A shape is equable if its area is equal to its perimeter. Given ordered coordinates of polygon find whether the shape is equable or not.
Examples :
Input : X[] = {0, 5, 0}
Y[] = {0, 0, 12}
Output : Equable Shape
Input : X[] = {0, 4, 4, 0}
Y[] = {0, 0, 4, 4}
Output : Equable Shape
Input: X[] = {0, 6, 6, 0}
Y[] = {0, 0, 4, 4}
Output: Not Equable Shape
We can find area of polygon using shoelace formula which is described in Area of a polygon with given n ordered vertices. We can also find its perimeter simply by adding distances between adjacent points.
C++
// C++ program to find equable shape#include <bits/stdc++.h>using namespace std;// To calculate area of polygondouble polygonArea(double X[], double Y[], int n){ double area = 0.0; // Calculate value of area using shoelace // formula int j = n - 1; for (int i = 0; i < n; i++) { area += (X[j] + X[i]) * (Y[j] - Y[i]); j = i; // j is previous vertex to i } return abs(area / 2.0);}// To calculate perimeter of polygondouble polygonPerimeter(double X[], double Y[], int n){ double perimeter = 0.0; // Calculate value of perimeter int j = n - 1; for (int i = 0; i < n; i++) { perimeter += sqrt((X[j] - X[i]) * (X[j] - X[i]) + (Y[j] - Y[i]) * (Y[j] - Y[i])); j = i; // j is previous vertex to i } return perimeter;}// To find equable shapevoid equableShape(double X[], double Y[], int n){ // Find area and perimeter of polygon if // they are equal then it is equable shape if (polygonPerimeter(X, Y, n) == polygonArea(X, Y, n)) cout << "Equable Shape"; else cout << "Not Equable Shape";}// Driver program to test above functionint main(){ double X[] = { 0, 5, 0 }; double Y[] = { 0, 0, 12 }; int n = sizeof(X) / sizeof(X[0]); equableShape(X, Y, n); return 0;} |
Java
// Java program to find equable shapeclass equable { // To calculate area of polygon static double polygonArea(double X[], double Y[], int n) { double area = 0.0; // Calculate value of area using shoelace formula int j = n - 1; for (int i = 0; i < n; i++) { area += (X[j] + X[i]) * (Y[j] - Y[i]); j = i; // j is previous vertex to i } return Math.abs(area / 2.0); } // To calculate perimeter of polygon static double polygonPerimeter(double X[], double Y[], int n) { double perimeter = 0.0; // Calculate value of perimeter int j = n - 1; for (int i = 0; i < n; i++) { perimeter += Math.sqrt((X[j] - X[i]) * (X[j] - X[i]) + (Y[j] - Y[i]) * (Y[j] - Y[i])); j = i; // j is previous vertex to i } return perimeter; } // To find equable shape static void equableShape(double X[], double Y[], int n) { // Find area and perimeter of polygon if // they are equal then it is equable shape if (polygonPerimeter(X, Y, n) == polygonArea(X, Y, n)) System.out.println("Equable Shape"); else System.out.println("Not Equable Shape"); } // Driver program to test above function public static void main(String[] args) { double X[] = { 0, 5, 0 }; double Y[] = { 0, 0, 12 }; int n = X.length; equableShape(X, Y, n); }} |
Python3
# Python 3 program to find equable shape# To calculate area of polygonimport mathdef polygonArea(X, Y, n): area = 0.0 # Calculate value of area # using shoelace formula j = n - 1 for i in range(n): area += (X[j] + X[i]) * (Y[j] - Y[i]) # j is previous vertex to i j = i return abs(area / 2.0) # To calculate perimeter of polygondef polygonPerimeter(X, Y, n): perimeter = 0.0 # Calculate value of perimeter j = n - 1 for i in range(n): perimeter += math.sqrt((X[j] - X[i]) * (X[j] - X[i]) + (Y[j] - Y[i]) * (Y[j] - Y[i])) # j is previous vertex to i j = i return perimeter # To find equable shapedef equableShape(X, Y, n): # Find area and perimeter of polygon if # they are equal then it is equable shape if (polygonPerimeter(X, Y, n) == polygonArea(X, Y, n)): print("Equable Shape") else: print("Not Equable Shape")# Driver program to test above functionX = [ 0, 5, 0 ]Y = [ 0, 0, 12 ]n = len(X)equableShape(X, Y, n)# This code is contributed by Azkia Anam. |
C#
// C# program to find equable shapeusing System;class equable { // To calculate area of polygon static double polygonArea(double []X, double []Y, int n) { double area = 0.0; // Calculate value of area using // Shoelace Formula int j = n - 1; for (int i = 0; i < n; i++) { area += (X[j] + X[i]) * (Y[j] - Y[i]); j = i; // j is previous vertex to i } return Math.Abs(area / 2.0); } // To calculate perimeter of polygon static double polygonPerimeter(double []X, double []Y, int n) { double perimeter = 0.0; // Calculate value of perimeter int j = n - 1; for (int i = 0; i < n; i++) { perimeter += Math.Sqrt((X[j] - X[i]) * (X[j] - X[i]) + (Y[j] - Y[i]) * (Y[j] - Y[i])); j = i; // j is previous vertex to i } return perimeter; } // To find equable shape static void equableShape(double []X, double []Y, int n) { // Find area and perimeter of // polygon if they are equal // then it is equable shape if (polygonPerimeter(X, Y, n) == polygonArea(X, Y, n)) Console.WriteLine("Equable Shape"); else Console.WriteLine("Not Equable Shape"); } // Driver Code public static void Main(String []args) { double []X = {0, 5, 0}; double []Y = {0, 0, 12}; int n = X.Length; // Calling Function equableShape(X, Y, n); }}// This Code is contributed by vt_m. |
PHP
<?php// PHP program to find// equable shape// To calculate area // of polygonfunction polygonArea($X, $Y, $n){ $area = 0.0; // Calculate value of area // using shoelace formula $j = $n - 1; for ($i = 0; $i < $n; $i++) { $area += ($X[$j] + $X[$i]) * ($Y[$j] - $Y[$i]); // j is previous vertex to i $j = $i; } return abs($area / 2.0);}// To calculate perimeter of polygonfunction polygonPerimeter($X, $Y, $n) { $perimeter = 0.0; // Calculate value of perimeter $j = $n - 1; for ($i = 0; $i < $n; $i++) { $perimeter += sqrt(($X[$j] - $X[$i]) * ($X[$j] - $X[$i]) + ($Y[$j] - $Y[$i]) * ($Y[$j] - $Y[$i])); // j is previous vertex to i $j = $i; } return $perimeter;}// To find equable shapefunction equableShape($X, $Y, $n){ // Find area and perimeter of // polygon if they are equal // then it is equable shape if (polygonPerimeter($X, $Y, $n) == polygonArea($X, $Y, $n)) echo "Equable Shape"; else echo "Not Equable Shape";}// Driver Code$X = array( 0, 5, 0 );$Y = array( 0, 0, 12 );$n = sizeof($X);equableShape($X, $Y, $n);// This code is contributed by ajit?> |
Javascript
<script>// Javascript program to find equable shape// To calculate area of polygonfunction polygonArea(X, Y, n){ let area = 0.0; // Calculate value of area using // Shoelace Formula let j = n - 1; for(let i = 0; i < n; i++) { area += (X[j] + X[i]) * (Y[j] - Y[i]); // j is previous vertex to i j = i; } return Math.abs(area / 2.0);}// To calculate perimeter of polygonfunction polygonPerimeter(X, Y, n){ let perimeter = 0.0; // Calculate value of perimeter let j = n - 1; for(let i = 0; i < n; i++) { perimeter += Math.sqrt((X[j] - X[i]) * (X[j] - X[i]) + (Y[j] - Y[i]) * (Y[j] - Y[i])); // j is previous vertex to i j = i; } return perimeter;}// To find equable shapefunction equableShape(X, Y, n){ // Find area and perimeter of // polygon if they are equal // then it is equable shape if (polygonPerimeter(X, Y, n) == polygonArea(X, Y, n)) document.write("Equable Shape" + "</br>"); else document.write("Not Equable Shape" + "</br>");}// Driver codelet X = [ 0, 5, 0 ];let Y = [ 0, 0, 12 ];let n = X.length;// Calling FunctionequableShape(X, Y, n);// This code is contributed by suresh07 </script> |
Output :
Equable Shape
Time Complexity: O(NlogN)
Auxiliary Space: O(N)
Reference:
https://en.wikipedia.org/wiki/Equable_shape
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