如果给定边长，求三角形的中线长度

给定三角形所有三边的长度a , b和c 。任务是计算三角形中线的长度。

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：思路是利用阿波罗尼乌斯定理来解决这个问题。

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 Theorem 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，由上述方程得出的三角形的中线长度由下式给出：

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

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

Javascript

 
// JavaScript program to find the length of the
// median using sides of the triangle
 
// Function to return the length of
// the median using sides of triangle
function median(a, b, c)
{
    let n = (Math.sqrt(2 * b * b +
                                2 * c * c -
                                a * a) / 2);
    return n;
}
    
 
// Driver Code
 
     let a, b, c;
    a = 4;
    b = 3;
    c = 5;
   
    // Function call
    let ans = median(a, b, c);
   
    // Print final answer with 2
    // digits after decimal
    document.write(ans, 2);
           

输出：

3.61

时间复杂度： O(1)
空间复杂度： O(1)

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