小浩算法|一文讓你學會如何用代碼判斷"24"點

時間 2020-02-27

標籤算法一文讓你學會如何代碼判斷简体版

原文原文鏈接

「24點」是一種數學遊戲，正如象棋、圍棋同樣是一種人們喜聞樂見的娛樂活動。它始於何年何月已無從考究，但它以本身獨具的數學魅力和豐富的內涵正逐漸被愈來愈多的人們所接受。今天就爲你們分享一道關於「24點」的算法題目。算法

話很少說，直接看題。編程

題目：你有 4 張寫有 1 到 9 數字的牌。你須要判斷是否能經過 *，/，+，-，(，) 的運算獲得 24。學習

示例 1：
輸入: [4, 1, 8, 7]spa

輸出: Truecode

解釋: (8-4) * (7-1) = 24blog

示例 2：遊戲

輸入: [1, 2, 1, 2]rem

輸出: False數學

注意：it

除法運算符 / 表示實數除法，而不是整數除法。例如：4 / (1 - 2/3) = 12 。
每一個運算符對兩個數進行運算。特別是咱們不能用 - 做爲一元運算符。例如，[1, 1, 1, 1] 做爲輸入時，表達式 -1 - 1 - 1 - 1 是不容許的。
你不能將數字鏈接在一塊兒。例如，輸入爲 [1, 2, 1, 2] 時，不能寫成 12 + 12 。

題目分析

拿到題目，第一反應就能夠想到暴力求解。若是咱們要判斷給出的4張牌是否能夠經過組合獲得24，那咱們只需找出全部的可組合的方式進行遍歷。

4個數字，3個操做符，外加括號，基本目測就能想到組合數不會大到超出邊界。因此，咱們只要把他們通通列出來，不就能夠進行求解了嗎？說幹就幹！

咱們首先定義個方法，用來判斷兩個數的的全部操做符組合是否能夠獲得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 
}

可是這個方法寫的正確嗎？其實不對！由於在計算機中，實數在計算和存儲過程當中會有一些微小的偏差，對於一些與零做比較的語句來講，有時會因偏差而致使本來是等於零但結果卻小於或大於零之類的狀況發生，因此經常使用一個很小的數 1e-6 代替 0，進行判讀！

(1e-6：表示1乘以10的負6次方。Math.abs(x)<1e-6 其實至關於x==0。1e-6(也就是0.000001)叫作epslon，用來抵消浮點運算中由於偏差形成的相等沒法判斷的狀況。這個知識點須要掌握！)

舉個例子：

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

這裏直接用 a==0 就會獲得false，可是經過 a < 1e-6 && a > -(1e-6) 卻能夠進行準確的判斷。

因此咱們將上面的方法改寫：

//go語言
 //judgePoint24_2：判斷兩個數的全部操做符組合是否能夠獲得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) 
}

完善了經過兩個數來判斷是否能夠獲得24的方法，如今咱們加一個判斷三個數是否能夠獲得24的方法。

//硬核代碼，不服來辯！
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。三個數的也出來了，咱們再加一個判斷4個數爲24點的方法：（排列組合，我想你們都會....）

前方高能！！！

//硬核代碼，不服來辯！
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語言示例

搞定收工，咱們整合所有代碼以下：

//硬核編程...
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)
}

因爲代碼過於硬核，

咱們直接擊敗100%的對手：

（沒想到吧！代碼還能夠這麼寫~）