C# 24点游戏求解
1.24点游戏规则及算法
规则：给出4个自然数，找出能够求出24的四则运算式，要求数字不能重复使用
分析：
本算法是一种暴力求解法：
给出任意两个数字，可以进行6种四则运算，求出最多6个值。以数字a和b为例，有：
加（a+b）、减（a-b）、被减（b-a）、乘以（a*b）、除以(a/b)和除(b/a)
abcd共计四个数，如果顺序固定，则有5种计算顺序（★代表上面6种四则运算中的一种）：
((a★b)★c)★d、(a★b)★(c★d)、(a★(b★c))★d、a★((b★c)★d)、a★(b★(c★d))
给出的四个数字，n1n2n3n4，有4*3*2=24种全排列的方法
2.相关函数
/// <summary>
/// 判断abcd四个数进行任意四则运算后能不能得出24，每个数字只能用一次
/// </summary>
/// <param name="a">数字a</param>
/// <param name="b">数字b</param>
/// <param name="c">数字c</param>
/// <param name="d">数字d</param>
/// <param name="expression"></param>
/// <returns></returns>
private static bool Try24(int a, int b, int c, int d, ref string expression)
{
//a字头
if (TryEach(a, b, c, d, ref expression)) return true;
if (TryEach(a, b, d, c, ref expression)) return true;
if (TryEach(a, c, b, d, ref expression)) return true;
if (TryEach(a, c, d, b, ref expression)) return true;
if (TryEach(a, d, b, c, ref expression)) return true;
if (TryEach(a, d, c, b, ref expression)) return true;
//b字头
if (TryEach(b, a, c, d, ref expression)) return true;
if (TryEach(b, a, d, c, ref expression)) return true;
if (TryEach(b, c, a, d, ref expression)) return true;
if (TryEach(b, c, d, a, ref expression)) return true;
if (TryEach(b, d, a, c, ref expression)) return true;
if (TryEach(b, d, c, a, ref expression)) return true;
//c字头
if (TryEach(c, a, b, d, ref expression)) return true;
if (TryEach(c, a, d, b, ref expression)) return true;
if (TryEach(c, b, a, c, ref expression)) return true;
if (TryEach(c, b, c, a, ref expression)) return true;
if (TryEach(c, d, a, b, ref expression)) return true;
if (TryEach(c, d, b, a, ref expression)) return true;
//d字头
if (TryEach(d, a, b, c, ref expression)) return true;
if (TryEach(d, a, c, b, ref expression)) return true;
if (TryEach(d, b, a, c, ref expression)) return true;
if (TryEach(d, b, c, a, ref expression)) return true;
if (TryEach(d, c, a, b, ref expression)) return true;
if (TryEach(d, c, b, a, ref expression)) return true;
return false;
}
/// <summary>
/// 判断指定顺序的四个数abcd进行任意四则运算后能不能得出24，每个数字只能用一次
/// </summary>
/// <param name="a">数字1</param>
/// <param name="b">数字2</param>
/// <param name="c">数字3</param>
/// <param name="d">数字4</param>
/// <param name="expression"></param>
/// <returns></returns>
private static bool TryEach(int a, int b, int c, int d, ref string expression)
{
expression = "";
//两个数可以做6种运算：加、减、被减、乘以、除以、除
//四个数共可以进行6*6*6=216种不同次序的四则运算
//初始化数组
for (int i = 0; i < 6 * 6 * 6; i++)
{
//a与b间的运算符：i / 36
//b与c间的运算符：i % 36 / 6
//c与d间的运算符：i % 6
//1.运算顺序：a和b，再和c，再和d
{
string expression1 = "", expression2 = "";
int temp1 = ResultOf(a, b, i / 36, ref expression1);
int temp2 = ResultOf(temp1, c, i % 36 / 6, ref expression2, expression1);
int result = ResultOf(temp2, d, i % 6, ref expression, expression2);
if (result == 24) return true;
}
//2.运算顺序：a和b，c和d，前面部分和后面部分
{
string expression1 = "", expression2 = "";
int temp1 = ResultOf(a, b, i / 36, ref expression1);
int temp2 = ResultOf(c, d, i % 6, ref expression2);
int result = ResultOf(temp1, temp2, i % 36 / 6,
ref expression, expression1, expression2);
if (result == 24) return true;
}
//3.运算顺序：b和c运算，再与a运算，再与d运算
{
string expression1 = "", expression2 = "";
int temp1 = ResultOf(b, c, i % 36 / 6, ref expression1);
int temp2 = ResultOf(a, temp1, i / 36, ref expression2, "", expression1);
int result = ResultOf(temp2, d, i % 6, ref expression, expression2);
if (result == 24) return true;
}
//4.运算顺序：b和c运算，再与d运算，再与a运算
{
string expression1 = "", expression2 = "";
int temp1 = ResultOf(b, c, i % 36 / 6, ref expression1);
int temp2 = ResultOf(temp1, d, i % 6, ref expression2, expression1);
int result = ResultOf(a, temp2, i / 36, ref expression, "", expression2);
if (result == 24) return true;
}
//5.运算顺序：c和d运算，再和b运算，再和a运算
{
string expression1 = "", expression2 = "";
int temp1 = ResultOf(c, d, i % 6, ref expression1);
int temp2 = ResultOf(b, temp1, i % 36 / 6, ref expression2, "", expression1);
int result = ResultOf(a, temp2, i / 36, ref expression, "", expression2);
if (result == 24) return true;
}
}
expression = "Abandoned";
return false;
}
/// <summary>
/// 求两数进行某一四则运算后的结果
/// </summary>
/// <param name="x">数字1</param>
/// <param name="y">数字2</param>
/// <param name="method">（0-5分别代表：加、减、被减、乘以、除以、除）</param>
/// <param name="expression">返回的表达式</param>
/// <param name="expressionLeft">数字1表达式</param>
/// <param name="expressionRight">数字2表达式</param>
/// <returns></returns>
private static int ResultOf(int x, int y, int method,
ref string expression, string expressionLeft = "", string expressionRight = "")
{
//左右表达式之前被判定为无效则不计算，除数为0时不计算
if (expressionLeft == "Abandoned" || expressionRight == "Abandoned" ||
(x == 0 && method == 5) || (y == 0 && method == 4))
{
expression = "Abandoned";
return -1;
}
int result = 0;
switch (method)
{
case 0:
{
//加
result = x + y;
expression = string.Format("{0}+{1}",
expressionLeft == "" ? x.ToString() : expressionLeft,
expressionRight == "" ? y.ToString() : expressionRight);
}
break;
case 1:
{
//减
result = x - y;
expression = string.Format("{0}-{1}",
expressionLeft == "" ? x.ToString() : expressionLeft,
expressionRight == "" ? y.ToString() : expressionRight);
}
break;
case 2:
{
//被减
result = y - x;
expression = string.Format("{1}-{0}",
expressionLeft == "" ? x.ToString() : expressionLeft,
expressionRight == "" ? y.ToString() : expressionRight);
}
break;
case 3:
{
//乘以
result = x * y;
expression = string.Format("({0})*({1})",
expressionLeft == "" ? x.ToString() : expressionLeft,
expressionRight == "" ? y.ToString() : expressionRight);
}
break;
case 4:
{
//除以
if (x % y == 0)
{
result = x / y;
expression = string.Format("({0})/({1})",
expressionLeft == "" ? x.ToString() : expressionLeft,
expressionRight == "" ? y.ToString() : expressionRight);
}
else
{
expression = "Abandoned";
}
}
break;
case 5:
{
//除
if (y % x == 0)
{
result = y / x;
expression = string.Format("({1})/({0})",
expressionLeft == "" ? x.ToString() : expressionLeft,
expressionRight == "" ? y.ToString() : expressionRight);
}
else
{
expression = "Abandoned";
}
}
break;
}
//运算不合法，则返回-1，表达式为Abandoned，
if (expression == "Abandoned")
{
return -1;
}
return result;
}
3.Main函数调用
static void Main(string[] args)
{
string s = "";
bool try24;
try24 = Try24(1, 2, 3, 4, ref s); Console.WriteLine("1,2,3,4: " + s);
try24 = Try24(1, 3, 5, 7, ref s); Console.WriteLine("1,3,5,7: " + s);
try24 = Try24(2, 3, 6, 4, ref s); Console.WriteLine("2,3,6,4: " + s);
try24 = Try24(5, 7, 9, 4, ref s); Console.WriteLine("5,7,9,4: " + s);
try24 = Try24(6, 3, 4, 5, ref s); Console.WriteLine("6,3,4,5: " + s);
try24 = Try24(9, 5, 2, 7, ref s); Console.WriteLine("9,5,2,7: " + s);
try24 = Try24(4, 9, 8, 3, ref s); Console.WriteLine("4,9,8,3: " + s);
try24 = Try24(4, 9, 8, 2, ref s); Console.WriteLine("4,9,8,2: " + s);
try24 = Try24(10, 10, 10, 10, ref s); Console.WriteLine("10,10,10,10: " + s);
Console.ReadLine();
}
4.程序运行结果
