Largest lexicographic triplet from a given Array that forms a triangle
Last Updated :
01 Jul, 2022
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++
// C++ Program to implement
// 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;
}
// Java program to implement
// 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
# 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
// C# program to implement
// 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
<script>
// JavaScript Program to implement
// the above approach
// Function to find lexicographically
// largest triplet that forms a
// triangle in the given array
function findTriplet(arr, N) {
// Sort the array
arr.sort((a, b) => a - b);
var 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
document.write(
arr[i - 2] +
" " +
arr[i - 1] +
" " +
arr[i] +
"<br>"
);
}
// Otherwise
else {
document.write(-1 + "<br>");
}
}
// Driver Code
var arr = [4, 2, 10, 3, 5];
var N = arr.length;
findTriplet(arr, N);
</script>
Time Complexity: O(N*log(N))
Auxiliary Space: O(1)
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