如何运用算法实现“24点”数学游戏？
admin
2023-02-15 15:40:10
0次

“24点”是一种数学游戏，正如象棋、围棋一样是一种人们喜闻乐见的娱乐活动。它始于何年何月已无从考究，但它以自己独具的数学魅力和丰富的内涵正逐渐被越来越多的人们所接受。今天就为大家分享一道关于“24点”的算法题目。

话不多说，直接看题。

题目：你有 4 张写有 1 到 9 数字的牌。你需要判断是否能通过 *，/，+，-，(，) 的运算得到 24。

示例 1：

输入: [4, 1, 8, 7]

输出: True

解释: (8-4) * (7-1) = 24

示例 2：

输入: [1, 2, 1, 2]

输出: False

注意：

  • 除法运算符 / 表示实数除法，而不是整数除法。例如 ：4 / (1 - 2/3) = 12 。
  • 每个运算符对两个数进行运算。特别是我们不能用 - 作为一元运算符。例如，[1, 1, 1, 1] 作为输入时，表达式 -1 - 1 - 1 - 1 是不允许的。
  • 你不能将数字连接在一起。例如，输入为 [1, 2, 1, 2] 时，不能写成 12 + 12 。

题目分析

拿到题目，第一反应就可以想到暴li求解。如果我们要判断给出的4张牌是否可以通过组合得到24，那我们只需找出所有的可组合的方式进行遍历。

4个数字，3个操作符，外加括号，基本目测就能想到组合数不会大到超出边界。所以，我们只要把他们统统列出来，不就可以进行求解了吗？说干就干！

我们首先定义个方法，用来判断两个数的的所有操作符组合是否可以得到24。

func judgePoint24_2(a, b float64) bool {
    return a+b == 24 || a*b == 24 || a-b == 24 || b-a == 24 || a/b == 24 || b/a == 24 
}

但是这个方法写的正确吗？其实不对！因为在计算机中，实数在计算和存储过程中会有一些微小的误差，对于一些与零作比较的语句来说，有时会因误差而导致原本是等于零但结果却小于或大于零之类的情况发生，所以常用一个很小的数 1e-6 代替 0，进行判读！

(1e-6：表示1乘以10的负6次方。Math.abs(x)<1e-6 其实相当于x==0。1e-6(也就是0.000001)叫做epslon，用来抵消浮点运算中因为误差造成的相等无法判断的情况。这个知识点需要掌握！)

举个例子：

func main() {
    var a float64
    var b float64
    b = 2.0
    //math.Sqrt：开平方根
    c := math.Sqrt(2)
    a = b - c*c
    fmt.Println(a == 0)                  //false
    fmt.Println(a < 1e-6 && a > -(1e-6)) //true
}

这里直接用 a==0 就会得到false，但是通过 a < 1e-6 && a > -(1e-6) 却可以进行准确的判断。

所以我们将上面的方法改写：

 //go语言
 //judgePoint24_2：判断两个数的所有操作符组合是否可以得到24
 func judgePoint24_2(a, b float64) bool {
     return (a+b < 24+1e-6 && a+b > 24-1e-6) ||
         (a*b < 24+1e-6 && a*b > 24-1e-6) ||
         (a-b < 24+1e-6 && a-b > 24-1e-6) ||
         (b-a < 24+1e-6 && b-a > 24-1e-6) ||
         (a/b < 24+1e-6 && a/b > 24-1e-6) ||
         (b/a < 24+1e-6 && b/a > 24-1e-6) 
}

完善了通过两个数来判断是否可以得到24的方法，现在我们加一个判断三个数是否可以得到24的方法。

//硬核代码，不服来辩！
func judgePoint24_3(a, b, c float64) bool {
    return judgePoint24_2(a+b, c) ||
        judgePoint24_2(a-b, c) ||
        judgePoint24_2(a*b, c) ||
        judgePoint24_2(a/b, c) ||
        judgePoint24_2(b-a, c) ||
        judgePoint24_2(b/a, c) ||

        judgePoint24_2(a+c, b) ||
        judgePoint24_2(a-c, b) ||
        judgePoint24_2(a*c, b) ||
        judgePoint24_2(a/c, b) ||
        judgePoint24_2(c-a, b) ||
        judgePoint24_2(c/a, b) ||

        judgePoint24_2(c+b, a) ||
        judgePoint24_2(c-b, a) ||
        judgePoint24_2(c*b, a) ||
        judgePoint24_2(c/b, a) ||
        judgePoint24_2(b-c, a) ||
        judgePoint24_2(b/c, a)
}

好了。三个数的也出来了，我们再加一个判断4个数为24点的方法：（排列组合，我想大家都会....）

前方高能！！！

前方高能！！！

前方高能！！！

//硬核代码，不服来辩！
func judgePoint24(nums []int) bool {
    return judgePoint24_3(float64(nums[0])+float64(nums[1]), float64(nums[2]), float64(nums[3])) ||
        judgePoint24_3(float64(nums[0])-float64(nums[1]), float64(nums[2]), float64(nums[3])) ||
        judgePoint24_3(float64(nums[0])*float64(nums[1]), float64(nums[2]), float64(nums[3])) ||
        judgePoint24_3(float64(nums[0])/float64(nums[1]), float64(nums[2]), float64(nums[3])) ||
        judgePoint24_3(float64(nums[1])-float64(nums[0]), float64(nums[2]), float64(nums[3])) ||
        judgePoint24_3(float64(nums[1])/float64(nums[0]), float64(nums[2]), float64(nums[3])) ||

        judgePoint24_3(float64(nums[0])+float64(nums[2]), float64(nums[1]), float64(nums[3])) ||
        judgePoint24_3(float64(nums[0])-float64(nums[2]), float64(nums[1]), float64(nums[3])) ||
        judgePoint24_3(float64(nums[0])*float64(nums[2]), float64(nums[1]), float64(nums[3])) ||
        judgePoint24_3(float64(nums[0])/float64(nums[2]), float64(nums[1]), float64(nums[3])) ||
        judgePoint24_3(float64(nums[2])-float64(nums[0]), float64(nums[1]), float64(nums[3])) ||
        judgePoint24_3(float64(nums[2])/float64(nums[0]), float64(nums[1]), float64(nums[3])) ||

        judgePoint24_3(float64(nums[0])+float64(nums[3]), float64(nums[2]), float64(nums[1])) ||
        judgePoint24_3(float64(nums[0])-float64(nums[3]), float64(nums[2]), float64(nums[1])) ||
        judgePoint24_3(float64(nums[0])*float64(nums[3]), float64(nums[2]), float64(nums[1])) ||
        judgePoint24_3(float64(nums[0])/float64(nums[3]), float64(nums[2]), float64(nums[1])) ||
        judgePoint24_3(float64(nums[3])-float64(nums[0]), float64(nums[2]), float64(nums[1])) ||
        judgePoint24_3(float64(nums[3])/float64(nums[0]), float64(nums[2]), float64(nums[1])) ||

        judgePoint24_3(float64(nums[2])+float64(nums[3]), float64(nums[0]), float64(nums[1])) ||
        judgePoint24_3(float64(nums[2])-float64(nums[3]), float64(nums[0]), float64(nums[1])) ||
        judgePoint24_3(float64(nums[2])*float64(nums[3]), float64(nums[0]), float64(nums[1])) ||
        judgePoint24_3(float64(nums[2])/float64(nums[3]), float64(nums[0]), float64(nums[1])) ||
        judgePoint24_3(float64(nums[3])-float64(nums[2]), float64(nums[0]), float64(nums[1])) ||
        judgePoint24_3(float64(nums[3])/float64(nums[2]), float64(nums[0]), float64(nums[1])) ||

        judgePoint24_3(float64(nums[1])+float64(nums[2]), float64(nums[0]), float64(nums[3])) ||
        judgePoint24_3(float64(nums[1])-float64(nums[2]), float64(nums[0]), float64(nums[3])) ||
        judgePoint24_3(float64(nums[1])*float64(nums[2]), float64(nums[0]), float64(nums[3])) ||
        judgePoint24_3(float64(nums[1])/float64(nums[2]), float64(nums[0]), float64(nums[3])) ||
        judgePoint24_3(float64(nums[2])-float64(nums[1]), float64(nums[0]), float64(nums[3])) ||
        judgePoint24_3(float64(nums[2])/float64(nums[1]), float64(nums[0]), float64(nums[3])) ||

        judgePoint24_3(float64(nums[1])+float64(nums[3]), float64(nums[2]), float64(nums[0])) ||
        judgePoint24_3(float64(nums[1])-float64(nums[3]), float64(nums[2]), float64(nums[0])) ||
        judgePoint24_3(float64(nums[1])*float64(nums[3]), float64(nums[2]), float64(nums[0])) ||
        judgePoint24_3(float64(nums[1])/float64(nums[3]), float64(nums[2]), float64(nums[0])) ||
        judgePoint24_3(float64(nums[3])-float64(nums[1]), float64(nums[2]), float64(nums[0])) ||
        judgePoint24_3(float64(nums[3])/float64(nums[1]), float64(nums[2]), float64(nums[0]))
}

Go语言示例

搞定收工，我们整合全部代码如下：

//硬核编程...
func judgePoint24(nums []int) bool {
    return judgePoint24_3(float64(nums[0])+float64(nums[1]), float64(nums[2]), float64(nums[3])) ||
        judgePoint24_3(float64(nums[0])-float64(nums[1]), float64(nums[2]), float64(nums[3])) ||
        judgePoint24_3(float64(nums[0])*float64(nums[1]), float64(nums[2]), float64(nums[3])) ||
        judgePoint24_3(float64(nums[0])/float64(nums[1]), float64(nums[2]), float64(nums[3])) ||
        judgePoint24_3(float64(nums[1])-float64(nums[0]), float64(nums[2]), float64(nums[3])) ||
        judgePoint24_3(float64(nums[1])/float64(nums[0]), float64(nums[2]), float64(nums[3])) ||

        judgePoint24_3(float64(nums[0])+float64(nums[2]), float64(nums[1]), float64(nums[3])) ||
        judgePoint24_3(float64(nums[0])-float64(nums[2]), float64(nums[1]), float64(nums[3])) ||
        judgePoint24_3(float64(nums[0])*float64(nums[2]), float64(nums[1]), float64(nums[3])) ||
        judgePoint24_3(float64(nums[0])/float64(nums[2]), float64(nums[1]), float64(nums[3])) ||
        judgePoint24_3(float64(nums[2])-float64(nums[0]), float64(nums[1]), float64(nums[3])) ||
        judgePoint24_3(float64(nums[2])/float64(nums[0]), float64(nums[1]), float64(nums[3])) ||

        judgePoint24_3(float64(nums[0])+float64(nums[3]), float64(nums[2]), float64(nums[1])) ||
        judgePoint24_3(float64(nums[0])-float64(nums[3]), float64(nums[2]), float64(nums[1])) ||
        judgePoint24_3(float64(nums[0])*float64(nums[3]), float64(nums[2]), float64(nums[1])) ||
        judgePoint24_3(float64(nums[0])/float64(nums[3]), float64(nums[2]), float64(nums[1])) ||
        judgePoint24_3(float64(nums[3])-float64(nums[0]), float64(nums[2]), float64(nums[1])) ||
        judgePoint24_3(float64(nums[3])/float64(nums[0]), float64(nums[2]), float64(nums[1])) ||

        judgePoint24_3(float64(nums[2])+float64(nums[3]), float64(nums[0]), float64(nums[1])) ||
        judgePoint24_3(float64(nums[2])-float64(nums[3]), float64(nums[0]), float64(nums[1])) ||
        judgePoint24_3(float64(nums[2])*float64(nums[3]), float64(nums[0]), float64(nums[1])) ||
        judgePoint24_3(float64(nums[2])/float64(nums[3]), float64(nums[0]), float64(nums[1])) ||
        judgePoint24_3(float64(nums[3])-float64(nums[2]), float64(nums[0]), float64(nums[1])) ||
        judgePoint24_3(float64(nums[3])/float64(nums[2]), float64(nums[0]), float64(nums[1])) ||

        judgePoint24_3(float64(nums[1])+float64(nums[2]), float64(nums[0]), float64(nums[3])) ||
        judgePoint24_3(float64(nums[1])-float64(nums[2]), float64(nums[0]), float64(nums[3])) ||
        judgePoint24_3(float64(nums[1])*float64(nums[2]), float64(nums[0]), float64(nums[3])) ||
        judgePoint24_3(float64(nums[1])/float64(nums[2]), float64(nums[0]), float64(nums[3])) ||
        judgePoint24_3(float64(nums[2])-float64(nums[1]), float64(nums[0]), float64(nums[3])) ||
        judgePoint24_3(float64(nums[2])/float64(nums[1]), float64(nums[0]), float64(nums[3])) ||

        judgePoint24_3(float64(nums[1])+float64(nums[3]), float64(nums[2]), float64(nums[0])) ||
        judgePoint24_3(float64(nums[1])-float64(nums[3]), float64(nums[2]), float64(nums[0])) ||
        judgePoint24_3(float64(nums[1])*float64(nums[3]), float64(nums[2]), float64(nums[0])) ||
        judgePoint24_3(float64(nums[1])/float64(nums[3]), float64(nums[2]), float64(nums[0])) ||
        judgePoint24_3(float64(nums[3])-float64(nums[1]), float64(nums[2]), float64(nums[0])) ||
        judgePoint24_3(float64(nums[3])/float64(nums[1]), float64(nums[2]), float64(nums[0]))
}

func judgePoint24_3(a, b, c float64) bool {
    return judgePoint24_2(a+b, c) ||
        judgePoint24_2(a-b, c) ||
        judgePoint24_2(a*b, c) ||
        judgePoint24_2(a/b, c) ||
        judgePoint24_2(b-a, c) ||
        judgePoint24_2(b/a, c) ||

        judgePoint24_2(a+c, b) ||
        judgePoint24_2(a-c, b) ||
        judgePoint24_2(a*c, b) ||
        judgePoint24_2(a/c, b) ||
        judgePoint24_2(c-a, b) ||
        judgePoint24_2(c/a, b) ||

        judgePoint24_2(c+b, a) ||
        judgePoint24_2(c-b, a) ||
        judgePoint24_2(c*b, a) ||
        judgePoint24_2(c/b, a) ||
        judgePoint24_2(b-c, a) ||
        judgePoint24_2(b/c, a)
}

func judgePoint24_2(a, b float64) bool {
    return (a+b < 24+1e-6 && a+b > 24-1e-6) ||
        (a*b < 24+1e-6 && a*b > 24-1e-6) ||
        (a-b < 24+1e-6 && a-b > 24-1e-6) ||
        (b-a < 24+1e-6 && b-a > 24-1e-6) ||
        (a/b < 24+1e-6 && a/b > 24-1e-6) ||
        (b/a < 24+1e-6 && b/a > 24-1e-6)
}

由于代码过于硬核，

我们直接击败100%的对手：

（没想到吧！代码还可以这么写~）

如何运用算法实现“24点”数学游戏？


上一篇：golang快速入门[6.1]-集成开发环境-goland详解

下一篇：gem详解

相关内容

热门资讯

神龙拜耳光伏有限公司生产支架 光伏支架，到底“支”起了什么？ 提到光伏电站，很多人第一反应是那一块块深蓝色的电池板。但真正让这些电...
食品级制冰袋厂家选型指南：上海... 导语：在餐饮、物流、医药等行业中，制冰袋作为低温保鲜的核心耗材，其性能稳定性直接影响产品品质与运营效...
南通崇川发放首笔“算力券”补贴 购买、领券、付款……近日，随着在南通市公共算力服务平台算力超市完成中国移动算力服务的租用下单操作，江...
百万上下文之后，拼什么？ 文 | 科技不许冷 过去几天，科技圈的视线全被DeepSeek吸走了。 满屏都是传闻中的估值溢价，...
成语之都 好玩邯郸丨邯山区AI... （来源：邯郸新闻网） 转自：邯郸新闻网 近日，在邯山区科技创新产业园内的邯郸人工智能教育基地，一拨拨...
量子计算机联手超级计算机，创下... 5 月 5 日消息，量子计算机最具前景的应用方向之一是模拟蛋白质，助力人类研发新药，但目前这类设备误...
我国新一代人工智能技术加速落地... 2026 年 5 月 5 日，工信部、科技部、国家网信办联合发布《人工智能产业高质量发展行动计划（2...
老黄可能开始焦虑了 文 | 象先志 2026年4月15日，黄仁勋在Dwarkesh Patel 的播客里经历了一场他很...
俄外长与美国务卿通话，讨论双边... △鲁比奥（左）与拉夫罗夫（右）当地时间5月5日，据俄罗斯外交部消息，俄罗斯外长拉夫罗夫与美国国务卿鲁...
即使中东冲突今天停止，欧盟在未... 新华社布鲁塞尔5月5日电（记者康逸）欧盟能源委员丹·约根森5日警告说，由于伊朗战事以及霍尔木兹海峡遭...