检查基于给定条件从数组构造的图是否包含循环

给定一个由前N个自然数组成的数组arr [] ，请使用该数组元素构造一个无向图，以便对于任何数组元素，将一条边与左侧和右侧的下一个更大的元素相连。

例子：

 Input: arr = {1, 2, 3, 4, 5}
Output: No
Explanation:     
It is clear from the below image that final graph will be a tree. 

Input: arr[] = {1, 4, 2, 5, 3}
Output: Yes

天真的方法：最简单的方法是使用上述条件构造所需的图，并检查是否存在长度至少为3的循环。如果存在一个循环，则打印“是”。否则，打印“ No ”。
时间复杂度： O(N + E)，其中E是边数。
辅助空间： O(N)

高效的方法：最佳方法是检查给定的排列是单峰还是非单峰，即检查是否存在任何数组元素，且数组元素在两侧均具有较大的相邻元素。如果发现是真的，则打印“是”。否则，打印“否”。

下面是上述方法的实现：

C++

// C++ program for the above approach
 
#include 
using namespace std;
 
// Function to check if the graph
// constructed from given array
// contains a cycle or not
void isCycleExists(int arr[], int N)
{
    bool valley = 0;
 
    // Traverse the array
    for (int i = 1; i < N; i++) {
 
        // If arr[i] is less than
        // arr[i - 1] and arr[i]
        if (arr[i] < arr[i - 1]
            && arr[i] < arr[i + 1]) {
 
            cout << "Yes" << endl;
            return;
        }
    }
 
    cout << "No";
}
 
// Driver Code
int main()
{
    // Given array
    int arr[] = { 1, 3, 2, 4, 5 };
 
    // Size of the array
    int N = sizeof(arr)
            / sizeof(arr[0]);
 
    isCycleExists(arr, N);
 
    return 0;
}

Java

// Java program for the above approach
import java.io.*;
class GFG
{
 
  // Function to check if the graph
  // constructed from given array
  // contains a cycle or not
  static void isCycleExists(int[] arr, int N)
  {
 
    // Traverse the array
    for (int i = 1; i < N; i++)
    {
 
      // If arr[i] is less than
      // arr[i - 1] and arr[i]
      if (arr[i] < arr[i - 1]
          && arr[i] < arr[i + 1])
      {
        System.out.println("Yes");
        return;
      }
    }
    System.out.println("No");
  }
 
  // Driver Code
  public static void main(String[] args)
  {
 
    // Given array
    int[] arr = { 1, 3, 2, 4, 5 };
 
    // Size of the array
    int N = arr.length;
    isCycleExists(arr, N);
  }
}
 
// This code is contributed by Dharanendra L V.

Python3

# Python3 program for the above approach
 
# Function to check if the graph
# constructed from given array
# contains a cycle or not
def isCycleExists(arr, N):
    valley = 0
 
    # Traverse the array
    for i in range(1, N):
 
        # If arr[i] is less than
        # arr[i - 1] and arr[i]
        if (arr[i] < arr[i - 1] and arr[i] < arr[i + 1]):
            print("Yes")
            return
    print("No")
 
# Driver Code
if __name__ == '__main__':
   
    # Given array
    arr = [1, 3, 2, 4, 5]
 
    # Size of the array
    N = len(arr)
    isCycleExists(arr, N)
 
# This code is contributed by mohit kumar 29

C#

// C# program for the above approach
using System;
class GFG
{
 
  // Function to check if the graph
  // constructed from given array
  // contains a cycle or not
  static void isCycleExists(int[] arr, int N)
  {
 
    // Traverse the array
    for (int i = 1; i < N; i++)
    {
 
      // If arr[i] is less than
      // arr[i - 1] and arr[i]
      if (arr[i] < arr[i - 1]
          && arr[i] < arr[i + 1])
      {
        Console.WriteLine("Yes");
        return;
      }
    }
    Console.WriteLine("No");
  }
 
  // Driver Code
  public static void Main()
  {
     
    // Given array
    int[] arr = { 1, 3, 2, 4, 5 };
 
    // Size of the array
    int N = arr.Length;
    isCycleExists(arr, N);
  }
}
 
// This code is contributed by chitranayal.

输出：

Yes

时间复杂度： O(N)
辅助空间： O(1)