24點破解的Java實現

一、基本思想

要想計算24點游戲的結果，則必須要采用基於搜索的算法（即窮舉法）對每種情況進行遍歷，我們怎麼樣才能遍歷所有的情況呢？其實我們只要總結一下，還是有規律可以找的。

輸入a、b、c、d，組成a Op1 bOp2 c Op3 d的表達式，其中先算哪個子表達式未知，一共有5種計算方式，如下圖所示：

此時如果要實現該程序，需要存儲5棵樹，為了能夠使得存儲量達到最小，通過分析，其實總的來說，只需要存儲2棵樹即可，即：

其他樹都是冗余的，因為我們可以通過a、b、c、d的交換，比如((a+(b*c))+d)可以變為(((b*c)+a)+d)；

對於每棵樹來說，abcd的可能性為4*3*2*1=24;op1op2 op3的可能性為4*4*4=64,因此總個數為1536，而兩棵樹的總個數為3072。因此只需要窮舉這些方法，就可以知道結果。

TfUtils類為實現窮舉24點所有可能情況的類，calculate函數用於計算，參數a、b、c、d分別為給定的4個數，而TfUtils類中的expr屬性為求解的表達式。

二、代碼實現

CalculatorUtils.java

1. package org.xiazdong;  
2.   
3. import java.util.Stack;  
4.   
5. public class CalculatorUtils {  
6.   
7.     /** 
8.      * 計算後綴表達式 
9.      */  
10.     public static String calculateReversePolish(String str) {  
11.   
12.         String[] splitStr = str.split(" ");  
13.         Stack<String> s = new Stack<String>();  
14.         for (int i = 0; i < splitStr.length; i++) {  
15.             String ch = splitStr[i];  
16.             if (ch.matches("\\d+.\\d+")||ch.matches("\\d+")) {  
17.                 s.push(ch);  
18.             } else {  
19.                 if (s.size() >= 2) {  
20.                     String c1 = s.pop();  
21.                     String c2 = s.pop();  
22.                     if (ch.equals("+")) {  
23.                         if(c1.contains(".")||c2.contains(".")){  
24.                             s.push(String.valueOf((Double.parseDouble(c2 + "") + Double  
25.                                 .parseDouble(c1 + ""))));  
26.                         }  
27.                         else{  
28.                             s.push(String.valueOf((Integer.parseInt(c2 + "") + Integer  
29.                                     .parseInt(c1 + ""))));  
30.                         }  
31.                           
32.                     } else if ("-".equals(ch)) {  
33.                         if(c1.contains(".")||c2.contains(".")){  
34.                         s.push(String.valueOf((Double.parseDouble(c2 + "") - Double  
35.                                 .parseDouble(c1 + ""))));  
36.                         }  
37.                         else{  
38.                             s.push(String.valueOf((Integer.parseInt(c2 + "") - Integer  
39.                                     .parseInt(c1 + ""))));  
40.                         }  
41.                     } else if ("*".equals(ch)) {  
42.                         if(c1.contains(".")||c2.contains(".")){  
43.                         s.push(String.valueOf((Double.parseDouble(c2 + "") * Double  
44.                                 .parseDouble(c1 + ""))));  
45.                         }  
46.                         else{  
47.                             s.push(String.valueOf((Integer.parseInt(c2 + "") * Integer  
48.                                     .parseInt(c1 + ""))));  
49.                         }  
50.                     } else if ("/".equals(ch)) {  
51.                         s.push(String.valueOf((Double.parseDouble(c2 + "") / Double  
52.                                 .parseDouble(c1 + ""))));  
53.                     }  
54.   
55.                 } else {  
56.                     System.out.println("式子有問題!");  
57.                     return null;  
58.                 }  
59.             }  
60.         }  
61.         return s.pop();  
62.     }  
63. }  

TfUtils.java

1. package org.xiazdong;  
2.   
3. import java.io.Serializable;  
4.   
5. public class TfUtils implements Serializable{  
6.     private int result;  
7.     private String expr = "";   //存放中綴表達式   
8.       
9.     public String getExpr() {  
10.         return expr;  
11.     }  
12.   
13.     public void setExpr(String expr) {  
14.         this.expr = expr;  
15.     }  
16.   
17.     /* 
18.                         (操作符1) 
19.                         /      \  
20.                    (操作符2) (操作數4)  
21.                    /     \  
22.               (操作符3)  (操作數3)  
23.                /     \  
24.           (操作數1) (操作數2) 
25.      */  
26.     private int tree1[] = new int[7];; // 存放第一棵樹   
27.     //private int tree2[]; // 存放第二棵樹   
28.     private final int PLUS = 1; // 加   
29.     private final int MINUS = 2; // 減   
30.     private final int MULT = 3; // 乘   
31.     private final int DIV = 4; // 除   
32.   
33.     /** 
34.      * 計算24點的主函數 
35.      */  
36.     public void calculate(int a, int b, int c, int d) {  
37.   
38.         int data[] = { a, b, c, d };  
39.   
40.           
41.         // 1.用數組構建一棵樹，其中0,1,3處填操作符；2,4,5,6填充操作數   
42.         // 2.按照參數a,b,c,d不同順序填充樹，+-*/也填充   
43.         for (int h = 0; h < 4; h++) {  
44.             for (int i = 0; i < 4; i++) {  
45.                 if (i == h) {  
46.                     continue;  
47.                 }  
48.                 for (int j = 0; j < 4; j++) {  
49.                     if (j == i || j == h) {  
50.                         continue;  
51.                     }  
52.                     for (int k = 0; k < 4; k++) {  
53.                         if (k == h || k == i || k == j) {  
54.                             continue;  
55.                         }  
56.                         tree1[2] = data[h];  
57.                         tree1[4] = data[i];  
58.                         tree1[5] = data[j];  
59.                         tree1[6] = data[k];  
60.   
61.                         // 填充操作符   
62.                         for (int m = PLUS; m <= DIV; m++) {  
63.                             for (int n = PLUS; n <= DIV; n++) {  
64.                                 for (int o = PLUS; o <= DIV; o++) {  
65.                                     tree1[0] = m;  
66.                                     tree1[1] = n;  
67.                                     tree1[3] = o;  
68.                                     String t[] = new String[4];  
69.                                     for (int z = 0; z < 4; z++) {  
70.                                         switch (tree1[z]) {  
71.                                         case PLUS:  
72.                                             t[z] = "+";  
73.                                             break;  
74.                                         case MINUS:  
75.                                             t[z] = "-";  
76.                                             break;  
77.                                         case MULT:  
78.                                             t[z] = "*";  
79.                                             break;  
80.                                         case DIV:  
81.                                             t[z] = "/";  
82.                                             break;  
83.                                         }  
84.                                     }  
85.   
86.                                     // 目前為止tree數組全部已賦值   
87.                                     String postexpr = tree1[5] + " " + tree1[6]  
88.                                             + " " + t[3] + " " + tree1[4] + " "  
89.                                             + t[1] + " " + tree1[2] + " " + t[0];  
90.                                     String result = CalculatorUtils  
91.                                             .calculateReversePolish(postexpr);  
92.                                     if (Double.parseDouble((result)) == 24.0) {  
93.                                         expr = "(((" + tree1[5] + t[3] + tree1[6]  
94.                                                 + ")" + t[1] + tree1[4] + ")"  
95.                                                 + t[0] + tree1[2] + ")";  
96.                                         System.out.println(expr);  
97.                                         return;  
98.                                     }  
99.                                 }  
100.                             }  
101.                         }  
102.                     }  
103.                 }  
104.             }  
105.         }  
106.         //tree2 = new int[7];   
107.         for (int h = 0; h < 4; h++) {  
108.             for (int i = 0; i < 4; i++) {  
109.                 if (i == h) {  
110.                     continue;  
111.                 }  
112.                 for (int j = 0; j < 4; j++) {  
113.                     if (j == i || j == h) {  
114.                         continue;  
115.                     }  
116.                     for (int k = 0; k < 4; k++) {  
117.                         if (k == h || k == i || k == j) {  
118.                             continue;  
119.                         }  
120.                         tree1[3] = data[h];  
121.                         tree1[4] = data[i];  
122.                         tree1[5] = data[j];  
123.                         tree1[6] = data[k];  
124.   
125.                         // 填充操作符   
126.                         for (int m = PLUS; m <= DIV; m++) {  
127.                             for (int n = PLUS; n <= DIV; n++) {  
128.                                 for (int o = PLUS; o <= DIV; o++) {  
129.                                     tree1[0] = m;  
130.                                     tree1[1] = n;  
131.                                     tree1[2] = o;  
132.                                     String t[] = new String[3];  
133.                                     for (int z = 0; z < 3; z++) {  
134.                                         switch (tree1[z]) {  
135.                                         case PLUS:  
136.                                             t[z] = "+";  
137.                                             break;  
138.                                         case MINUS:  
139.                                             t[z] = "-";  
140.                                             break;  
141.                                         case MULT:  
142.                                             t[z] = "*";  
143.                                             break;  
144.                                         case DIV:  
145.                                             t[z] = "/";  
146.                                             break;  
147.                                         }  
148.                                     }  
149.                                     // 目前為止tree數組全部已賦值   
150.                                     String postexpr = tree1[4] + " " + tree1[3]  
151.                                             + " " + t[1] + " " + tree1[6] + " "  
152.                                             + tree1[5] + " " + t[2] + " " + t[0];  
153.                                     String result = CalculatorUtils  
154.                                             .calculateReversePolish(postexpr);  
155.                                     if (Double.parseDouble((result)) == 24.0) {  
156.                                         expr = "((" + tree1[3] + t[1] + tree1[4]  
157.                                                 + ")" + t[0] +"("+tree1[5]  
158.                                                 + t[2] + tree1[6] + "))";  
159.                                         System.out.println(expr);  
160.                                         return;  
161.                                     }  
162.                                 }  
163.                             }  
164.                         }  
165.                     }  
166.                 }  
167.             }  
168.         }  
169.         expr = "無解";  
170.     }  
171.   
172.     public int getResult() {  
173.         return result;  
174.     }  
175.   
176.     public void setResult(int result) {  
177.         this.result = result;  
178.     }  
179.   
180.   
181.       
182. }  

測試代碼：

1. TfUtils tf = new TfUtils();  
2. tf.calculate(d1, d2, d3, d4);  
3. System.out.println(tf.getExpr());  

輸入為：3,3,7,7

輸出為：（（（3/7）+3）*7）