算法8：已知 a^2+b^2=c^2（a,b,c 为自然数,a<b<c），且a+b+c=1000，求abc的值?

 

 

已知  a^2+b^2=c^2（a,b,c 为自然数,a<b<c），且a+b+c=1000，求abc的值?

 

    public static int getABC() {
        int resVal = 1;
        for (int a = 0; a <= 1000; a++) {
            for (int b = 1; b <= 1000; b++) {
                for (int c = 2; c <= 1000; c++) {
                    if (a * a + b * b == c * c && a + b + c == 1000 && a < b && b < c) {
                        resVal = a * b * c;

                        System.out.println("[a = " + a + ", b = " + b + ", c = " + c + "]");
                        System.out.println("=>  a^2 + b^2 = " + (a * a + b * b) + " = c^2 = " + c * c);
                        System.out.println("=>  a + b + c = " + (a + b + c));
                        System.out.println("=>  a * b * c = " + (a * b * c));
                    }
                }
            }
        }
        return resVal;
    }

    public static void main(String[] args) {
        getABC();
    }

 

 

结果：

[a = 200, b = 375, c = 425]
=> a^2 + b^2 = 180625 = c^2 = 180625
=> a + b + c = 1000
=> a * b * c = 31875000