📌  相关文章
📜  检查基于给定条件从数组构造的图是否包含循环

📅  最后修改于: 2021-09-06 05:05:36             🧑  作者: Mango

给定一个由前N 个自然数组成的数组arr[] ,使用数组元素构造一个无向图,使得对于任何数组元素,将一条边与左侧和右侧的下一个更大的元素连接起来。

例子:

朴素的方法:最简单的方法是使用上述条件构建所需的图,并检查是否存在至少长度为 3 的循环。如果存在循环,则打印“”。否则,打印“”。
时间复杂度: O(N + E),其中 E 是边数。
辅助空间: O(N)

有效的方法:最佳的想法是检查给定的排列是单峰的还是非单峰的,即简单地检查是否存在任何数组元素的两侧具有更大的相邻元素。如果发现是真的,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)

如果您想与行业专家一起参加直播课程,请参阅Geeks Classes Live