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 = 1.4142Input: 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++ program for the above approach #include <bits/stdc++.h> using namespace std;
// Function to find the shortest distance // between the diagonal of a cube and // an edge skew to it float diagonalLength( float a)
{ // Stores the required distance
float L = a / sqrt (2);
// Print the required distance
cout << L;
} // Driver Code int main()
{ // Given side of the cube
float a = 2;
// Function call to find the shortest
// distance between the diagonal of a
// cube and an edge skew to it
diagonalLength(a);
return 0;
} |
// Java program for the above approach class GFG {
// Function to find the shortest
// distance between the diagonal of a
// cube and an edge skew to it
static void diagonalLength( float a)
{
// Stores the required distance
float L = a / ( float )Math.sqrt( 2 );
// Print the required distance
System.out.println(L);
}
// Driver Code
public static void main(String[] args)
{
// Given side of the cube
float a = 2 ;
// Function call to find the shortest
// distance between the diagonal of a
// cube and an edge skew to it
diagonalLength(a);
}
} |
# Python3 program for the above approach from math import sqrt
# Function to find the shortest # distance between the diagonal of a # cube and an edge skew to it def diagonalLength(a):
# Stores the required distance
L = a / sqrt( 2 )
# Print the required distance
print (L)
# Given side of the cube a = 2
# Function call to find the shortest # distance between the diagonal of a # cube and an edge skew to it diagonalLength(a) |
// C# program for the above approach using System;
class GFG {
// Function to find the shortest
// distance between the diagonal of a
// cube and an edge skew to it
static void diagonalLength( float a)
{
// Stores the required distance
float L = a / ( float )Math.Sqrt(2);
// Print the required distance
Console.Write(L);
}
// Driver Code
public static void Main()
{
// Given side of the cube
float a = 2;
// Function call to find the shortest
// distance between the diagonal of a
// cube and an edge skew to it
diagonalLength(a);
}
} |
<?php // PHP program for the above approach // Function to find the shortest // distance between the diagonal of a // cube and an edge skew to it function diagonalLength( $a )
{ // Stores the required distance
$L = $a / sqrt(2);
# Print the required distance
echo $L ;
} // Given side of the cube $a = 2;
// Function call to find the shortest // distance between the diagonal of a // cube and an edge skew to it diagonalLength( $a );
?> |
<script> // javascript program for the above approach // Function to find the shortest distance // between the diagonal of a cube and // an edge skew to it function diagonalLength( a)
{ // Stores the required distance
let L = a / Math.sqrt(2);
// Print the required distance
document.write( L.toFixed(5));
} // Driver Code // Given side of the cube
let a = 2;
// Function call to find the shortest
// distance between the diagonal of a
// cube and an edge skew to it
diagonalLength(a);
// This code is contributed by todaysgaurav </script> |
1.41421
Time Complexity: O(1)
Auxiliary Space: O(1)