Related Articles
Find a triplet in an array such that arr[i] arr[k] and i < j < k
• Last Updated : 26 Apr, 2021

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, arr, arr)
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 conditions``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``            ``cout << i - 1 << ``" "``                 ``<< i << ``" "` `<< i + 1;``            ` `            ``return``;``        ``}``    ``}``    ` `    ``// If no triplet found``    ``cout << -1;``}` `// Driver Code``int` `main()``{``    ``int` `arr[] = { 2, 1, 4, 3 };``    ` `    ``int` `N = ``sizeof``(arr) / ``sizeof``(arr);``    ` `    ``FindTrip(arr, N);``    ` `    ``return` `0;``}` `// This code is contributed by jyoti369`

## Java

 `// Java program to implement``// the above approach``import` `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 conditions``def` `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 Code``if` `__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 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``            ``Console.WriteLine((i - 1) + ``" "` `+``                              ``(i) + ``" "` `+ (i + 1));``            ``return``;``        ``}``    ``}` `    ``// If no triplet found``    ``Console.WriteLine(-1);``}` `// Driver Code``public` `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