如果一个形状的面积等于它的周长,则该形状是相等的。给定多边形的有序坐标,找出形状是否相等。
例子 :
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
我们可以使用鞋带公式找到多边形的面积,该公式在具有给定 n 个有序顶点的多边形的面积中描述。我们也可以简单地通过添加相邻点之间的距离来找到它的周长。
C++
// C++ program to find equable shape
#include
using namespace std;
// To calculate area of polygon
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 abs(area / 2.0);
}
// To calculate perimeter of polygon
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 += 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
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))
cout << "Equable Shape";
else
cout << "Not Equable Shape";
}
// Driver program to test above function
int 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 shape
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))
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 polygon
import math
def 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 polygon
def 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 shape
def 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 function
X = [ 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 shape
using 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
Javascript
输出 :
Equable Shape
参考:
https://en.wikipedia.org/wiki/Equable_shape
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