24点运算2

这是本人2年前业余时间写的application版本的24点游戏的简单实现。共享出来，希望能起到抛砖引玉的作用，一起探讨24点的实现。

1、计算方式的改变——引入分数计算概念

求24点涉及到除法，所以必须转变直接计算的思路。经过一段时间的摸索，本人发现可以采用分数计算。任何两个数的计算都可以转换成对应的分数计算形式。

例如：3 / 8 可以转换成 (3/1) / (8/1)

1.1 待计算数字的初始化

于是待计算的4个值必须先转换成分数：

Java代码

private int[] aArray = new int[2];
private int[] bArray = new int[2];
private int[] cArray = new int[2];
private int[] dArray = new int[2];

当然，我们得初始化它们：　效果就是２－＞２/ １

Java代码

aArray[0] = a;
aArray[1] = 1;
bArray[0] = b;
bArray[1] = 1;
cArray[0] = c;
cArray[1] = 1;
dArray[0] = d;
dArray[1] = 1;

1.2 分数的计算

小学的时候就学过，分数的加减法用到最小公倍数和最大公约数。

Java代码

/**
* 求最小公倍数
*
* @param a
* @param b
* @return
*/
public int leaseCommonMultiple(int a, int b) {
return a * b / greatestCommonDivisor(a, b);
}
/**
* 求最大公约数
*
* @param a
* @param b
* @return
*/
public int greatestCommonDivisor(int a, int b) {
if (0 == a && 0 == b) {
return 1;
}
if (0 == a) {
return b;
}
if (0 == b) {
return a;
}
if (a > b) {
int c = a;
a = b;
b = c;
}
for (int c = a % b; c > 0; c = a % b) {
a = b;
b = c;
}
return b;
}

对应的加减方法如下：

Java代码

/**
* 加
*/
public int[] plus(int[] a, int[] b) {
if (0 == a[1]) {
return new int[] { 0, 0 };
}
if (0 == b[1]) {
return new int[] { 0, 0 };
}
int denominator = leaseCommonMultiple(a[1], b[1]);
return new int[] {
denominator / a[1] * a[0] + denominator / b[1] * b[0],
denominator };
}
/**
* 减
*
* @param a
* @param b
* @return
*/
public int[] reduce(int[] a, int[] b) {
if (0 == a[1]) {
return new int[] { 0, 0 };
}
if (0 == b[1]) {
return new int[] { 0, 0 };
}
int denominator = leaseCommonMultiple(a[1], b[1]);
return new int[] {
denominator / a[1] * a[0] - denominator / b[1] * b[0],
denominator };
}

相对来说，乘除方法就简单多了：

Java代码

/**
* 乘
*
* @param a
* @param b
* @return
*/
public int[] multiply(int[] a, int[] b) {
return new int[] { a[0] * b[0], a[1] * b[1] };
}
/**
* 除
*
* @param a
* @param b
* @return
*/
public int[] divide(int[] a, int[] b) {
return new int[] { a[0] * b[1], a[1] * b[0] };
}

2、计算规则

2.1 算法——穷举法

24点的计算涉及到以下三种元素：

待计算的4个数、三个计算符号（加减乘除）、括号

本人采用的是穷举法，进行一个一个数值和符号的尝试——这样的话，在循环中数值和符号都必须是动态的。

Java代码

/**
* 动态加载符号数
* @param i
* @param a
* @param b
* @return
*/
public int[] dispose(int i, int a[], int[] b){
if(i == 0){
return plus(a, b);
}else if(i == 1){
return reduce(a, b);
}else if(i == 2){
return multiply(a, b);
}else{
return divide(a, b);
}
}
/**
* 动态加载计算数
* @param i
* @param a
* @param b
* @param c
* @param d
* @return
*/
public int[] number(int i, int[] a, int[] b, int[] c, int[] d){
if(i == 0){
return a;
}else if(i == 1){
return b;
}else if(i == 2){
return c;
}else if(i == 3){
return d;
}else{
return new int[]{0,1};
}
}

2.2 括号规则：

类型1：A(A(A(a,b),c),d)

类型2：A(A(a,A(b,c)),d)

类型3：A(a,A(b,A(c,d)))

类型4：A(a,A(A(b,c),d))

类型5：A(A(a,b),A(c,d))

注：A就是1个符号，A(a,b)就是指：a+b, a-b, a*b, a/b四种情况

2.3 数值与符号的穷举

把每个数值和符号一个进行尝试：

i,j,k ：符号

m,n,o,p ：数值

Java代码

for(int i = 0; i < 4; i++){
for(int j = 0; j < 4; j++){
for(int k = 0; k < 4; k++){
for(int m = 0; m < 4; m++){
for(int n = 0; n < 4; n++){
if(n == m)
continue;
for(int o = 0; o < 4; o++){
if(o == m || o == n)
continue;
for(int p = 0; p < 4; p++){
if(p == m || p == n || p == o)
continue;
。。。计算方法。。。
}
}
}
}
}
}
}

计算方法：

Java代码

//类型1：A(A(A(a,b),c),d)
int[] result1 = dispose(k,dispose(j,dispose(i,number(m,a,b,c,d),number(n,a,b,c,d)),number(o,a,b,c,d)),number(p,a,b,c,d));
//类型2：A(A(a,A(b,c)),d)
int[] result2 = dispose(k,dispose(i,number(m,a,b,c,d),dispose(j,number(n,a,b,c,d),number(o,a,b,c,d))),number(p,a,b,c,d));
//类型3：A(a,A(b,A(c,d)))
int[] result3 = dispose(i,number(m,a,b,c,d),dispose(j,number(n,a,b,c,d),dispose(k,number(o,a,b,c,d),number(p,a,b,c,d))));
//类型4：A(a,A(A(b,c),d))
int[] result4 = dispose(i,number(m,a,b,c,d),dispose(k,dispose(j,number(n,a,b,c,d),number(o,a,b,c,d)),number(p,a,b,c,d)));
//类型5：A(A(a,b),A(c,d))
int[] result5 = dispose(j,dispose(i,number(m,a,b,c,d),number(n,a,b,c,d)),dispose(k,number(o,a,b,c,d),number(p,a,b,c,d)));
if (0 != result1[1]) {
if (result1[0] % result1[1] == 0) {
if (result1[0] / result1[1] == 24) {
if ((!map.containsKey(new Integer(i)))|| (!map.containsKey(new Integer(j)))|| (!map.containsKey(new Integer(k)))) {
map.put(new Integer(i),new Integer(i));
map.put(new Integer(j),new Integer(j));
map.put(new Integer(k),new Integer(k));
count += 1;
System.out.println("((" + printNumber(m) + printSymbol(i) + printNumber(n) + ")" + printSymbol(j) + printNumber(o) + ")" + printSymbol(k) + printNumber(p));
}
}
}
}
if (0 != result2[1]) {
if (result2[0] % result2[1] == 0) {
if (result2[0] / result2[1] == 24) {
if ((!map.containsKey(new Integer(i)))|| (!map.containsKey(new Integer(j)))|| (!map.containsKey(new Integer(k)))) {
map.put(new Integer(i),new Integer(i));
map.put(new Integer(j),new Integer(j));
map.put(new Integer(k),new Integer(k));
count += 1;
System.out.println("(" + printNumber(m) + printSymbol(i) +"(" + printNumber(n) + printSymbol(j) + printNumber(o) + "))" + printSymbol(k) + printNumber(p));
}
}
}
}
if (0 != result3[1]) {
if (result3[0] % result3[1] == 0) {
if (result3[0] / result3[1] == 24) {
if ((!map.containsKey(new Integer(i))) || (!map.containsKey(new Integer(j)))|| (!map.containsKey(new Integer(k)))) {
map.put(new Integer(i),new Integer(i));
map.put(new Integer(j),new Integer(j));
map.put(new Integer(k),new Integer(k));
count += 1;
System.out.println(printNumber(m) + printSymbol(i) +"(" + printNumber(n) + printSymbol(j) + "(" + printNumber(o) + printSymbol(k) + printNumber(p) + "))");
}
}
}
}
if (0 != result4[1]) {
if (result4[0] % result4[1] == 0) {
if (result4[0] / result4[1] == 24) {
if ((!map
.containsKey(new Integer(i)))|| (!map.containsKey(new Integer(j)))|| (!map.containsKey(new Integer(k)))) {
map.put(new Integer(i),new Integer(i));
map.put(new Integer(j),new Integer(j));
map.put(new Integer(k),new Integer(k));
count += 1;
System.out.println(printNumber(m) + printSymbol(i) +"((" + printNumber(n) + printSymbol(j) + printNumber(o) + ")" + printSymbol(k) + printNumber(p) + ")");
}
}
}
}
if (0 != result5[1]) {
if (result5[0] % result5[1] == 0) {
if (result5[0] / result5[1] == 24) {
if ((!map.containsKey(new Integer(i)))|| (!map.containsKey(new Integer(j)))|| (!map.containsKey(new Integer(k)))) {
map.put(new Integer(i),new Integer(i));
map.put(new Integer(j),new Integer(j));
map.put(new Integer(k),new Integer(k));
count += 1;
System.out.println("(" + printNumber(m) + printSymbol(i) + printNumber(n) + ")" + printSymbol(j) + "(" + printNumber(o) + printSymbol(k) + printNumber(p) + ")");
}
}
}
}

该程序目前存在的一些问题：

1）、存在括号多余的情况——如：1 + (2 + (3 * 7))和((2 + 7) - 1) * 3

2）、结果打印耦合在核心计算方法中

具体代码：

package com.chanson;
/*
 * @date   Aug 3, 2006
 * @project 学习
 * @company 个人
 * @author  chanson
 * @version 1.0
 */
import java.util.HashMap;

public class TwentyFour {
    
    private int[] aArray = new int[2];
    private int[] bArray = new int[2];
    private int[] cArray = new int[2];
    private int[] dArray = new int[2];
    
    /**
     * main方法
     * 
     * @param args
     */
    public static void main(String[] args) {
        new TwentyFour().dispose(3, 3, 8, 8);
    }
    

    public void dispose(int a, int b, int c, int d){
        aArray[0] = a;
        aArray[1] = 1;
        bArray[0] = b;
        bArray[1] = 1;
        cArray[0] = c;
        cArray[1] = 1;
        dArray[0] = d;
        dArray[1] = 1;
        core(aArray, bArray, cArray, dArray);
    }
    
    /**
     * 加
     */
    public  int[] plus(int[] a, int[] b){
        
        if(0 == a[1]){
            return new int[]{0,0};
        }
        if(0 == b[1]){
            return new int[]{0,0};
        }
        int denominator = leaseCommonMultiple(a[1],b[1]);
        
        return new int[]{denominator/a[1]*a[0] + denominator/b[1]*b[0] ,denominator};
    }
    
    /**
     * 减
     * @param a
     * @param b
     * @return
     */
    public  int[] reduce(int[] a, int[] b){
        if(0 == a[1]){
            return new int[]{0,0};
        }
        if(0 == b[1]){
            return new int[]{0,0};
        }
        int denominator = leaseCommonMultiple(a[1],b[1]);
        
        return new int[]{denominator/a[1]*a[0] - denominator/b[1]*b[0] ,denominator};
    }
    
    /**
     * 乘
     * @param a
     * @param b
     * @return
     */
    public  int[] multiply(int[] a, int[] b){
        return new int[]{a[0] * b[0], a[1] * b[1]};
    }
    
    /**
     * 除
     * @param a
     * @param b
     * @return
     */
    public  int[] divide(int[] a, int[] b){
        return new int[]{a[0] * b[1], a[1] * b[0]};
    }
    
    /**
     * 求最小公倍数
     * @param a
     * @param b
     * @return
     */
    public  int leaseCommonMultiple(int a, int b){
        return a*b/greatestCommonDivisor(a,b);
    }
    
    /**
     * 求最大公约数
     * @param a
     * @param b
     * @return
     */
    public  int greatestCommonDivisor(int a, int b) {
        if(0 == a && 0 == b){
            return 1;
        }
        if (0 == a) {
            return b;
        }
        if (0 == b) {
            return a;
        }
        if (a > b) {
            int c = a;
            a = b;
            b = c;
        }
        for (int c = a % b; c > 0; c = a % b) {
            a = b;
            b = c;
        }
        return b;
    }
    
    /**
     * 动态加载符号数
     * @param i
     * @param a
     * @param b
     * @return
     */
    public  int[] dispose(int i, int a[], int[] b){
        if(i == 0){
            return plus(a, b);
        }else if(i == 1){
            return reduce(a, b);
        }else if(i == 2){
            return multiply(a, b);
        }else{
            return divide(a, b);
        }
    }
    
    /**
     * 动态加载计算数
     * @param i
     * @param a
     * @param b
     * @param c
     * @param d
     * @return
     */
    public int[] number(int i, int[] a, int[] b, int[] c, int[] d){
        if(i == 0){
            return a;
        }else if(i == 1){
            return b;
        }else if(i == 2){
            return c;
        }else if(i == 3){
            return d;
        }else{
            return new int[]{0,1};
        }
    }

    /**
     * 核心算法部分
     * @param a
     * @param b
     * @param c
     * @param d
     */
    private  void core(int[] a, int[] b, int[] c, int[] d) {
        HashMap map = new HashMap();
        
        int count = 0;
        
        for(int i = 0; i < 4; i++){
            for(int j = 0; j < 4; j++){
                for(int k = 0; k < 4; k++){
                    for(int m = 0; m < 4; m++){
                        for(int n = 0; n < 4; n++){
                            if(n == m)
                                continue;
                            for(int o = 0; o < 4; o++){
                                if(o == m || o == n)
                                    continue;
                                for(int p = 0; p < 4; p++){
                                    if(p == m || p == n || p == o)
                                        continue;
                                    //类型1：A(A(A(a,b),c),d)
                                    int[] result1 = dispose(k,dispose(j,dispose(i,number(m,a,b,c,d),number(n,a,b,c,d)),number(o,a,b,c,d)),number(p,a,b,c,d));
                                    //类型2：A(A(a,A(b,c)),d)
                                    int[] result2 = dispose(k,dispose(i,number(m,a,b,c,d),dispose(j,number(n,a,b,c,d),number(o,a,b,c,d))),number(p,a,b,c,d));
                                    //类型3：A(a,A(b,A(c,d)))
                                    int[] result3 = dispose(i,number(m,a,b,c,d),dispose(j,number(n,a,b,c,d),dispose(k,number(o,a,b,c,d),number(p,a,b,c,d))));
                                    //类型4：A(a,A(A(b,c),d))
                                    int[] result4 = dispose(i,number(m,a,b,c,d),dispose(k,dispose(j,number(n,a,b,c,d),number(o,a,b,c,d)),number(p,a,b,c,d)));                                    
                                    //类型5：A(A(a,b),A(c,d))
                                    int[] result5 = dispose(j,dispose(i,number(m,a,b,c,d),number(n,a,b,c,d)),dispose(k,number(o,a,b,c,d),number(p,a,b,c,d)));
                                    if (0 != result1[1]) {
                                        if (result1[0] % result1[1] == 0) {
                                            if (result1[0] / result1[1] == 24) {
                                                if ((!map.containsKey(new Integer(i)))|| (!map.containsKey(new Integer(j)))|| (!map.containsKey(new Integer(k)))) {
                                                    map.put(new Integer(i),new Integer(i));
                                                    map.put(new Integer(j),new Integer(j));
                                                    map.put(new Integer(k),new Integer(k));
                                                    count += 1;
                                                    System.out.println("((" + printNumber(m) + printSymbol(i) + printNumber(n) + ")" + printSymbol(j) + printNumber(o) + ")" + printSymbol(k) + printNumber(p));
                                                }
                                            }
                                        }
                                    }
                                    if (0 != result2[1]) {
                                        if (result2[0] % result2[1] == 0) {
                                            if (result2[0] / result2[1] == 24) {
                                                if ((!map.containsKey(new Integer(i)))|| (!map.containsKey(new Integer(j)))|| (!map.containsKey(new Integer(k)))) {
                                                    map.put(new Integer(i),new Integer(i));
                                                    map.put(new Integer(j),new Integer(j));
                                                    map.put(new Integer(k),new Integer(k));
                                                    count += 1;
                                                    System.out.println("(" + printNumber(m) + printSymbol(i) +"(" + printNumber(n) + printSymbol(j) + printNumber(o) + "))" + printSymbol(k) + printNumber(p));
                                                }
                                            }
                                        }
                                    }
                                    if (0 != result3[1]) {
                                        if (result3[0] % result3[1] == 0) {
                                            if (result3[0] / result3[1] == 24) {
                                                if ((!map.containsKey(new Integer(i))) || (!map.containsKey(new Integer(j)))|| (!map.containsKey(new Integer(k)))) {
                                                    map.put(new Integer(i),new Integer(i));
                                                    map.put(new Integer(j),new Integer(j));
                                                    map.put(new Integer(k),new Integer(k));
                                                    count += 1;
                                                    System.out.println(printNumber(m) + printSymbol(i) +"(" + printNumber(n) + printSymbol(j) + "(" + printNumber(o) +  printSymbol(k) + printNumber(p) + "))");
                                                }
                                            }
                                        }
                                    }
                                    if (0 != result4[1]) {
                                        if (result4[0] % result4[1] == 0) {
                                            if (result4[0] / result4[1] == 24) {
                                                if ((!map
                                                        .containsKey(new Integer(i)))|| (!map.containsKey(new Integer(j)))|| (!map.containsKey(new Integer(k)))) {
                                                    map.put(new Integer(i),new Integer(i));
                                                    map.put(new Integer(j),new Integer(j));
                                                    map.put(new Integer(k),new Integer(k));
                                                    count += 1;
                                                    System.out.println(printNumber(m) + printSymbol(i) +"((" + printNumber(n) + printSymbol(j) + printNumber(o) + ")" +  printSymbol(k) + printNumber(p) + ")");
                                                }
                                            }
                                        }
                                    }
                                    if (0 != result5[1]) {
                                        if (result5[0] % result5[1] == 0) {
                                            if (result5[0] / result5[1] == 24) {
                                                if ((!map.containsKey(new Integer(i)))|| (!map.containsKey(new Integer(j)))|| (!map.containsKey(new Integer(k)))) {
                                                    map.put(new Integer(i),new Integer(i));
                                                    map.put(new Integer(j),new Integer(j));
                                                    map.put(new Integer(k),new Integer(k));
                                                    count += 1;
                                                    System.out.println("(" + printNumber(m) + printSymbol(i) + printNumber(n) + ")" + printSymbol(j) + "(" + printNumber(o) + printSymbol(k) + printNumber(p) + ")");
                                                }
                                            }
                                        }
                                    }
                                }
                            }
                        }
                    }
                }
            }
        }
        //总共几种答案，过滤了类似的答案 
        System.out.println("count: " + count);
    }
    
    public int printNumber(int i){
        if(i == 0){
            return aArray[0];
        }
        if(i == 1){
            return bArray[0];
        }
        if(i == 2){
            return cArray[0];
        }
        if(i == 3){
            return dArray[0];
        }
        return 0;
    }
    
    public String printSymbol(int i){
        
        if(i == 0){
            return " + ";
        }
        if(i == 1){
            return " - ";
        }
        if(i == 2){
            return " * ";
        }
        if(i == 3){
            return " / ";
        }
        return "";
    }
}