完整源码 - Eclipse项目文件 - GitHub地址
题目描述
关于本算法
两个晚上写完的，不足之处多多指教…
启发函数的选择：
一开始选用不在位数码个数+节点深度作为启发函数，效果不是很好。
后来改用所有数码到目标位置的矩形距离+节点深度作为启发函数，计算出：
- 从初始到达目标状态深度为14（步），见附录
- 一共进行了68次拓展
- 最后一次拓展时Open表Board个数为70
/**
* 设计一个启发函数,利用A*算法求解15数码问题
*
* 要求: 尽可能用与A*算法一致的思路实现算法, 力求简单明了地给出一个解.
* 1)打印并上交带有关键步骤说明的程序代码.
* 2)演示运行过程,并回答老师的询问
*
* @author luyang.gong
*
* f(n)=g(n)+h(n)
* g(n):已经走过
* h(n):对未来的估计
*
*
Begin：
读入初始状态和目标状态，并计算初始状态评价函数值f；
初始化两个open表和closed表，将初始状态放入open表中
If（open表为空）
查找失败；
End if
else
① 在open表中找到评价值最小的节点，作为当前结点，并放入closed表中；
② 判断当前结点状态和目标状态是否一致，若一致，跳出循环；否则跳转到③；
③ 对当前结点，分别按照上、下、左、右方向移动空格位置来扩展新的状态结点，并计算新扩展结点的评价值f并记录其父节点；
④ 对于新扩展的状态结点，进行如下操作：
A．新节点既不在open表中，也不在closed表中，则ADD (mj, OPEN)；
B．新节点在open表中，则 IF f(n-mk) < f(mk)
THEN f(mk):=f(n-mk)，
C．新节点在closed表中，则IF f(n-ml) < f(ml)
THEN f(ml):=f(n-ml)，
⑤ 把当前结点从open表中移除；
End if
End
*
*/
题解 - 目录结构
题解 - 代码实现 Java
Main.java
public class Main {
public static Board beginBoard = new Board(Init.BEGINARR);
public static Board endBoard = new Board(Init.ENDARR);
public static void main(String[] args) {
OpenTable openTable = new OpenTable();
openTable.tbArr.add(beginBoard);// 这里需要拷贝逻辑 否则复制的只是指针
CloseTable closeTable = new CloseTable();
System.out.println(openTable);
Board curBoard = null;
int count = 0;
while (openTable.tbArr.size() != 0) {
System.out.println("第" + ++count + "次拓展");
openTable.sortItSelf();
curBoard = openTable.getMinBoard();
closeTable.tbArr.add(curBoard);
// 是否为end
if (curBoard.equals(endBoard)) {
System.out.println("SUCCESS:" + curBoard);
while (curBoard.parentBoard != null) {
System.out.println("上一步：");
System.out.println(curBoard.parentBoard);
curBoard = curBoard.parentBoard;
}
break;
}
// 4方向拓展
for (int s = 0; s < 4; s++) {
Board newBoard = null;
if (s == 0) {
if (curBoard.canDown()) {
newBoard = curBoard.goDown();
} else {
continue;
}
} else if (s == 1) {
if (curBoard.canUp()) {
newBoard = curBoard.goUp();
} else {
continue;
}
} else if (s == 2) {
if (curBoard.canRight()) {
newBoard = curBoard.goRight();
} else {
continue;
}
} else if (s == 3) {
if (curBoard.canLeft()) {
newBoard = curBoard.goLeft();
} else {
continue;
}
}
if (openTable.hasBoard(newBoard)) {// 新节点在open表中 比较已有fn和新节点fn的大小
Board oldBoard = openTable.getBoardByArr(newBoard.arr);
if (newBoard.fn < oldBoard.fn) {// 新的比旧的fn小
// 更新指针
newBoard.childBoards = oldBoard.childBoards;
for (int i = 0; i < newBoard.childBoards.size(); i++) {
newBoard.childBoards.get(i).parentBoard = newBoard;
}
// 删旧的 增新的
openTable.tbArr.remove(openTable.getIndex(oldBoard));
openTable.tbArr.add(newBoard);
System.out.println("openTable:update");
}
} else if (closeTable.hasBoard(newBoard)) {// 新节点在close表中
Board oldBoard = closeTable.getBoardByArr(newBoard.arr);
if (newBoard.fn < oldBoard.fn) {
newBoard.childBoards = oldBoard.childBoards;
for (int i = 0; i < newBoard.childBoards.size(); i++) {
newBoard.childBoards.get(i).parentBoard = newBoard;
}
closeTable.tbArr.remove(closeTable.getIndex(oldBoard));
// closeTable.tbArr.add(newBoard);
openTable.tbArr.add(newBoard);// 重新放回open表中
System.out.println("openTable:update");
}
} else {// 两表都不在
openTable.tbArr.add(newBoard);
System.out.println("openTable:add");
}
}
openTable.tbArr.remove(openTable.getIndex(curBoard));
}
}
}Init.java
package cn.hanquan.ai;
public class Init {
/**
* 数组大小
*/
public static final int SIZE = 4;
/**
* 初始状态
*/
public static final int[][] BEGINARR = { { 5, 1, 2, 4 }, { 9, 6, 3, 8 }, { 13, 15, 10, 11 }, { 14, 0, 7, 12 } };
/**
* 目标状态
*/
public static final int[][] ENDARR = { { 1, 2, 3, 4 }, { 5, 6, 7, 8 }, { 9, 10, 11, 12 }, { 13, 14, 15, 0 } };
}Utils.java
package cn.hanquan.ai;
public class Utils {
/**
* 计算不在位的将牌个数
* @param tbArr 15数码的一个状态
* @return 不在位的将牌个数
*/
public static int getAbsentCount(Board curBoard, Board endBoard) {
// System.out.println(curBoard);
// System.out.println(endBoard);
int count = 0;
for (int i = 0; i < Init.SIZE; i++) {
for (int j = 0; j < Init.SIZE; j++) {
label: for (int m = 0; m < Init.SIZE; m++) {
for (int n = 0; n < Init.SIZE; n++) {
if (curBoard.arr[i][j] == endBoard.arr[m][n]) {
count += getDistance(i, j, m, n);
break label;
}
}
}
}
}
return count;
}
/**
* 计算两坐标的矩形距离
* @param x1
* @param y1
* @param x2
* @param y2
* @return
*/
public static int getDistance(int x1,int y1,int x2,int y2) {
return Math.abs(x1-x2)+Math.abs(y1-y2);
}
/**
* 计算不在位的将牌个数 重载
* @param arr 15数码的一个状态
* @return 不在位的将牌个数
*/
public static int getAbsentCount(Board curBoard, int[][] arr) {
// System.out.println(curBoard);
// System.out.println(endBoard);
int count = 0;
for (int i = 0; i < Init.SIZE; i++) {
for (int j = 0; j < Init.SIZE; j++) {
if (curBoard.arr[i][j] != 0 && curBoard.arr[i][j] != arr[i][j]) {
count++;
}
}
}
return count;
}
}Board.java
package cn.hanquan.ai;
import java.util.ArrayList;
import java.util.Arrays;
public class Board {
/**
* 将牌状态
*/
public int[][] arr;
/**
* 总耗散值
*/
public int fn=-1;
/**
* 当前已走深度(耗散值)
*/
public int dn=0;
/**
* 不在位将牌个数(耗散值)
*/
public int hn=-1;
/**
* 父节点
*/
public Board parentBoard;
/**
* 子节点列表
*/
public ArrayList<Board> childBoards=new ArrayList<Board>();
public Board(int[][] arr) {
super();
this.arr = arr;
this.dn = 0;
this.hn = Utils.getAbsentCount(this, Init.ENDARR);
this.fn = this.dn + this.hn;
}
public Board() {
super();
}
@Override
public String toString() {
StringBuilder sb = new StringBuilder();
sb.append("\n");
for (int i = 0; i < Init.SIZE; i++) {
for (int j = 0; j < Init.SIZE; j++) {
sb.append(arr[i][j] + "\t");
}
sb.append("\n");
}
sb.append("fn gn hn = " + fn + " " + dn + " " + hn+"\n");
return sb.toString();
}
/**
* 复制本身arr数值
* @return
*/
public int[][] copySelfArr() {
int[][] newArr = { { 0, 0, 0, 0 }, { 0, 0, 0, 0 }, { 0, 0, 0, 0 }, { 0, 0, 0, 0 } };
for (int i = 0; i < Init.SIZE; i++) {
for (int j = 0; j < Init.SIZE; j++) {
newArr[i][j] = arr[i][j];
}
}
return newArr;
}
/**
* 判断两个board是否arr值相等
* @param board
* @return
*/
public boolean equals(Board board) {
boolean isEqual = true;
for (int i = 0; i < Init.SIZE && isEqual == true; i++) {
for (int j = 0; j < Init.SIZE; j++) {
if (arr[i][j] != board.arr[i][j]) {
isEqual = false;
break;
}
}
}
return isEqual;
}
/**
* 重载，判断board和arr是否值相等
* @param board
* @return
*/
public boolean equals(int[][] array) {
boolean isEqual = true;
for (int i = 0; i < Init.SIZE && isEqual == true; i++) {
for (int j = 0; j < Init.SIZE; j++) {
if (arr[i][j] != array[i][j]) {
isEqual = false;
break;
}
}
}
return isEqual;
}
/**
* 是否可以向下移动
* @return
*/
public boolean canDown() {
boolean isOK = true;
label: for (int i = 0; i < Init.SIZE; i++) {
for (int j = 0; j < Init.SIZE; j++) {
if (arr[i][j] == 0 && i == Init.SIZE-1) {
isOK = false;
break label;
}
}
}
System.out.println("canDown:"+isOK);
return isOK;
}
/**
* 是否可以向右移动
* @return
*/
public boolean canRight() {
boolean isOK = true;
label: for (int i = 0; i < Init.SIZE; i++) {
for (int j = 0; j < Init.SIZE; j++) {
if (arr[i][j] == 0 && j == Init.SIZE-1) {
isOK = false;
break label;
}
}
}
System.out.println("canRight:"+isOK);
return isOK;
}
/**
* 是否可以向左移动
* @return
*/
public boolean canLeft() {
boolean isOK = true;
label: for (int i = 0; i < Init.SIZE; i++) {
for (int j = 0; j < Init.SIZE; j++) {
if (arr[i][j] == 0 && j == 0) {
isOK = false;
break label;
}
}
}
System.out.println("canLeft:"+isOK);
return isOK;
}
/**
* 是否可以向上移动
* @return
*/
public boolean canUp() {
boolean isOK = true;
label: for (int i = 0; i < Init.SIZE; i++) {
for (int j = 0; j < Init.SIZE; j++) {
if (arr[i][j] == 0 && i == 0) {
isOK = false;
break label;
}
}
}
System.out.println("canUp:" + isOK);
return isOK;
}
/**
* 向下移动
* @return
*/
public Board goDown() {
System.out.println("Go Down");
Board newBoard = new Board(this.copySelfArr());
label: for (int i = 0; i < Init.SIZE; i++) {
for (int j = 0; j < Init.SIZE; j++) {
if (newBoard.arr[i][j] == 0) {
int t;
t = newBoard.arr[i][j];
newBoard.arr[i][j] = newBoard.arr[i + 1][j];
newBoard.arr[i + 1][j] = t;
break label;// 这里label退出循环！！避免重复操作！！
}
}
}
newBoard.dn = this.dn + 1;// 深度
newBoard.hn = Utils.getAbsentCount(newBoard, Main.endBoard);// 不在位将牌个数
newBoard.fn = newBoard.dn + newBoard.hn;
newBoard.parentBoard=this;
this.childBoards.add(newBoard);
return newBoard;
}
/**
* 向上移动
* @return
*/
public Board goUp() {
System.out.println("Go Up");
Board newBoard = new Board(this.copySelfArr());//这里不能这样复制
label: for (int i = 0; i < Init.SIZE; i++) {
for (int j = 0; j < Init.SIZE; j++) {
if (newBoard.arr[i][j] == 0) {
int t;
t = newBoard.arr[i][j];
newBoard.arr[i][j] = newBoard.arr[i - 1][j];
newBoard.arr[i - 1][j] = t;
break label;
}
}
}
newBoard.dn = this.dn + 1;// 深度
newBoard.hn = Utils.getAbsentCount(newBoard, Main.endBoard);// 不在位将牌个数
newBoard.fn = newBoard.dn + newBoard.hn;
newBoard.parentBoard = this;
this.childBoards.add(newBoard);
return newBoard;
}
/**
* 向右移动
* @return
*/
public Board goRight() {
System.out.println("Go Right");
Board newBoard = new Board(this.copySelfArr());
label: for (int i = 0; i < Init.SIZE; i++) {
for (int j = 0; j < Init.SIZE; j++) {
if (newBoard.arr[i][j] == 0) {
int t;
t = newBoard.arr[i][j];
newBoard.arr[i][j] = newBoard.arr[i][j+1];
newBoard.arr[i][j+1] = t;
break label;
}
}
}
newBoard.dn = this.dn + 1;// 深度
newBoard.hn = Utils.getAbsentCount(newBoard, Main.endBoard);// 不在位将牌个数
newBoard.fn = newBoard.dn + newBoard.hn;
newBoard.parentBoard=this;
this.childBoards.add(newBoard);
return newBoard;
}
/**
* 向左移动
* @return
*/
public Board goLeft() {
System.out.println("Go Left");
Board newBoard = new Board(this.copySelfArr());
label: for (int i = 0; i < Init.SIZE; i++) {
for (int j = 0; j < Init.SIZE; j++) {
if (newBoard.arr[i][j] == 0) {
int t;
t = newBoard.arr[i][j];
newBoard.arr[i][j] = newBoard.arr[i][j-1];
newBoard.arr[i][j-1] = t;
break label;
}
}
}
newBoard.dn = this.dn + 1;// 深度
newBoard.hn = Utils.getAbsentCount(newBoard, Main.endBoard);// 不在位将牌个数
newBoard.fn = newBoard.dn + newBoard.hn;
newBoard.parentBoard=this;
this.childBoards.add(newBoard);
return newBoard;
}
}OpenTable.java
package cn.hanquan.ai;
import java.util.ArrayList;
import java.util.Collections;
import java.util.Comparator;
/**
* Open表
* @author luyang.gong
*
*/
public class OpenTable {
public ArrayList<Board> tbArr = new ArrayList<Board>();
/**
* Open表排序
*/
public void sortItSelf() {
Collections.sort(tbArr, new Comparator<Board>() {
@Override
public int compare(Board b1, Board b2) {// 重写 Comparator 函数
if (b1.fn < b2.fn)//小的排前面
return -1;
else if (b1.fn > b2.fn)
return 1;
else
return 0;
}
});
System.out.println("Open表Board个数："+this.tbArr.size());
// System.out.println("排序后：\n"+tbArr);
System.out.println("最小fn="+tbArr.get(0));
System.out.println("\n");
}
/**
* 返回fn最小Board
* @return
*/
public Board getMinBoard() {
return tbArr.get(0);
}
/**
* 判断Table中是否包含某个board
* @param board
* @return
*/
public boolean hasBoard(Board board) {
boolean hasBoard = false;
for (int i = 0; i < tbArr.size(); i++) {
if (tbArr.get(i).equals(board)) {
hasBoard = true;
break;
}
}
return hasBoard;
}
/**
* 获取Board在OpenTable中的索引
* @param board
* @return 索引值
*/
public int getIndex(Board board) {
int index=-1;
for (int i = 0; i < tbArr.size(); i++) {
if (tbArr.get(i).equals(board)) {
index = i;
break;
}
}
return index;
}
public Board getBoardByArr(int[][] array){
for (int i = 0; i < tbArr.size(); i++) {
if (tbArr.get(i).equals(array)) {
return tbArr.get(i);
}
}
try {
throw new Exception("Opentable:不存在该arr!");
} catch (Exception e) {
e.printStackTrace();
}
return null;
}
@Override
public String toString() {
StringBuilder sb=new StringBuilder();
sb.append("\n");
sb.append("OpenTable:\n");
for(int i=0;i<tbArr.size();i++) {
sb.append(tbArr.get(i).toString());
sb.append("\n");
}
return sb.toString();
}
}CloseTable.java
package cn.hanquan.ai;
import java.util.ArrayList;
public class CloseTable {
ArrayList<Board> tbArr = new ArrayList<Board>();
/**
* 判断Table中是否包含某个board
* @param board
* @return
*/
public boolean hasBoard(Board board) {
boolean hasBoard = false;
for (int i = 0; i < tbArr.size(); i++) {
if (tbArr.get(i).equals(board)) {
hasBoard = true;
break;
}
}
return hasBoard;
}
/**
* 获取Board在CloseTable中的索引
* @param board
* @return 索引值
*/
public int getIndex(Board board) {
int index=-1;
for (int i = 0; i < tbArr.size(); i++) {
if (tbArr.get(i).equals(board)) {
index = i;
break;
}
}
return index;
}
public Board getBoardByArr(int[][] array){
for (int i = 0; i < tbArr.size(); i++) {
if (tbArr.get(i).equals(array)) {
return tbArr.get(i);
}
}
try {
throw new Exception("Closetable:不存在该arr!");
} catch (Exception e) {
e.printStackTrace();
}
return null;
}
}附：输出结果
（这个倒着看，在SUCCESS之后，反向输出了一下过程）
OpenTable:
5 1 2 4
9 6 3 8
13 15 10 11
14 0 7 12
fn gn hn = 12 0 12
第1次拓展
Open表Board个数：1
最小fn=
5 1 2 4
9 6 3 8
13 15 10 11
14 0 7 12
fn gn hn = 12 0 12
canDown:false
canUp:true
Go Up
openTable:add
canRight:true
Go Right
openTable:add
canLeft:true
Go Left
openTable:add
第2次拓展
Open表Board个数：3
最小fn=
5 1 2 4
9 6 3 8
13 0 10 11
14 15 7 12
fn gn hn = 17 1 16
canDown:true
Go Down
canUp:true
Go Up
openTable:add
canRight:true
Go Right
openTable:add
canLeft:true
Go Left
openTable:add
第3次拓展
Open表Board个数：5
最小fn=
5 1 2 4
9 6 3 8
13 10 0 11
14 15 7 12
fn gn hn = 16 2 14
canDown:true
Go Down
openTable:add
canUp:true
Go Up
openTable:add
canRight:true
Go Right
openTable:add
canLeft:true
Go Left
第4次拓展
Open表Board个数：7
最小fn=
5 1 2 4
9 6 3 8
13 10 7 11
14 15 0 12
fn gn hn = 15 3 12
canDown:false
canUp:true
Go Up
canRight:true
Go Right
openTable:add
canLeft:true
Go Left
openTable:add
第5次拓展
Open表Board个数：8
最小fn=
5 1 2 4
9 6 3 8
13 10 11 0
14 15 7 12
fn gn hn = 15 3 12
canDown:true
Go Down
openTable:add
canUp:true
Go Up
openTable:add
canRight:false
canLeft:true
Go Left
第6次拓展
Open表Board个数：9
最小fn=
5 1 2 4
9 6 3 8
13 10 11 12
14 15 7 0
fn gn hn = 14 4 10
canDown:false
canUp:true
Go Up
canRight:false
canLeft:true
Go Left
openTable:add
第7次拓展
Open表Board个数：9
最小fn=
5 1 2 4
9 6 3 8
13 10 7 11
14 15 12 0
fn gn hn = 16 4 12
canDown:false
canUp:true
Go Up
openTable:add
canRight:false
canLeft:true
Go Left
第8次拓展
Open表Board个数：9
最小fn=
5 1 2 4
9 6 3 8
13 10 7 11
14 0 15 12
fn gn hn = 16 4 12
canDown:false
canUp:true
Go Up
openTable:add
canRight:true
Go Right
canLeft:true
Go Left
openTable:add
第9次拓展
Open表Board个数：10
最小fn=
5 1 2 4
9 6 3 8
13 15 10 11
14 7 0 12
fn gn hn = 17 1 16
canDown:false
canUp:true
Go Up
openTable:add
canRight:true
Go Right
openTable:add
canLeft:true
Go Left
第10次拓展
Open表Board个数：11
最小fn=
5 1 2 4
9 6 3 8
13 15 10 11
0 14 7 12
fn gn hn = 17 1 16
canDown:false
canUp:true
Go Up
openTable:add
canRight:true
Go Right
canLeft:false
第11次拓展
Open表Board个数：11
最小fn=
5 1 2 4
9 6 3 8
13 10 11 12
14 15 0 7
fn gn hn = 17 5 12
canDown:false
canUp:true
Go Up
openTable:add
canRight:true
Go Right
canLeft:true
Go Left
openTable:add
第12次拓展
Open表Board个数：12
最小fn=
5 1 2 4
9 6 3 8
13 10 7 11
0 14 15 12
fn gn hn = 17 5 12
canDown:false
canUp:true
Go Up
openTable:add
canRight:true
Go Right
canLeft:false
第13次拓展
Open表Board个数：12
最小fn=
5 1 2 4
9 6 3 0
13 10 11 8
14 15 7 12
fn gn hn = 18 4 14
canDown:true
Go Down
canUp:true
Go Up
openTable:add
canRight:false
canLeft:true
Go Left
openTable:add
第14次拓展
Open表Board个数：13
最小fn=
5 1 2 4
9 6 3 8
13 15 10 11
14 7 12 0
fn gn hn = 18 2 16
canDown:false
canUp:true
Go Up
openTable:add
canRight:false
canLeft:true
Go Left
第15次拓展
Open表Board个数：13
最小fn=
5 1 2 4
9 6 3 8
0 15 10 11
13 14 7 12
fn gn hn = 18 2 16
canDown:true
Go Down
canUp:true
Go Up
openTable:add
canRight:true
Go Right
openTable:add
canLeft:false
第16次拓展
Open表Board个数：14
最小fn=
5 1 2 4
9 6 3 8
13 10 11 12
14 0 15 7
fn gn hn = 18 6 12
canDown:false
canUp:true
Go Up
openTable:add
canRight:true
Go Right
canLeft:true
Go Left
openTable:add
第17次拓展
Open表Board个数：15
最小fn=
5 1 2 4
9 6 3 8
0 10 7 11
13 14 15 12
fn gn hn = 18 6 12
canDown:true
Go Down
canUp:true
Go Up
openTable:add
canRight:true
Go Right
openTable:add
canLeft:false
第18次拓展
Open表Board个数：16
最小fn=
5 1 2 4
9 6 0 8
13 10 3 11
14 15 7 12
fn gn hn = 19 3 16
canDown:true
Go Down
canUp:true
Go Up
openTable:add
canRight:true
Go Right
openTable:add
canLeft:true
Go Left
openTable:add
第19次拓展
Open表Board个数：18
最小fn=
5 1 2 4
9 6 3 8
13 10 7 0
14 15 12 11
fn gn hn = 19 5 14
canDown:true
Go Down
canUp:true
Go Up
openTable:add
canRight:false
canLeft:true
Go Left
openTable:add
第20次拓展
Open表Board个数：19
最小fn=
5 1 2 4
9 6 3 8
13 0 7 11
14 10 15 12
fn gn hn = 19 5 14
canDown:true
Go Down
canUp:true
Go Up
openTable:add
canRight:true
Go Right
openTable:add
canLeft:true
Go Left
openTable:add
第21次拓展
Open表Board个数：21
最小fn=
5 1 2 4
0 6 3 8
9 15 10 11
13 14 7 12
fn gn hn = 19 3 16
canDown:true
Go Down
canUp:true
Go Up
openTable:add
canRight:true
Go Right
openTable:add
canLeft:false
第22次拓展
Open表Board个数：22
最小fn=
5 1 2 4
9 6 3 8
15 0 10 11
13 14 7 12
fn gn hn = 19 3 16
canDown:true
Go Down
openTable:add
canUp:true
Go Up
openTable:add
canRight:true
Go Right
openTable:add
canLeft:true
Go Left
第23次拓展
Open表Board个数：24
最小fn=
5 1 2 4
9 6 3 8
15 10 0 11
13 14 7 12
fn gn hn = 18 4 14
canDown:true
Go Down
openTable:add
canUp:true
Go Up
openTable:add
canRight:true
Go Right
openTable:add
canLeft:true
Go Left
第24次拓展
Open表Board个数：26
最小fn=
5 1 2 4
9 6 3 8
15 10 7 11
13 14 0 12
fn gn hn = 17 5 12
canDown:false
canUp:true
Go Up
canRight:true
Go Right
openTable:add
canLeft:true
Go Left
openTable:add
第25次拓展
Open表Board个数：27
最小fn=
5 1 2 4
9 6 3 8
15 10 11 0
13 14 7 12
fn gn hn = 17 5 12
canDown:true
Go Down
openTable:add
canUp:true
Go Up
openTable:add
canRight:false
canLeft:true
Go Left
第26次拓展
Open表Board个数：28
最小fn=
5 1 2 4
9 6 3 8
15 10 11 12
13 14 7 0
fn gn hn = 16 6 10
canDown:false
canUp:true
Go Up
canRight:false
canLeft:true
Go Left
openTable:add
第27次拓展
Open表Board个数：28
最小fn=
5 1 2 4
9 6 3 8
15 10 7 11
13 14 12 0
fn gn hn = 18 6 12
canDown:false
canUp:true
Go Up
openTable:add
canRight:false
canLeft:true
Go Left
第28次拓展
Open表Board个数：28
最小fn=
5 1 2 4
9 6 3 8
13 10 11 12
0 14 15 7
fn gn hn = 19 7 12
canDown:false
canUp:true
Go Up
openTable:add
canRight:true
Go Right
canLeft:false
第29次拓展
Open表Board个数：28
最小fn=
5 1 2 4
0 6 3 8
9 10 7 11
13 14 15 12
fn gn hn = 19 7 12
canDown:true
Go Down
canUp:true
Go Up
openTable:add
canRight:true
Go Right
openTable:add
canLeft:false
第30次拓展
Open表Board个数：29
最小fn=
5 1 2 4
9 6 3 8
10 0 7 11
13 14 15 12
fn gn hn = 19 7 12
canDown:true
Go Down
openTable:add
canUp:true
Go Up
openTable:add
canRight:true
Go Right
openTable:add
canLeft:true
Go Left
第31次拓展
Open表Board个数：31
最小fn=
5 1 2 4
9 6 3 8
15 10 11 12
13 14 0 7
fn gn hn = 19 7 12
canDown:false
canUp:true
Go Up
openTable:add
canRight:true
Go Right
canLeft:true
Go Left
openTable:add
第32次拓展
Open表Board个数：32
最小fn=
5 1 2 4
9 0 3 8
13 6 10 11
14 15 7 12
fn gn hn = 20 2 18
canDown:true
Go Down
canUp:true
Go Up
openTable:add
canRight:true
Go Right
openTable:add
canLeft:true
Go Left
openTable:add
第33次拓展
Open表Board个数：34
最小fn=
5 1 2 4
9 6 3 8
0 13 10 11
14 15 7 12
fn gn hn = 20 2 18
canDown:true
Go Down
openTable:add
canUp:true
Go Up
openTable:add
canRight:true
Go Right
canLeft:false
第34次拓展
Open表Board个数：35
最小fn=
5 1 2 4
9 6 3 8
13 15 0 11
14 7 10 12
fn gn hn = 20 2 18
canDown:true
Go Down
canUp:true
Go Up
openTable:add
canRight:true
Go Right
openTable:add
canLeft:true
Go Left
openTable:add
第35次拓展
Open表Board个数：37
最小fn=
5 1 2 4
9 6 3 8
13 15 11 0
14 7 10 12
fn gn hn = 19 3 16
canDown:true
Go Down
openTable:add
canUp:true
Go Up
openTable:add
canRight:false
canLeft:true
Go Left
第36次拓展
Open表Board个数：38
最小fn=
5 1 2 4
9 6 3 8
13 15 11 12
14 7 10 0
fn gn hn = 18 4 14
canDown:false
canUp:true
Go Up
canRight:false
canLeft:true
Go Left
openTable:add
第37次拓展
Open表Board个数：38
最小fn=
5 1 2 4
9 6 3 8
13 10 0 12
14 15 11 7
fn gn hn = 20 6 14
canDown:true
Go Down
canUp:true
Go Up
openTable:add
canRight:true
Go Right
openTable:add
canLeft:true
Go Left
openTable:add
第38次拓展
Open表Board个数：40
最小fn=
5 1 2 4
9 6 8 0
13 10 3 11
14 15 7 12
fn gn hn = 20 4 16
canDown:true
Go Down
openTable:add
canUp:true
Go Up
openTable:add
canRight:false
canLeft:true
Go Left
第39次拓展
Open表Board个数：41
最小fn=
5 1 2 4
9 6 3 8
13 7 0 11
14 10 15 12
fn gn hn = 20 6 14
canDown:true
Go Down
openTable:add
canUp:true
Go Up
openTable:add
canRight:true
Go Right
openTable:add
canLeft:true
Go Left
第40次拓展
Open表Board个数：43
最小fn=
5 1 2 4
9 6 3 8
13 7 11 0
14 10 15 12
fn gn hn = 19 7 12
canDown:true
Go Down
openTable:add
canUp:true
Go Up
openTable:add
canRight:false
canLeft:true
Go Left
第41次拓展
Open表Board个数：44
最小fn=
5 1 2 4
9 6 3 8
13 7 11 12
14 10 15 0
fn gn hn = 18 8 10
canDown:false
canUp:true
Go Up
canRight:false
canLeft:true
Go Left
openTable:add
第42次拓展
Open表Board个数：44
最小fn=
0 1 2 4
5 6 3 8
9 15 10 11
13 14 7 12
fn gn hn = 20 4 16
canDown:true
Go Down
canUp:false
canRight:true
Go Right
openTable:add
canLeft:false
第43次拓展
Open表Board个数：44
最小fn=
1 0 2 4
5 6 3 8
9 15 10 11
13 14 7 12
fn gn hn = 19 5 14
canDown:true
Go Down
openTable:add
canUp:false
canRight:true
Go Right
openTable:add
canLeft:true
Go Left
第44次拓展
Open表Board个数：45
最小fn=
1 2 0 4
5 6 3 8
9 15 10 11
13 14 7 12
fn gn hn = 18 6 12
canDown:true
Go Down
openTable:add
canUp:false
canRight:true
Go Right
openTable:add
canLeft:true
Go Left
第45次拓展
Open表Board个数：46
最小fn=
1 2 3 4
5 6 0 8
9 15 10 11
13 14 7 12
fn gn hn = 17 7 10
canDown:true
Go Down
openTable:add
canUp:true
Go Up
canRight:true
Go Right
openTable:add
canLeft:true
Go Left
openTable:add
第46次拓展
Open表Board个数：48
最小fn=
1 2 3 4
5 6 10 8
9 15 0 11
13 14 7 12
fn gn hn = 18 8 10
canDown:true
Go Down
openTable:add
canUp:true
Go Up
canRight:true
Go Right
openTable:add
canLeft:true
Go Left
openTable:add
第47次拓展
Open表Board个数：50
最小fn=
1 2 3 4
5 6 10 8
9 15 7 11
13 14 0 12
fn gn hn = 17 9 8
canDown:false
canUp:true
Go Up
canRight:true
Go Right
openTable:add
canLeft:true
Go Left
openTable:add
第48次拓展
Open表Board个数：51
最小fn=
1 2 3 4
5 6 10 8
9 15 11 0
13 14 7 12
fn gn hn = 17 9 8
canDown:true
Go Down
openTable:add
canUp:true
Go Up
openTable:add
canRight:false
canLeft:true
Go Left
第49次拓展
Open表Board个数：52
最小fn=
1 2 3 4
5 6 10 8
9 15 11 12
13 14 7 0
fn gn hn = 16 10 6
canDown:false
canUp:true
Go Up
canRight:false
canLeft:true
Go Left
openTable:add
第50次拓展
Open表Board个数：52
最小fn=
1 2 3 4
5 6 8 0
9 15 10 11
13 14 7 12
fn gn hn = 18 8 10
canDown:true
Go Down
openTable:add
canUp:true
Go Up
openTable:add
canRight:false
canLeft:true
Go Left
第51次拓展
Open表Board个数：53
最小fn=
1 2 3 4
5 6 10 8
9 15 7 11
13 14 12 0
fn gn hn = 18 10 8
canDown:false
canUp:true
Go Up
openTable:add
canRight:false
canLeft:true
Go Left
第52次拓展
Open表Board个数：53
最小fn=
1 2 4 0
5 6 3 8
9 15 10 11
13 14 7 12
fn gn hn = 19 7 12
canDown:true
Go Down
openTable:add
canUp:false
canRight:false
canLeft:true
Go Left
第53次拓展
Open表Board个数：53
最小fn=
1 2 3 4
5 6 10 8
9 0 15 11
13 14 7 12
fn gn hn = 19 9 10
canDown:true
Go Down
openTable:add
canUp:true
Go Up
openTable:add
canRight:true
Go Right
canLeft:true
Go Left
openTable:add
第54次拓展
Open表Board个数：55
最小fn=
1 2 3 4
5 6 10 8
9 15 11 12
13 14 0 7
fn gn hn = 19 11 8
canDown:false
canUp:true
Go Up
openTable:add
canRight:true
Go Right
canLeft:true
Go Left
openTable:add
第55次拓展
Open表Board个数：56
最小fn=
1 2 3 4
5 6 8 11
9 15 10 0
13 14 7 12
fn gn hn = 19 9 10
canDown:true
Go Down
openTable:add
canUp:true
Go Up
canRight:false
canLeft:true
Go Left
openTable:add
第56次拓展
Open表Board个数：57
最小fn=
1 2 3 4
5 6 8 11
9 15 10 12
13 14 7 0
fn gn hn = 18 10 8
canDown:false
canUp:true
Go Up
canRight:false
canLeft:true
Go Left
openTable:add
第57次拓展
Open表Board个数：57
最小fn=
5 1 2 4
6 0 3 8
9 15 10 11
13 14 7 12
fn gn hn = 20 4 16
canDown:true
Go Down
openTable:add
canUp:true
Go Up
openTable:add
canRight:true
Go Right
openTable:add
canLeft:true
Go Left
第58次拓展
Open表Board个数：59
最小fn=
5 1 2 4
9 6 3 8
15 14 10 11
13 0 7 12
fn gn hn = 20 4 16
canDown:false
canUp:true
Go Up
canRight:true
Go Right
openTable:add
canLeft:true
Go Left
openTable:add
第59次拓展
Open表Board个数：60
最小fn=
5 1 2 4
9 6 3 8
15 10 7 11
13 0 14 12
fn gn hn = 20 6 14
canDown:false
canUp:true
Go Up
openTable:add
canRight:true
Go Right
canLeft:true
Go Left
openTable:add
第60次拓展
Open表Board个数：61
最小fn=
5 1 2 4
9 6 3 0
15 10 11 8
13 14 7 12
fn gn hn = 20 6 14
canDown:true
Go Down
canUp:true
Go Up
openTable:add
canRight:false
canLeft:true
Go Left
openTable:add
第61次拓展
Open表Board个数：62
最小fn=
5 1 2 4
9 6 3 8
0 10 11 12
13 14 15 7
fn gn hn = 20 8 12
canDown:true
Go Down
canUp:true
Go Up
openTable:add
canRight:true
Go Right
openTable:add
canLeft:false
第62次拓展
Open表Board个数：63
最小fn=
0 1 2 4
5 6 3 8
9 10 7 11
13 14 15 12
fn gn hn = 20 8 12
canDown:true
Go Down
canUp:false
canRight:true
Go Right
openTable:add
canLeft:false
第63次拓展
Open表Board个数：63
最小fn=
1 0 2 4
5 6 3 8
9 10 7 11
13 14 15 12
fn gn hn = 19 9 10
canDown:true
Go Down
openTable:add
canUp:false
canRight:true
Go Right
openTable:add
canLeft:true
Go Left
第64次拓展
Open表Board个数：64
最小fn=
1 2 0 4
5 6 3 8
9 10 7 11
13 14 15 12
fn gn hn = 18 10 8
canDown:true
Go Down
openTable:add
canUp:false
canRight:true
Go Right
openTable:add
canLeft:true
Go Left
第65次拓展
Open表Board个数：65
最小fn=
1 2 3 4
5 6 0 8
9 10 7 11
13 14 15 12
fn gn hn = 17 11 6
canDown:true
Go Down
openTable:add
canUp:true
Go Up
canRight:true
Go Right
openTable:add
canLeft:true
Go Left
openTable:add
第66次拓展
Open表Board个数：67
最小fn=
1 2 3 4
5 6 7 8
9 10 0 11
13 14 15 12
fn gn hn = 16 12 4
canDown:true
Go Down
openTable:add
canUp:true
Go Up
canRight:true
Go Right
openTable:add
canLeft:true
Go Left
openTable:add
第67次拓展
Open表Board个数：69
最小fn=
1 2 3 4
5 6 7 8
9 10 11 0
13 14 15 12
fn gn hn = 15 13 2
canDown:true
Go Down
openTable:add
canUp:true
Go Up
openTable:add
canRight:false
canLeft:true
Go Left
第68次拓展
Open表Board个数：70
最小fn=
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 0
fn gn hn = 14 14 0
SUCCESS:
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 0
fn gn hn = 14 14 0
上一步：
1 2 3 4
5 6 7 8
9 10 11 0
13 14 15 12
fn gn hn = 15 13 2
上一步：
1 2 3 4
5 6 7 8
9 10 0 11
13 14 15 12
fn gn hn = 16 12 4
上一步：
1 2 3 4
5 6 0 8
9 10 7 11
13 14 15 12
fn gn hn = 17 11 6
上一步：
1 2 0 4
5 6 3 8
9 10 7 11
13 14 15 12
fn gn hn = 18 10 8
上一步：
1 0 2 4
5 6 3 8
9 10 7 11
13 14 15 12
fn gn hn = 19 9 10
上一步：
0 1 2 4
5 6 3 8
9 10 7 11
13 14 15 12
fn gn hn = 20 8 12
上一步：
5 1 2 4
0 6 3 8
9 10 7 11
13 14 15 12
fn gn hn = 19 7 12
上一步：
5 1 2 4
9 6 3 8
0 10 7 11
13 14 15 12
fn gn hn = 18 6 12
上一步：
5 1 2 4
9 6 3 8
13 10 7 11
0 14 15 12
fn gn hn = 17 5 12
上一步：
5 1 2 4
9 6 3 8
13 10 7 11
14 0 15 12
fn gn hn = 16 4 12
上一步：
5 1 2 4
9 6 3 8
13 10 7 11
14 15 0 12
fn gn hn = 15 3 12
上一步：
5 1 2 4
9 6 3 8
13 10 0 11
14 15 7 12
fn gn hn = 16 2 14
上一步：
5 1 2 4
9 6 3 8
13 0 10 11
14 15 7 12
fn gn hn = 17 1 16
上一步：
5 1 2 4
9 6 3 8
13 15 10 11
14 0 7 12
fn gn hn = 12 0 12
本文章为转载内容，我们尊重原作者对文章享有的著作权。如有内容错误或侵权问题，欢迎原作者联系我们进行内容更正或删除文章。
