Find a triplet (i, j, k) from an array such that i < j < k and arr[i] < arr[j] > arr[k]

Given an array arr[] which consists of a permutation of first N natural numbers, the task is to find any triplet (i, j, k) from the given array such that 0 ? i < j < k ? (N – 1) and arr[i] < arr[j] and arr[j] > arr[k]. If no such triplet exists, then print “-1”.

Examples:

Input: arr[] = {4, 3, 5, 2, 1, 6}
Output: 1 2 3
Explanation: For the triplet (1, 2, 3), arr[2] > arr[1]( i.e. 5 > 3) and arr[2] > arr[3]( i.e. 5 > 2).

Input: arr[] = {3, 2, 1}
Output: -1

Naive Approach: The simplest approach is to generate all possible triplets from the given array arr[] and if there exists any such triplet that satisfies the given condition, then print that triplet. Otherwise, print “-1”. 

Time Complexity: O(N³)
Auxiliary Space: O(1)

Efficient Approach: The above approach can be optimized by observing the fact that the array contains only distinct elements from the range [1, N]. If there exists any triplet with the given criteria, then that triplet must be adjacent to each other.

Therefore, the idea is to traverse the given array arr[] over the range [1, N – 2] and if there exist any index i such that arr[i – 1] < arr[i] and arr[i] > arr[i + 1], then print the triplet (i – 1, i, i + 1) as the result. Otherwise, print “-1”.

Below is the implementation of the above approach:

C++

// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;

// Function to find a triplet such
// that i < j < k and arr[i] < arr[j]
// and arr[j] > arr[k]
void print_triplet(int arr[], int n)
{
    // Traverse the array
    for (int i = 1; i <= n - 2; i++) {

        // Condition to satisfy for
        // the resultant triplet
        if (arr[i - 1] < arr[i]
            && arr[i] > arr[i + 1]) {

            cout << i - 1 << " "
                 << i << " " << i + 1;
            return;
        }
    }

    // Otherwise, triplet doesn't exist
    cout << -1;
}

// Driver Code
int main()
{
    int arr[] = { 4, 3, 5, 2, 1, 6 };
    int N = sizeof(arr) / sizeof(int);
    print_triplet(arr, N);

    return 0;
}

Java

// Java program for the above approach
import java.util.*;

class GFG{

// Function to find a triplet such
// that i < j < k and arr[i] < arr[j]
// and arr[j] > arr[k]
static void print_triplet(int arr[], int n)
{

    // Traverse the array
    for(int i = 1; i <= n - 2; i++)
    {

        // Condition to satisfy for
        // the resultant triplet
        if (arr[i - 1] < arr[i] &&
            arr[i] > arr[i + 1])
        {
            System.out.print(i - 1 + " " + i + " " +
                            (i + 1));
            return;
        }
    }

    // Otherwise, triplet doesn't exist
    System.out.print(-1);
}

// Driver code
public static void main(String[] args)
{
    int arr[] = { 4, 3, 5, 2, 1, 6 };
    int N = arr.length;

    print_triplet(arr, N);
}
}

// This code is contributed by sanjoy_62

Python3

# Python3 program for the above approach

# Function to find a triplet such
# that i < j < k and arr[i] < arr[j]
# and arr[j] > arr[k]
def print_triplet(arr, n):

    # Traverse the array
    for i in range(1, n - 1):

        # Condition to satisfy for
        # the resultant triplet
        if (arr[i - 1] < arr[i] and
            arr[i] > arr[i + 1]):
            print(i - 1, i, i + 1)
            return

    # Otherwise, triplet doesn't exist
    print(-1)

# Driver Code
if __name__ == "__main__":

    arr = [ 4, 3, 5, 2, 1, 6 ]
    N = len(arr)

    print_triplet(arr, N)

# This code is contributed by chitranayal

C#

// C# program to implement
// the above approach
using System;
public class GFG
{

// Function to find a triplet such
// that i < j < k and arr[i] < arr[j]
// and arr[j] > arr[k]
static void print_triplet(int[] arr, int n)
{

    // Traverse the array
    for(int i = 1; i <= n - 2; i++)
    {

        // Condition to satisfy for
        // the resultant triplet
        if (arr[i - 1] < arr[i] &&
            arr[i] > arr[i + 1])
        {
            Console.Write(i - 1 + " " + i + " " +
                            (i + 1));
            return;
        }
    }

    // Otherwise, triplet doesn't exist
    Console.Write(-1);
}

// Driver Code
public static void Main(String[] args)
{
    int[] arr = { 4, 3, 5, 2, 1, 6 };
    int N = arr.Length;

    print_triplet(arr, N);
}
}

// This code is contributed by splevel62.

Javascript

<script>

      // JavaScript program to implement
      // the above approach

      // Function to find a triplet such
      // that i < j < k and arr[i] < arr[j]
      // and arr[j] > arr[k]
      function print_triplet(arr, n)
      {
        // Traverse the array
        for (var i = 1; i <= n - 2; i++)
        {
          // Condition to satisfy for
          // the resultant triplet
          if (arr[i - 1] < arr[i] && arr[i] > arr[i + 1])
          {
            document.write(i - 1 + " " + i + " " + (i + 1));
            return;
          }
        }

        // Otherwise, triplet doesn't exist
        document.write(-1);
      }

      // Driver Code
      var arr = [4, 3, 5, 2, 1, 6];
      var N = arr.length;

      print_triplet(arr, N);

</script>

Output:

1 2 3

Time Complexity: O(N)
Auxiliary Space: O(1)