求 N 边正多边形的旋转对称角
给定一个整数 N ，它是一个正多边形的边数。任务是找到最小的旋转角度，使得生成的正多边形具有相似的位置和尺寸，即新的旋转多边形与初始多边形对称。
如果在[1，360 ]到的范围内存在旋转，使得新形状与初始形状完全重叠，则称该形状具有旋转对称性。
示例:
输入: N = 4 输出: 90 解释: 一个 4 边正多边形是一个正方形，当它旋转 90 度时，会产生相似的正方形。
输入:N = 8 T3】输出: 45
方法:对于任何 N 边的正多边形，当旋转 360 度时，它会在多边形的原始位置对齐。为了找到最小旋转角，我们利用正多边形的对称性。对于 N 边正多边形，当旋转 360/N 度时，旋转的多边形与原始多边形处于相同的位置，这是 N 边正多边形的外角。
例如: 考虑 N = 4，
下面是上述方法的实现。
C++
// C++ program to find the angle
// of Rotational Symmetry of
// an N-sided regular polygon
#include <bits/stdc++.h>
using namespace std;
// function to find required
// minimum angle of rotation
double minAnglRot(int N)
{
// Store the answer in
// a double variable
double res;
// Calculating the angle
// of rotation and type-
// casting the integer N
// to double type
res = 360 / (double)N;
return res;
}
// Driver code
int main()
{
int N = 4;
cout << "Angle of Rotational Symmetry: "
<< minAnglRot(N);
return 0;
}
Java 语言(一种计算机语言，尤用于创建网站)
// Java program to find the angle
// of Rotational Symmetry of
// an N-sided regular polygon
import java.io.*;
class GFG
{
// function to find required
// minimum angle of rotation
static double minAnglRot(int N)
{
// Store the answer in
// a double variable
double res;
// Calculating the angle
// of rotation and type-
// casting the integer N
// to double type
res = 360 / (double)N;
return res;
}
// Driver code
public static void main (String[] args)
{
int N = 4;
System.out.println("Angle of Rotational Symmetry: " +
minAnglRot(N));
}
}
// This code is contributed by shivanisinghss2110
Python 3
# Python3 program to find the angle
# of Rotational Symmetry of
# an N-sided regular polygon
# Function to find required
# minimum angle of rotation
def minAnglRot(N):
# Store the answer in a
# variable
# Calculating the angle
# of rotation and type-
# casting the integer N
# to type
res = 360 // N
return res
# Driver code
if __name__ == '__main__':
N = 4;
print("Angle of Rotational Symmetry: ",
minAnglRot(N))
# This code is contributed by mohit kumar 29
C
// C# program to find the angle
// of Rotational Symmetry of
// an N-sided regular polygon
using System;
class GFG
{
// function to find required
// minimum angle of rotation
static double minAnglRot(int N)
{
// Store the answer in
// a double variable
double res;
// Calculating the angle
// of rotation and type-
// casting the integer N
// to double type
res = 360 / (double)N;
return res;
}
// Driver code
public static void Main (string[] args)
{
int N = 4;
Console.Write("Angle of Rotational Symmetry: " +
minAnglRot(N));
}
}
// This code is contributed by rock_cool
java 描述语言
<script>
// Javascript program to find the angle
// of Rotational Symmetry of an N-sided
// regular polygon
// Function to find required
// minimum angle of rotation
function minAnglRot(N)
{
// Store the answer in
// a double variable
let res;
// Calculating the angle of
// rotation and type-casting
// the integer N to double type
res = 360 / N;
return res;
}
// Driver code
let N = 4;
document.write("Angle of Rotational Symmetry: " +
minAnglRot(N));
// This code is contributed by divyeshrabadiya07
</script>
Output:
Angle of Rotational Symmetry: 90
时间复杂度: O (1) 辅助空间: O (1)
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