检查两个凸正多边形是否有相同的中心

给定两个正整数 N 和 M，它们表示凸正多边形的边，其中 N < M，任务是检查多边形是否具有相同的中心，如果 N 边多边形内接在 M 边多边形中。
多边形中心：指向与多边形的每个顶点等距的多边形内部。
例子：

Input: N = 9, M = 3 
Output: YES 
Explanation: 
Polygon of side 3 when inscribed in a polygon of side 9, then both polygons have same center.
Input: N = 10, M = 3 
Output: NO 
Explanation: 
Polygon of side 3 when inscribed in a polygon of side 10, then both polygons don’t have same center. 
 

方法：这个问题的关键观察是当M % N == 0 时，这意味着 N 边多边形的边相等地覆盖 M 边多边形的边，这意味着两个多边形具有相同的中心。
算法：

• 检查 M 是否可被 N 整除，如果是，则两个多边形具有相同的中心。
• 否则两个多边形具有不同的中心。

下面是上述方法的实现：

C++

// C++ implementation to check whether
// two convex polygons have same center
 
#include
using namespace std;
 
// Function to check whether two convex
// polygons have the same center or not
int check(int n, int m){
    if (m % n == 0){
        cout << "YES";
    }
    else{
        cout << "NO";
    }
    return 0;
}
 
// Driver Code
int main()
{
    int n = 5;
    int m = 10;
     
    check(n, m);
    return 0;
}

Java

// Java implementation to check whether
// two convex polygons have same center
class GFG{
  
// Function to check whether two convex
// polygons have the same center or not
static int check(int n, int m){
    if (m % n == 0){
        System.out.print("YES");
    }
    else{
        System.out.print("NO");
    }
    return 0;
}
  
// Driver Code
public static void main(String[] args)
{
    int n = 5;
    int m = 10;
      
    check(n, m);
}
}
 
// This code is contributed by sapnasingh4991

Python3

# Python3 implementation to check whether
# two convex polygons have same center
 
# Function to check whether two convex
# polygons have the same center or not
def check(n, m):
    if (m % n == 0):
        print("YES")
    else:
        print("NO")
 
# Driver Code
n = 5
m = 10
 
check(n, m)
 
# This code is contributed by mohit kumar 29

C#

// C# implementation to check whether
// two convex polygons have same center
using System;
 
class GFG{
   
// Function to check whether two convex
// polygons have the same center or not
static int check(int n, int m){
    if (m % n == 0){
        Console.Write("YES");
    }
    else{
        Console.Write("NO");
    }
    return 0;
}
   
// Driver Code
public static void Main(String[] args)
{
    int n = 5;
    int m = 10;
       
    check(n, m);
}
}
  
// This code is contributed by Rajput-Ji

Javascript

 
// Javascript implementation to check whether
// two convex polygons have same center
 
// Function to check whether two convex
// polygons have the same center or not
function check(n, m)
{
    if (m % n == 0)
    {
        document.write("YES");
    }
    else
    {
        document.write("NO");
    }
    return 0;
}
 
// Driver code
var n = 5;
var m = 10;
  
check(n, m);
            
// This code is contributed by Kirti
 

输出：

YES

性能分析：

• 时间复杂度： O(1)。
• 辅助空间： O(1)。