# Find a triplet in an array such that arr[i] arr[k] and i < j < k

• Last Updated : 28 Feb, 2022

Given an array arr[] consisting of a permutation of first N natural numbers, the task is to find a triplet (i, j, k) from the given array such that arr[i] < arr[j] > arr[k], where (i < j < k). If multiple triplets exist, then print any valid triplet of indices. Otherwise, print -1.

Examples:

Input: arr[] = {2, 1, 4, 3}
Output: 1 2 3
Explanation: Triplet that satisfy the given condition is (arr[1], arr[2], arr[3])
Therefore, the required output is 1 2 3.

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

Naive Approach: The simplest approach to solve this problem is to traverse the array and generate all possible triplets of the given array and for each triplet, check if it satisfies the given conditions or not. If found to be true, then print that triplet. Otherwise, print -1

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

Efficient Approach: To optimize the above approach the idea is based on the following observations:

• If the given array is sorted in ascending order or descending order from the index range [1, N – 2], then the solution does not exist.
• Otherwise, at least one index exists in the given array such that the element just before and after that concerning index is less than the current element.

Follow the steps below to solve the problem:

• Traverse the given array and for each array index, check if the element just before and after the current index is less than the current element or not. If found to be true, then print that the triplet (i – 1, i, i + 1).
• Otherwise, print -1.

Below is the implementation of the above approach:

## C++

 // C++ program to implement// the above approach#include using namespace std; // Function to find a triplet// that satisfy the conditionsvoid FindTrip(int arr[], int N){         // Traverse the given array    for(int i = 1; i < N - 1; i++)    {                 // Stores current element        int p = arr[i - 1];                 // Stores element just before        // the current element        int q = arr[i];                 // Stores element just after        // the current element        int r = arr[i + 1];                 // Check the given conditions        if (p < q && q > r)        {                         // Print a triplet            cout << i - 1 << " "                 << i << " " << i + 1;                         return;        }    }         // If no triplet found    cout << -1;} // Driver Codeint main(){    int arr[] = { 2, 1, 4, 3 };         int N = sizeof(arr) / sizeof(arr[0]);         FindTrip(arr, N);         return 0;} // This code is contributed by jyoti369

## Java

 // Java program to implement// the above approachimport java.util.*;class GFG {     // Function to find a triplet    // that satisfy the conditions    static void FindTrip(int arr[],                        int N)    {        // Traverse the given array        for (int i = 1; i < N - 1;            i++) {             // Stores current element            int p = arr[i - 1];             // Stores element just before            // the current element            int q = arr[i];             // Stores element just after            // the current element            int r = arr[i + 1];             // Check the given conditions            if (p < q && q > r) {                 // Print a triplet                System.out.println(                    (i - 1) + " "                    + (i) + " "                    + (i + 1));                return;            }        }         // If no triplet found        System.out.println(-1);    }     // Driver Code    public static void main(String args[])    {        int arr[] = { 2, 1, 4, 3 };         int N = arr.length;        FindTrip(arr, N);    }}

## Python3

 # Python3 program to implement# the above approach # Function to find a triplet# that satisfy the conditionsdef FindTrip(arr, N):         # Traverse the given array    for i in range(1, N - 1):                 # Stores current element        p = arr[i - 1]         # Stores element just before        # the current element        q = arr[i]         # Stores element just after        # the current element        r = arr[i + 1]         # Check the given conditions        if (p < q and q > r):             # Print a triplet            print(i - 1, i, i + 1)             return     # If no triplet found    print(-1) # Driver Codeif __name__ == '__main__':         arr = [ 2, 1, 4, 3 ]     N = len(arr)     FindTrip(arr, N) # This code is contributed by mohit kumar 29

## C#

 // C# program to implement// the above approach using System; class GFG{  // Function to find a triplet// that satisfy the conditionsstatic void FindTrip(int[] arr, int N){         // Traverse the given array    for(int i = 1; i < N - 1; i++)    {                 // Stores current element        int p = arr[i - 1];         // Stores element just before        // the current element        int q = arr[i];         // Stores element just after        // the current element        int r = arr[i + 1];         // Check the given conditions        if (p < q && q > r)        {                         // Print a triplet            Console.WriteLine((i - 1) + " " +                              (i) + " " + (i + 1));            return;        }    }     // If no triplet found    Console.WriteLine(-1);} // Driver Codepublic static void Main(){    int[] arr = { 2, 1, 4, 3 };    int N = arr.Length;         FindTrip(arr, N);}} // This code is contributed by code_hunt

## Javascript



Output:

1 2 3

Time Complexity: O(N)

Auxiliary Space: O(1)

My Personal Notes arrow_drop_up