C# 24点游戏求解算法
经常跟儿子玩24点，有时候比较难算的，算一会儿，两人算不出来，就收了，当作没法算。
以我的数学能力，一般来说，算不出来的，大概率确实是算不出来的。
但是遇到比较变态的，当作算不出来是可能的，所以一直想找一个直接能解24点的程序。
可是网上找了一圈，一直没找到。
想着自己写一个，可是这里面的逻辑一直理不清楚，不知道这个算法应该怎么写。
下午坐在电脑前面想的时候，不知道为啥，像是突然开窍了。写着写着居然写出来了。
贴出来供有兴趣的朋友参考，有问题请指正。
using System;
using System.Collections.Generic;
using System.Diagnostics;
namespace Calc24Point
{
internal class Program
{
private static void Main(string[] args)
{
var items = CalcHelper.CalcResult(3, 3, 8, 8);
foreach (var item in items)
{
Console.WriteLine(item);
}
Console.ReadKey();
}
}
public class CalcHelper
{
public static List<string> CalcResult(double a, double b, double c, double d)
{
List<string> myList = new List<string>();
List<CalcInfo> items = MakeCalcs(a, b, c, d);
foreach (var item in items)
{
var result = item.GetResult();
if (double.IsNaN(result) == false && IsEqual(result, 24))
{
var text = item.GetString();
if (myList.Contains(text) == false)
{
myList.Add(text);
}
}
}
return myList;
}
private static bool IsEqual(double a, double b)
{
return Math.Abs(a - b) < 0.000001;
}
private static List<CalcInfo> MakeCalcs(double a, double b, double c, double d)
{
var items = new List<CalcInfo>();
items.AddRange(MakeCalcs(a, (b, c, d)));
items.AddRange(MakeCalcs(b, (a, c, d)));
items.AddRange(MakeCalcs(c, (b, a, d)));
items.AddRange(MakeCalcs(d, (b, c, a)));
return items;
}
private static IEnumerable<CalcInfo> MakeCalcs(double item1, (double b, double c, double d) p)
{
foreach (CalcInfo item2 in MakeCalcs(p.b, (p.c, p.d)))
{
yield return new CalcInfo(item1, item2, EMode.加);
yield return new CalcInfo(item1, item2, EMode.减);
yield return new CalcInfo(item2, item1, EMode.减);
yield return new CalcInfo(item1, item2, EMode.乘);
yield return new CalcInfo(item1, item2, EMode.除);
yield return new CalcInfo(item2, item1, EMode.除);
}
foreach (CalcInfo item2 in MakeCalcs(p.c, (p.b, p.d)))
{
yield return new CalcInfo(item1, item2, EMode.加);
yield return new CalcInfo(item1, item2, EMode.减);
yield return new CalcInfo(item2, item1, EMode.减);
yield return new CalcInfo(item1, item2, EMode.乘);
yield return new CalcInfo(item1, item2, EMode.除);
yield return new CalcInfo(item2, item1, EMode.除);
}
foreach (CalcInfo item2 in MakeCalcs(p.d, (p.b, p.c)))
{
yield return new CalcInfo(item1, item2, EMode.加);
yield return new CalcInfo(item1, item2, EMode.减);
yield return new CalcInfo(item2, item1, EMode.减);
yield return new CalcInfo(item1, item2, EMode.乘);
yield return new CalcInfo(item1, item2, EMode.除);
yield return new CalcInfo(item2, item1, EMode.除);
}
}
private static IEnumerable<CalcInfo> MakeCalcs(double item1, (double c, double d) p)
{
foreach (CalcInfo item2 in MakeCalcs(p.c, p.d))
{
yield return new CalcInfo(item1, item2, EMode.加);
yield return new CalcInfo(item1, item2, EMode.减);
yield return new CalcInfo(item2, item1, EMode.减);
yield return new CalcInfo(item1, item2, EMode.乘);
yield return new CalcInfo(item1, item2, EMode.除);
yield return new CalcInfo(item2, item1, EMode.除);
}
}
private static IEnumerable<CalcInfo> MakeCalcs(double item1, double item2)
{
yield return new CalcInfo(item1, item2, EMode.加);
yield return new CalcInfo(item1, item2, EMode.减);
yield return new CalcInfo(item2, item1, EMode.减);
yield return new CalcInfo(item1, item2, EMode.乘);
yield return new CalcInfo(item1, item2, EMode.除);
yield return new CalcInfo(item2, item1, EMode.除);
}
}
public class CalcInfo
{
public CalcInfo Items1 { get; set; }
public CalcInfo Items2 { get; set; }
public EMode? Mode { get; set; }
public double Result { get; set; }
public CalcInfo(double value)
{
Result = value;
}
public CalcInfo(double value1, double value2, EMode mode) : this(new CalcInfo(value1), new CalcInfo(value2), mode)
{
}
public CalcInfo(double value1, CalcInfo value2, EMode mode) : this(new CalcInfo(value1), value2, mode)
{
}
public CalcInfo(CalcInfo value1, double value2, EMode mode) : this(value1, new CalcInfo(value2), mode)
{
}
public CalcInfo(CalcInfo value1, CalcInfo value2, EMode mode)
{
Items1 = value1;
Items2 = value2;
Mode = mode;
}
public double GetResult()
{
if (Mode == null)
{
return Result;
}
var item1 = Items1.GetResult();
var item2 = Items2.GetResult();
if (double.IsNaN(item1) || double.IsNaN(item1))
{
return double.NaN;
}
switch (Mode.Value)
{
case EMode.加:
return item1 + item2;
case EMode.减:
return item1 - item2;
case EMode.乘:
return item1 * item2;
case EMode.除:
if (item2 == 0)
{
return double.NaN;
}
return item1 / item2;
default:
Debug.Assert(false);
break;
}
return double.NaN;
}
public string GetString()
{
if (Mode == null)
{
return Result.ToString();
}
switch (Mode.Value)
{
case EMode.加:
return $"({Items1.GetString()} + {Items2.GetString()})";
case EMode.减:
return $"({Items1.GetString()} - {Items2.GetString()})";
case EMode.乘:
return $"({Items1.GetString()} * {Items2.GetString()})";
case EMode.除:
return $"({Items1.GetString()} / {Items2.GetString()})";
default:
Debug.Assert(false);
break;
}
return null;
}
}
public enum EMode
{
加,
减,
乘,
除,
}
}
