Program to find the shortest distance between diagonal and edge skew of a Cube
Last Updated :
17 Mar, 2021
Given an integer A, denoting the length of a cube, the task is to find the shortest distance between the diagonal of a cube and an edge skew to it i.e. KL in the below figure.
Examples :
Input: A = 2
Output: 1.4142
Explanation:
Length of KL = A / ?2
Length of KL = 2 / 1.41 = 1.4142
Input: A = 3
Output: 2.1213
Approach: The idea to solve the problem is based on the following mathematical formula:
Let’s draw a perpendicular from K to down face of cube as Q.
Using Pythagorean Theorem in triangle QKL,
KL2 = QK2 + QL2
l2 = (a/2)2 + (a/2)2
l2 = 2 * (a/2)2
l = a / sqrt(2)
Below is the implementation of the above approach:
C++
#include <bits/stdc++.h>
using namespace std;
float diagonalLength(float a)
{
float L = a / sqrt(2);
cout << L;
}
int main()
{
float a = 2;
diagonalLength(a);
return 0;
}
|
Java
class GFG {
static void diagonalLength(float a)
{
float L = a / (float)Math.sqrt(2);
System.out.println(L);
}
public static void main(String[] args)
{
float a = 2;
diagonalLength(a);
}
}
|
Python3
from math import sqrt
def diagonalLength(a):
L = a / sqrt(2)
print(L)
a = 2
diagonalLength(a)
|
C#
using System;
class GFG {
static void diagonalLength(float a)
{
float L = a / (float)Math.Sqrt(2);
Console.Write(L);
}
public static void Main()
{
float a = 2;
diagonalLength(a);
}
}
|
PHP
<?php
function diagonalLength($a)
{
$L = $a / sqrt(2);
# Print the required distance
echo $L;
}
$a = 2;
diagonalLength($a);
?>
|
Javascript
<script>
function diagonalLength( a)
{
let L = a / Math.sqrt(2);
document.write( L.toFixed(5));
}
let a = 2;
diagonalLength(a);
</script>
|
Time Complexity: O(1)
Auxiliary Space: O(1)
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