Find number of diagonals in n sided convex polygon
Given n > 3, find number of diagonals in n sided convex polygon.
According to Wikipedia, In geometry, a diagonal is a line segment joining two vertices of a polygon or polyhedron, when those vertices are not on the same edge. Informally, any sloping line is called diagonal.
Examples :
Input : 5 Output : 5
Explanation: Five possible diagonals are : AC, AD, BD, BE, CE
Since for an n-sided convex polygon, from each vertex, we can draw n-3 diagonals leaving two adjacent vertices and itself. Following this way for n-vertices, there will be n*(n-3) diagonals but then we will be calculating each diagonal twice so total number of diagonals become n*(n-3)/2
Here is code for above formula.
C++
#include <iostream> using namespace std; // C++ function to find number of diagonals // in n sided convex polygon int numberOfDiagonals( int n) { return n * (n - 3) / 2; } // driver code to test above function int main() { int n = 5; cout << n << " sided convex polygon have " ; cout << numberOfDiagonals(n) << " diagonals" ; return 0; } |
Java
// Java function to find number of diagonals // in n sided convex polygon public class Diagonals { static int numberOfDiagonals( int n) { return n * (n - 3 ) / 2 ; } // driver code to test above function public static void main(String[] args) { int n = 5 ; System.out.print(n + " sided convex polygon have " ); System.out.println(numberOfDiagonals(n) + " diagonals" ); } } // This code is contributed by Saket Kumar |
Python3
# Python3 program to find number of diagonals # in n sided convex polygon def numberOfDiagonals(n): return n * (n - 3 ) / 2 # driver code to test above function def main(): n = 5 print (n , " sided convex polygon have " ) print (numberOfDiagonals(n) , " diagonals" ) if __name__ = = '__main__' : main() #this code contributed by 29AjayKumar |
C#
// C# function to find number of diagonals // in n sided convex polygon using System; class GFG { static int numberOfDiagonals( int n) { return n * (n - 3) / 2; } // driver code to test above function public static void Main() { int n = 5; Console.Write(n + " sided convex polygon have " ); Console.WriteLine(numberOfDiagonals(n) + " diagonals" ); } } // This code is contributed by Sam007 |
PHP
<?php // PHP function to find number // of diagonals in n sided // convex polygon function numberOfDiagonals( $n ) { return $n * ( $n - 3) / 2; } // Driver Code $n = 5; echo $n , " sided convex polygon have " ; echo numberOfDiagonals( $n ) , " diagonals" ; // This code is contributed by aj_36 ?> |
Javascript
<script> // Javascript function to find number of // diagonals in n sided convex polygon function numberOfDiagonals(n) { return n * (n - 3) / 2; } // Driver code var n = 5; document.write(n + " sided convex polygon have " ); document.write(numberOfDiagonals(n) + " diagonals" ); // This code is contributed by Ankita saini </script> |
Output :
5 sided convex polygon have 5 diagonals
Time Complexity: O(1)
Auxiliary Space: O(1)
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