如果给出边的长度，则求出三角形的中位数的长度

给定一个三角形的所有三个边的长度为a ， b和c 。任务是计算三角形中位数的长度。

A median of a triangle is a line segment joining a vertex to the midpoint of the opposite side, thus bisecting that side. 

例子：

Input: a = 8, b = 10, c = 13 
Output: 10.89
Input: a = 4, b = 3, c = 5 
Output: 3.61 

方法：想法是使用Apollonius定理解决该问题。

Apollonius’s Theorem states that “the sum of the squares of any two sides of a triangle equals twice the square on half the third side and twice the square on the median bisecting the third side”.
 

From the above figure, According to Apollonius’s Theorm we have: 
 

$b^{2} + c^{2} = 2*(a^{2}+m^{2})$

where a, b, and c are the length of sides of the triangle 
and m is the length of median of the triangle on side 2*a 

因此，根据上述等式，三角形的中值长度由下式给出：

$m = \frac{1}{2} \sqrt{2b^{2} + 2c^{2} - a^{2}}$

下面是上述方法的实现：

C++

// C++ program to find the length of the 
// median using sides of the triangle
#include
using namespace std;
  
// Function to return the length of
// the median using sides of triangle
float median(int a, int b, int c)
{
    float n = sqrt(2 * b * b + 
                   2 * c * c - a * a) / 2;
    return n;
}
  
// Driver code
int main()
{
    int a, b, c;
    a = 4;
    b = 3;
    c = 5;
  
    // Function call
    float ans = median(a, b, c); 
  
    // Print final answer with 2 
    // digits after decimal
    cout << fixed << setprecision(2) << ans;
    return 0;
}
  
// This code is contributed by himanshu77

Java

// Java program to find the length of the 
// median using sides of the triangle 
import java.util.*; 
  
class GFG{
      
// Function to return the length of 
// the median using sides of triangle 
public static float median(int a, int b, int c) 
{ 
    float n = (float)(Math.sqrt(2 * b * b + 
                                2 * c * c - 
                                a * a) / 2); 
    return n; 
} 
  
// Driver code
public static void main(String[] args)
{
    int a, b, c; 
    a = 4; 
    b = 3; 
    c = 5; 
  
    // Function call 
    float ans = median(a, b, c); 
  
    // Print final answer with 2 
    // digits after decimal 
    System.out.println(String.format("%.2f", ans)); 
}
}
  
// This code is contributed by divyeshrabadiya07

Python3

# Python3 implementation to Find the 
# length of the median using sides
# of the triangle
  
import math
  
# Function to return the length of 
# the median using sides of triangle. 
def median(a, b, c): 
   
    n = (1 / 2)*math.sqrt(2*(b**2) 
   + 2*(c**2)
 - a**2)  
  
    return n 
  
# Driver Code 
a = 4
b = 3
c = 5
  
# Function Call
ans = median(a, b, c)
  
# Print the final answer
print(round(ans, 2))

C#

// C# program to find the length of the 
// median using sides of the triangle 
using System;
  
class GFG{
      
// Function to return the length of 
// the median using sides of triangle 
public static float median(int a, int b, int c) 
{ 
    float n = (float)(Math.Sqrt(2 * b * b + 
                                2 * c * c - 
                                a * a) / 2); 
    return n; 
} 
  
// Driver code
public static void Main(String[] args)
{
    int a, b, c; 
    a = 4; 
    b = 3; 
    c = 5; 
  
    // Function call 
    float ans = median(a, b, c); 
  
    // Print readonly answer with 2 
    // digits after decimal 
    Console.WriteLine(String.Format("{0:F2}", ans)); 
}
}
  
// This code is contributed by gauravrajput1

输出：

3.61

时间复杂度： O(1)
空间复杂度： O(1)