zoukankan      html  css  js  c++  java
  • CodeForces

    Katya studies in a fifth grade. Recently her class studied right triangles and the Pythagorean theorem. It appeared, that there are triples of positive integers such that you can construct a right triangle with segments of lengths corresponding to triple. Such triples are called Pythagorean triples.

    For example, triples (3, 4, 5), (5, 12, 13) and (6, 8, 10) are Pythagorean triples.

    Here Katya wondered if she can specify the length of some side of right triangle and find any Pythagorean triple corresponding to such length? Note that the side which length is specified can be a cathetus as well as hypotenuse.

    Katya had no problems with completing this task. Will you do the same?

    Input

    The only line of the input contains single integer n (1 ≤ n ≤ 109) — the length of some side of a right triangle.

    Output

    Print two integers m and k (1 ≤ m, k ≤ 1018), such that nm and k form a Pythagorean triple, in the only line.

    In case if there is no any Pythagorean triple containing integer n, print  - 1 in the only line. If there are many answers, print any of them.

    Examples

    Input
    3
    Output
    4 5
    Input
    6
    Output
    8 10
    Input
    1
    Output
    -1
    Input
    17
    Output
    144 145
    Input
    67
    Output
    2244 2245


    构造直角三角形,设已知边为x,另两条边分别为x,y。
    则有a*a=y*y-x*x.即a*a=(y-x)(y+x),令A=y-x,B=y+x;
    解得 x=(A+B)/2,y=(A-B)/2.

    现在判断什么样的A,B可使x和y是整数。
    分类讨论,当a*a是偶数的时候,A=2,B=a*a/2.
    当a*a是奇数的时候,A=1,B=a*a.

    若解不出来,则输出-1.

     1 #include<cstdio>
     2 #include<cstdlib>
     3 #include<cstring>
     4 #include<string>
     5 #include<cmath>
     6 #include<algorithm>
     7 #include<queue>
     8 #include<stack>
     9 #include<deque>
    10 #include<map>
    11 #include<iostream>
    12 using namespace std;
    13 typedef long long  LL;
    14 const double pi=acos(-1.0);
    15 const double e=exp(1);
    16 const int N = 10;
    17 
    18 int main()
    19 {
    20     LL i,p,j;
    21     LL x,y,a;
    22     scanf("%lld",&a);
    23     if(a%2==0)
    24     {
    25         x=(a*a/2-2)/2;
    26         y=(a*a/2+2)/2;
    27         if(x<=0||y<=0||x==y)
    28             printf("-1
    ");
    29         else
    30             printf("%lld %lld
    ",x,y);
    31     }
    32     else
    33     {
    34         x=(a*a-1)/2;
    35         y=(a*a+1)/2;
    36         if(x<=0||y<=0||x==y)
    37             printf("-1
    ");
    38         else
    39             printf("%lld %lld
    ",x,y);
    40     }
    41     return 0;
    42 }
    View Code


  • 相关阅读:
    formValidator表单验证
    js中判断一个对象的类型的种种方法
    利用jQuery中的serialize方法大量获取页面中表单的数据,发送的服务器
    用html和css写一个头部header和左侧菜单栏menu-bar固定的的页面
    关于刚才那个全选问题的解决
    关于input[type='checkbox']全选的问题
    用CSS来定义<p>标签,要求实现以下效果:字体颜色再IE6下为黑色,IE7下为红色,IE8下为绿色,其他浏览器下为黄色。
    Vue.js(20)之 封装字母表(是这个名字吗0.0)
    Vue.js之calendar组件
    书:构造器模式
  • 原文地址:https://www.cnblogs.com/daybreaking/p/9691104.html
Copyright © 2011-2022 走看看