Largest lexicographic triplet from a given Array that forms a triangle

Given an array arr[], the task is to find the lexicographically largest triplet in that array that can form a triangle. If no such triplet exists, print -1.
Example: 
 

Input: arr[] = { 4, 2, 10, 3, 5 } 
Output: 3 4 5 
Explanation: 
The lexicographically largest triplet is (4, 5, 10). But it does not form a triangle. 
The next lexicographically largest triplet is (3, 4, 5). 
Since it forms a triangle, it is the required answer.
Input: arr[] = { 20, 12, 120, 3, 15 } 
Output: 12 15 20 
 

 

Approach: 
A triplet can form a triangle if and only if it follows the condition given below: 
 

If A, B and C forms a triplet, then the triplet can form a triangle if 
A < B + C or B < A + C or C < A + B 
 



The idea is to use Sorting. Sort the array in ascending order. Start traversing from the end of the array and check if any triplet satisfies the above condition. Print the first triplet to satisfy the condition, as the output. If no such triplet can be found, then print -1.
Below is the implementation of the above approach:

C++

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// C++ Program to implement
// the the above approach
#include <bits/stdc++.h>
using namespace std;
 
// Function to find lexicographically
// largest triplet that forms a
// triangle in the given array
void findTriplet(int arr[], int N)
{
 
    // Sort the array
    sort(arr, arr + N);
 
    int flag = 0, i;
 
    // Iterate from the end of the array
    for (i = N - 1; i - 2 >= 0; i--) {
 
        // If the triplet forms a triangle
        if (arr[i - 2] + arr[i - 1] > arr[i]) {
            flag = 1;
            break;
        }
    }
 
    // If triplet found
    if (flag) {
 
        // Print the triplet
        cout << arr[i - 2] << " "
             << arr[i - 1] << " "
             << arr[i] << endl;
    }
 
    // Otherwise
    else {
        cout << -1 << endl;
    }
}
 
// Driver Code
int main()
{
    int arr[] = { 4, 2, 10, 3, 5 };
 
    int N = sizeof(arr) / sizeof(arr[0]);
 
    findTriplet(arr, N);
 
    return 0;
}

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Java

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// Java program to implement
// the the above approach
import java.util.*;
 
class GFG{
     
// Function to find lexicographically
// largest triplet that forms a
// triangle in the given array
static void findTriplet(int arr[], int N)
{
     
    // Sort the array
    Arrays.sort(arr);
 
    int flag = 0, i;
 
    // Iterate from the end of the array
    for(i = N - 1; i - 2 >= 0; i--)
    {
         
        // If the triplet forms a triangle
        if (arr[i - 2] + arr[i - 1] > arr[i])
        {
            flag = 1;
            break;
        }
    }
 
    // If triplet found
    if (flag != 0)
    {
         
        // Print the triplet
        System.out.println(arr[i - 2] + " " +
                           arr[i - 1] + " " +
                           arr[i] );
    }
 
    // Otherwise
    else
    {
        System.out.println(-1);
    }
}
 
// Driver Code
public static void main (String []args)
{
    int arr[] = { 4, 2, 10, 3, 5 };
 
    int N = arr.length;
 
    findTriplet(arr, N);
}
}
 
// This code is contributed by chitranayal

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Python3

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# Python3 implementation of
# the above approach
 
# Function to find lexicographically
# largest triplet that forms a
# triangle in the given array
def findTriplet(arr, N):
 
    # Sort the array
    arr.sort()
 
    # Iterate from the end of the array
    i = N - 1
    while i - 2 >= 0:
 
        # If the triplet forms a triangle
        if(arr[i - 2] + arr[i - 1] > arr[i]):
            flag = 1
            break
 
        i -= 1
 
    # If triplet found
    if(flag):
 
        # Print the triplet
        print(arr[i - 2],
              arr[i - 1],
              arr[i])
 
    # Otherwise
    else:
        print(-1)
 
# Driver Code
if __name__ == '__main__':
 
    arr = [ 4, 2, 10, 3, 5 ]
 
    N = len(arr)
 
    findTriplet(arr, N)
 
# This code is contributed by Shivam Singh

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C#

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// C# program to implement
// the the above approach
using System;
class GFG{
     
// Function to find lexicographically
// largest triplet that forms a
// triangle in the given array
static void findTriplet(int []arr, int N)
{
     
    // Sort the array
    Array.Sort(arr);
 
    int flag = 0, i;
 
    // Iterate from the end of the array
    for(i = N - 1; i - 2 >= 0; i--)
    {
         
        // If the triplet forms a triangle
        if (arr[i - 2] + arr[i - 1] > arr[i])
        {
            flag = 1;
            break;
        }
    }
 
    // If triplet found
    if (flag != 0)
    {
         
        // Print the triplet
        Console.Write(arr[i - 2] + " " +
                      arr[i - 1] + " " +
                      arr[i] );
    }
 
    // Otherwise
    else
    {
        Console.Write(-1);
    }
}
 
// Driver Code
public static void Main (string []args)
{
    int []arr = { 4, 2, 10, 3, 5 };
 
    int N = arr.Length;
 
    findTriplet(arr, N);
}
}
 
// This code is contributed by Ritik Bansal

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Output: 

3 4 5


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

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