以編程來解kenchung的數學比賽

4년 전

參加了 @kenchung 的 「數學 × 程式編寫比賽 (第七回)」,大家可以到這裡看看他的比賽: https://steemit.com/contest/@kenchung/question-mathematics-programming-competition-7

這是我第一次參加cn區的比賽呢! 請先看問題:

在一個正方形內隨機選取一點,並將此點與四個頂點連上直線,從而將正方形分割為四個三角形。求四個三角形之中所有內角均不超過 120° 的概率,答案準確至小數點後 3 位。

我不懂數學的解法,因此只好用程式來做。方法是不斷隨機地在正方形內抽出一點,然後用cosine theorem (怎樣也要使用一點點數學,@kenchung 真狡猾 haha) 來計算是否有超過 120° 的內角。

程式如下:

function cosThm(x1, y1, x2, y2, x3, y3){
    a = Math.sqrt((x1-x2)*(x1-x2) + (y1-y2)*(y1-y2)); 
    b = Math.sqrt((x1-x3)*(x1-x3) + (y1-y3)*(y1-y3)); 
    return Math.acos((a*a + b*b - 1)/(2 * a * b))/Math.PI * 180;
}

const numLoop = 10000000;
var count = 0;

for (var i=0; i<numLoop; i++){
    x = Math.random();
    y = Math.random();
    if (cosThm(x, y, 0, 0, 1, 0) < 120 && cosThm(x, y, 0, 0, 0, 1) < 120 && cosThm(x, y, 0, 1, 1, 1) < 120 && cosThm(x, y, 1, 0, 1, 1) < 120) count++;
}
console.log(count/numLoop);

當時的輸出是 0.2126132

當然不太放心啦,於是就再運行了幾次,得出的頭3位小數都是0.213 (四捨五入後)

希望能得獎啦,謝謝!

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不錯啊,你的程式挺簡單,可能要比數學方法還要快呢~

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加油加油!学习了。

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