocks[i][j]) {
return false;
}
}
}
}
return true;
}
|
解决方案，swap 调用方错误，修改为 board 引用即可。
1
2
3
4
5
6
7
8
9
10
11
12
|
public Board twin() {
Board board = new Board(blocks);
for (int i = 0; i < blocks.length; i++) {
for (int j = 0; j < blocks.length - 1; j++) {
if (board.blocks[i][j] != 0 && board.blocks[i][j + 1] != 0) {
board.swap(i, j, i, j + 1);
return board;
}
}
}
return board;
}
|
最终，终于评分满分。
完整实现代码
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
|
import edu.princeton.cs.algs4.Stack;
import edu.princeton.cs.algs4.StdOut;
public class Board {
private final int[][] blocks;
// construct a board from an n-by-n array of blocks
// (where blocks[i][j] = block in row i, column j)
public Board(int[][] blocks) {
this.blocks = new int[blocks.length][blocks.length];
for (int i = 0; i < blocks.length; i++) {
for (int j = 0; j < blocks.length; j++) {
this.blocks[i][j] = blocks[i][j];
}
}
}
// board dimension n
public int dimension() {
return blocks.length;
}
// number of blocks out of place
public int hamming() {
int hammingNumber = 0;
for (int i = 0; i < blocks.length; i++) {
for (int j = 0; j < blocks.length; j++) {
if (blocks[i][j] != getGoalVal(i, j) && !isEnd(i, j)) {
hammingNumber++;
}
}
}
return hammingNumber;
}
// sum of Manhattan distances between blocks and goal
public int manhattan() {
int manhattanNumber = 0;
for (int i = 0; i < blocks.length; i++) {
for (int j = 0; j < blocks.length; j++) {
int value = blocks[i][j];
if (value != 0 && value != getGoalVal(i, j)) {
int ii = (value - 1) / blocks.length;
int jj = value - ii * blocks.length - 1;
int distance = Math.abs(i - ii) + Math.abs(j - jj);
manhattanNumber += distance;
}
}
}
return manhattanNumber;
}
// is this board the goal board?
public boolean isGoal() {
if (blocks[blocks.length - 1][blocks.length - 1] != 0) {
return false;
}
for (int i = 0; i < blocks.length; i++) {
for (int j = 0; j < blocks.length; j++) {
if (blocks[i][j] != getGoalVal(i, j)) {
return false;
}
}
}
return true;
}
// a board that is obtained by exchanging any pair of blocks
public Board twin() {
Board board = new Board(blocks);
for (int i = 0; i < blocks.length; i++) {
for (int j = 0; j < blocks.length - 1; j++) {
if (board.blocks[i][j] != 0 && board.blocks[i][j + 1] != 0) {
board.swap(i, j, i, j + 1);
return board;
}
}
}
return board;
}
// does this board equal y?
public boolean equals(Object other) {
if (other == null) {
return false;
}
if (other == this) {
return true;
}
if (other.getClass() != this.getClass()) {
return false;
}
if (other instanceof Board) {
Board that = (Board) other;
if (that.blocks.length != this.blocks.length) {
return false;
}
for (int i = 0; i < this.blocks.length; i++) {
for (int j = 0; j < this.blocks.length; j++) {
if (this.blocks[i][j] != that.blocks[i][j]) {
return false;
}
}
}
}
return true;
}
private int getGoalVal(int i, int j) {
if (isEnd(i, j)) {
return 0;
}
return i * blocks.length + j + 1;
}
private boolean isEnd(int i, int j) {
return i == blocks.length - 1 && j == blocks.length - 1;
}
private boolean swap(int i, int j, int si, int sj) {
if (si < 0 || si >= blocks.length || sj < 0 || sj >= blocks.length) {
return false;
}
int swap = blocks[i][j];
blocks[i][j] = blocks[si][sj];
blocks[si][sj] = swap;
return true;
}
// all neighboring boards
public Iterable<Board> neighbors() {
int i0 = 0, j0 = 0;
boolean isFind = false;
for (int i = 0; i < blocks.length; i++) {
for (int j = 0; j < blocks.length; j++) {
if (blocks[i][j] == 0) {
i0 = i;
j0 = j;
isFind = true;
break;
}
}
if (isFind) {
break;
}
}
Stack<Board> stack = new Stack<>();
Board board = new Board(blocks);
boolean isSwap = board.swap(i0, j0, i0 - 1, j0);
if (isSwap) {
stack.push(board);
}
board = new Board(blocks);
isSwap = board.swap(i0, j0, i0 + 1, j0);
if (isSwap) {
stack.push(board);
}
board = new Board(blocks);
isSwap = board.swap(i0, j0, i0, j0 - 1);
if (isSwap) {
stack.push(board);
}
board = new Board(blocks);
isSwap = board.swap(i0, j0, i0, j0 + 1);
if (isSwap) {
stack.push(board);
}
return stack;
}
// string representation of this board (in the output format specified below)
public String toString() {
StringBuilder sb = new StringBuilder();
sb.append(blocks.length).append("\n");
for (int[] block : blocks) {
for (int j = 0; j < blocks.length; j++) {
sb.append(" ").append(block[j]);
}
sb.append("\n");
}
return sb.toString();
}
// unit tests (not graded)
public static void main(String[] args) {
int[][] is = new int[3][3];
int start = 0;
for (int i = 0; i < is.length; i++) {
for (int j = 0; j < is.length; j++) {
is[i][j] = start++;
}
}
Board board = new Board(is);
StdOut.println(board);
}
}
|
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
|
import edu.princeton.cs.algs4.In;
import edu.princeton.cs.algs4.MinPQ;
import edu.princeton.cs.algs4.Stack;
import edu.princeton.cs.algs4.StdOut;
public class Solver {
private final Stack<Board> boards;
private boolean isSolvable;
// find a solution to the initial board (using the A* algorithm)
public Solver(Board initial) {
if (initial == null) {
throw new IllegalArgumentException("args board is null");
}
boards = new Stack<>();
if (initial.isGoal()) {
isSolvable = true;
boards.push(initial);
return;
}
if (initial.twin().isGoal()) {
isSolvable = false;
return;
}
MinPQ<SearchNode> minPQ = new MinPQ<>();
MinPQ<SearchNode> minPQTwin = new MinPQ<>();
Board board = initial;
Board boardTwin = initial.twin();
SearchNode node = new SearchNode(board, 0, null);
SearchNode nodeTwin = new SearchNode(boardTwin, 0, null);
minPQ.insert(node);
minPQTwin.insert(nodeTwin);
while (true) {
node = minPQ.delMin();
nodeTwin = minPQTwin.delMin();
board = node.board;
boardTwin = nodeTwin.board;
if (board.isGoal()) {
isSolvable = true;
boards.push(board);
while (node.previous != null) {
node = node.previous;
boards.push(node.board);
}
return;
}
if (boardTwin.isGoal()) {
isSolvable = false;
return;
}
node.moves++;
nodeTwin.moves++;
Iterable<Board> neighbors = board.neighbors();
for (Board b : neighbors) {
if (node.previous != null && node.previous.board.equals(b)) {
continue;
}
minPQ.insert(new SearchNode(b, node.moves, node));
}
Iterable<Board> neighborsTwin = boardTwin.neighbors();
for (Board b : neighborsTwin) {
if (nodeTwin.previous != null && nodeTwin.previous.board.equals(b)) {
continue;
}
minPQTwin.insert(new SearchNode(b, nodeTwin.moves, nodeTwin));
}
}
}
// is the initial board solvable?
public boolean isSolvable() {
return isSolvable;
}
// min number of moves to solve initial board; -1 if unsolvable
public int moves() {
if (isSolvable) {
return boards.size() - 1;
}
return -1;
}
// sequence of boards in a shortest solution; null if unsolvable
public Iterable<Board> solution() {
if (isSolvable) {
return boards;
}
return null;
}
private class SearchNode implements Comparable<SearchNode> {
private Board board;
private int moves;
private SearchNode previous;
private int cachedPriority = -1;
public SearchNode(Board board, int moves, SearchNode previous) {
this.board = board;
this.moves = moves;
this.previous = previous;
}
private int priority() {
if (cachedPriority == -1) {
cachedPriority = board.manhattan() + moves;
}
return cachedPriority;
}
@Override
public int compareTo(SearchNode that) {
return Integer.compare(this.priority(), that.priority());
}
}
// solve a slider puzzle (given below)
public static void main(String[] args) {
// create initial board from file
In in = new In(args[0]);
int n = in.readInt();
int[][] blocks = new int[n][n];
for (int i = 0; i < n; i++)
for (int j = 0; j < n; j++)
blocks[i][j] = in.readInt();
Board initial = new Board(blocks);
// solve the puzzle
Solver solver = new Solver(initial);
// print solution to standard output
if (!solver.isSolvable())
StdOut.println("No solution possible");
else {
StdOut.println("Minimum number of moves = " + solver.moves());
for (Board board : solver.solution())
StdOut.println(board);
}
}
}
|
以上，8Puzzle实现完成。