求给定最大长度的Pythogorean三重和

Question

最近，我一直无法找到解决问题的办法。我的代码在这个过程中跳过了某些Pythagorean三胞胎，因此给出了不正确的和。

例如，如果我给出最大长度15 (低音不能大于这个数字)。

它将印刷：

3-4-5

5-12-13

然而，有三个毕达哥拉斯三重奏，给定的最大边长为15：

3-4-5

8-6-10 -我错过了这个：

5-12-13

我理解手头的问题，但不确定如何创建有效的解决方案(而不需要创建不必要的循环)。也许有人可以为我指明正确的方向，并在可能的情况下简化我的代码。我总是愿意学习！

class toymeister{

public static void main(String args[]){
    int inputLength = 15;

    System.out.println("Given the length: " + inputLength + 
        " the sum of the pythagorean triplets in the given range is: " 
        + sumTripletsGivenLength(inputLength));
}

public static int sumTripletsGivenLength(int length){
    boolean isFinished = false;
    int m,n = 0;
    int sum=0;

    while(!isFinished){
        n++; {
            m=n+1; {

                int a,b,c;

                a = m*m - n*n;
                b = 2*m*n;
                c = m*m + n*n;

                if(c<length){
                    System.out.println(a + "-" + b + "-" + c);
                    sum = sum+a+b+c;
                } else {
                    isFinished = true;
                }
            }
        }
    }
    return sum;
}
}

Answer 1

下面是sumTripletsGivenLength()方法的一个工作实现：

public static int sumTripletsGivenLength(int length){
    int sum = 0;

    // the two for loops below are structured such that duplicate pairs
    // of values, e.g. (3, 4) and (4, 3), do not occur
    for (int a=1; a < length; ++a) {
        for (int b=a; b < length; ++b) {
            // calculate hypotenuse 'c' for each combintation of 'a' and 'b'
            double c = Math.sqrt(Math.pow(a, 2.0) + Math.pow(b, 2.0));

            // check if 1) 'c' be a whole number, and 2) its length is within range
            if (c == Math.ceil(c) && c < length) {
                sum = a + b + (int)c;
                System.out.println(a + "-" + b + "-" + (int)c);
            }
        }
    }

    return sum;
}

public static void main(String args[]) {
    int inputLength = 15;

    System.out.println("Given the length: " + inputLength + 
        " the sum of the pythagorean triplets in the given range is: " 
        + sumTripletsGivenLength(inputLength));
}

输出：

3-4-5
5-12-13
6-8-10
Given the length: 15 the sum of the pythagorean triplets in the given range is: 24