【人工智能导论】A*算法求解15数码问题 Java
2024-05-09 13:14:14
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 ifelse 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 ifEnd**/
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endif (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();}@Overridepublic 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>() {@Overridepublic 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;elsereturn 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;}@Overridepublic 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 12canDown: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 16canDown: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 14canDown: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 12canDown: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 12canDown: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 10canDown: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 12canDown: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 12canDown: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 16canDown: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 16canDown: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 12canDown: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 12canDown: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 14canDown: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 16canDown: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 16canDown: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 12canDown: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 12canDown: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 16canDown: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 14canDown: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 14canDown: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 16canDown: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 16canDown: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 14canDown: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 12canDown: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 12canDown: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 10canDown: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 12canDown: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 12canDown: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 12canDown: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 12canDown: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 12canDown: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 18canDown: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 18canDown: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 18canDown: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 16canDown: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 14canDown: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 14canDown: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 16canDown: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 14canDown: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 12canDown: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 10canDown: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 16canDown: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 14canDown: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 12canDown: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 10canDown: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 10canDown: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 8canDown: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 8canDown: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 6canDown: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 10canDown: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 8canDown: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 12canDown: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 10canDown: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 8canDown: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 10canDown: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 8canDown: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 16canDown: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 16canDown: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 14canDown: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 14canDown: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 12canDown: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 12canDown: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 10canDown: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 8canDown: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 6canDown: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 4canDown: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 2canDown: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 0SUCCESS:
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
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