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++
// 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 itfloat diagonalLength(float a){ // Stores the required distance float L = a / sqrt(2); // Print the required distance cout << L;}// Driver Codeint 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
// Java program for the above approachclass 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
# Python3 program for the above approachfrom math import sqrt# Function to find the shortest # distance between the diagonal of a # cube and an edge skew to itdef diagonalLength(a): # Stores the required distance L = a / sqrt(2) # Print the required distance print(L)# Given side of the cubea = 2# Function call to find the shortest # distance between the diagonal of a # cube and an edge skew to itdiagonalLength(a) |
C#
// C# program for the above approachusing 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 // PHP program for the above approach // Function to find the shortest // distance between the diagonal of a // cube and an edge skew to itfunction 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 itdiagonalLength($a); ?> |
Javascript
<script>// javascript program for the above approach// Function to find the shortest distance// between the diagonal of a cube and// an edge skew to itfunction 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> |
Output:
1.41421
Time Complexity: O(1)
Auxiliary Space: O(1)
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