求给定最大长度的Pythogorean三元组和

Question

最近我无法确定问题的解决方案。在这个过程中，我的代码跳过了某些勾股三元组，因此给出了错误的和。

例如，如果我给最大长度15（斜边不能大于这个数字）。

它将打印：

3-4-5

5-12-13

然而，有三个勾股三元组，给定的最大边长为15:

3-4-5

8-6-10-我错过了这个：（

5-12-13

我理解眼前的问题，但我不确定如何创建一个有效的解决方案（而不会创建不必要的循环）。也许有人可以为我指明正确的方向，如果可能的话，也许可以简化我的代码。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

以下是您的sumTripletsGivenLength()方法的工作实现：

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