找出直角三角形的其他两条边
给定直角三角形的一边，检查是否存在可能与三角形的任何其他两边成直角的三角形。如果可能的话打印其他两面的长度。 否则打印-1 注意:三角形的所有边必须是正整数
例 1:
Input : a = 3
Output : b = 4, c = 5
Explanation : a = 3, b = 4 and c = 5 form right
angle triangle because
32 + 42 = 9 + 16 = 25 = 52 => 32 + 42 = 52
例 2:
Input : a = 11
Output : b = 60, c = 61
Explanation : a = 11, b = 60 and c = 61 form
right angle triangle because
112 + 602 = 121 + 3600 = 3721 = 612 => 112 + 602 = 612
为了解决这个问题，我们首先观察毕达哥拉斯方程。如果 a 和 b 是直角三角形的边长，c 是斜边的长度，那么边长的平方和等于斜边长度的平方。
这种关系由以下公式表示:
a2 + b2 = c2
- 情况 1–a 是奇数:给定 a，求 b 和 c
c2 - b2 = a2
OR
c = (a2 + 1)/2;
b = (a2 - 1)/2;
- 上述解决方案仅适用于 a 为奇数的情况，因为 a 2 + 1 只能被奇数 a 的 2 整除。
- 情况 2–a 为偶数:当 c-b 为 2 时& c+b 为(a 2 )/2
c-b = 2 & c+b = (a2)/2
Hence,
c = (a2)/4 + 1;
b = (a2)/4 - 1;
当为偶数时，此方法有效。
这种解决方案不适用于 a = 1 和 a = 2 的情况，因为没有任何直角三角形的 1 边或 2 边都是整数边。
C++
// C++ program to print other two sides of right
// angle triangle given one side
#include <bits/stdc++.h>
using namespace std;
// Finds two sides of a right angle triangle
// if it exist.
void printOtherSides(int n)
{
// if n is odd
if (n & 1)
{
// case of n = 1 handled separately
if (n == 1)
cout << -1 << endl;
else
{
int b = (n*n-1)/2;
int c = (n*n+1)/2;
cout << "b = " << b
<< ", c = " << c << endl;
}
}
else
{
// case of n = 2 handled separately
if (n == 2)
cout << -1 << endl;
else
{
int b = n*n/4-1;
int c = n*n/4+1;
cout << "b = " << b
<< ", c = " << c << endl;
}
}
}
// Driver program to test above function
int main()
{
int a = 3;
printOtherSides(a);
return 0;
}
Java 语言(一种计算机语言，尤用于创建网站)
// Java program to print other two
// sides of right angle triangle
// given one side
class GFG
{
// Finds two sides of a right angle
// triangle if it they exist.
static void printOtherSides(int n)
{
// if n is odd
if (n % 2 != 0)
{
// case of n = 1 handled separately
if (n == 1)
System.out.println("-1");
else
{
int b = (n * n -1) / 2;
int c = (n *n +1) / 2;
System.out.println("b = "+ b +
", c = "+c);
}
}
else
{
// case of n = 2 handled separately
if (n == 2)
System.out.println("-1");
else
{
int b = n * n / 4 - 1;
int c = n * n / 4 + 1;
System.out.println("b = "+ b +
", c = "+c);
}
}
}
// Driver code
public static void main (String[] args)
{
int a = 3;
printOtherSides(a);
}
}
// This code is contributed by Anant Agarwal.
计算机编程语言
# Python program to print other
# two sides of right angle
# triangle given one side
# Finds two sides of a right angle
# triangle if it they exist.
def printOtherSides(n):
# if n is odd
if(n & 1):
# case of n = 1 handled
# separately
if(n == 1):
print(-1)
else:
b = (n * n - 1) // 2
c = (n * n + 1) // 2
print("b =", b, ", c =", c)
else:
# case of n = 2 handled
# separately
if(n == 2):
print(-1)
else:
b = n * n // 4 - 1
c = n * n // 4 + 1
print("b =", b", c =", c)
# Driver Code
a = 3
printOtherSides(a)
# This code is contributed by
# Sanjit_Prasad
C
// C# program to print other two
// sides of right angle triangle
// given one side
using System;
class GFG {
// Finds two sides of a right angle
// triangle if it they exist.
static void printOtherSides(int n)
{
// if n is odd
if (n % 2 != 0)
{
// case of n = 1 handled
// separately
if (n == 1)
Console.WriteLine("-1");
else
{
int b = (n * n - 1) / 2;
int c = (n * n + 1) / 2;
Console.Write("b = "+ b +
", c = "+ c);
}
}
else
{
// case of n = 2 handled
// separately
if (n == 2)
Console.Write("-1");
else
{
int b = n * n / 4 - 1;
int c = n * n / 4 + 1;
Console.Write("b = "+ b +
", c = "+ c);
}
}
}
// Driver code
public static void Main ()
{
int a = 3;
printOtherSides(a);
}
}
// This code is contributed by Nitin Mittal.
服务器端编程语言（Professional Hypertext Preprocessor 的缩写）
<?php
// PHP program to print other two
// sides of right angle triangle
// given one side
// Finds two sides of a right angle
// triangle if it they exist.
function printOtherSides($n)
{
// if n is odd
if ($n & 1)
{
// case of n = 1
// handled separately
if ($n == 1)
echo -1 ;
else
{
$b = ($n * $n - 1) / 2;
$c = ($n * $n + 1) / 2;
echo "b = " ,$b,", c = " ,$c ;
}
}
else
{
// case of n = 2
// handled separately
if ($n == 2)
echo -1 ;
else
{
$b = $n * $n / 4 - 1;
$c = $n * $n / 4 + 1;
echo "b = " ,$b, ", c = ", $c ;
}
}
}
// Driver Code
$a = 3;
printOtherSides($a);
return 0;
// This code is contributed by nitin mittal.
?>
java 描述语言
<script>
// javascript program to print other two
// sides of right angle triangle
// given one side
// Finds two sides of a right angle
// triangle if it they exist.
function printOtherSides(n)
{
// if n is odd
if (n % 2 != 0)
{
// case of n = 1 handled separately
if (n == 1)
document.write("-1");
else
{
var b = (n * n -1) / 2;
var c = (n *n +1) / 2;
document.write("b = "+ b +
", c = "+c);
}
}
else
{
// case of n = 2 handled separately
if (n == 2)
document.write("-1");
else
{
var b = n * n / 4 - 1;
var c = n * n / 4 + 1;
document.write("b = "+ b +
", c = "+c);
}
}
}
// Driver code
var a = 3;
printOtherSides(a);
// This code is contributed by 29AjayKumar
</script>
输出:
b = 4, c = 5
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