Sorted subsequence of size 3 in linear time using constant space

Given an array, the task is to find three elements of this array such that they are in sorted form i.e. for any three elements a[i], a[j] and a[k], they follow this relationship : a[i] < a[j] < a[k].

This problem is already solved below in linear time using linear space, you can read about that here:

Find a sorted subsequence of size 3 in linear time



In this post we will solve the problem without using any extra space.
Examples:

Input : arr[] = {12, 11, 10, 5, 2, 6, 30} 
Output : 5 6 30 
         or 2 6 30

As we are looking for sequence of length 3, at each index we can maintain smallest value we’ve got so far and second smallest value after smallest value’s index, now if we reach to an index whose value is larger than second smallest value, then we found our solution because we already maintained a sorted pair and we just found an element which is larger than both, so we found a 3 length sorted subsequence of array.

Please see below code for better understanding :

C++

filter_none

edit
close

play_arrow

link
brightness_4
code

// C/C++ program to find a sorted subsequence of
// size 3 using constant space
#include <bits/stdc++.h>
using namespace std;
  
// A function to fund a sorted subsequence of size 3
void find3Numbers(int arr[], int n)
{
    // Initializing small and large(second smaller)
    // by INT_MAX
    int small = INT_MAX, large = INT_MAX;
    int i;
    for (i = 0; i < n; i++)
    {
        // Update small for smallest value of array
        if (arr[i] <= small)
            small = arr[i];
  
        // Update large for second smallest value of
        // array after occurrence of small
        else if (arr[i] <= large)
            large = arr[i];
  
        // If we reach here, we found 3 numbers in
        // increasing order : small, large and arr[i]
        else
            break;
    }
  
    if (i == n)
    {
        printf("No such triplet found");
        return;
    }
  
    // last and second last will be same, but first
    // element can be updated retrieving first element
    // by looping upto i
    for (int j = 0; j <= i; j++)
    {
        if (arr[j] < large)
        {
            small = arr[j];
            break;
        }
    }
  
    printf("%d %d %d", small, large, arr[i]);
    return;
}
  
// Driver program to test above function
int main()
{
    int arr[] = {5, 7, 4, 8};
    int n = sizeof(arr)/sizeof(arr[0]);
    find3Numbers(arr, n);
    return 0;
}

chevron_right


Java

filter_none

edit
close

play_arrow

link
brightness_4
code

// Java program to find a sorted subsequence of
// size 3 using constant space
  
class GFG
{
    // A function to fund a sorted subsequence of size 3
    static void find3Numbers(int arr[], int n)
    {
        // Initializing small and large(second smaller)
        // by INT_MAX
        int small = +2147483647, large = +2147483647;
        int i;
        for (i = 0; i < n; i++)
        {
            // Update small for smallest value of array
            if (arr[i] <= small)
                small = arr[i];
      
            // Update large for second smallest value of
            // array after occurrence of small
            else if (arr[i] <= large)
                large = arr[i];
      
            // If we reach here, we found 3 numbers in
            // increasing order : small, large and arr[i]
            else
                break;
        }
      
        if (i == n)
        {
            System.out.print("No such triplet found");
            return;
        }
      
        // last and second last will be same, but first
        // element can be updated retrieving first element
        // by looping upto i
        for (int j = 0; j <= i; j++)
        {
            if (arr[j] < large)
            {
                small = arr[j];
                break;
            }
        }
      
        System.out.print(small+" "+large+" "+arr[i]);
        return;
    }
      
    // Driver program
    public static void main(String arg[])
    {
        int arr[] = {5, 7, 4, 8};
        int n = arr.length;
        find3Numbers(arr, n);
    }
}
  
// This code is contributed by Anant Agarwal.

chevron_right


Python3

filter_none

edit
close

play_arrow

link
brightness_4
code

# Python3 program to find a sorted subsequence 
# of size 3 using constant space
  
# Function to fund a sorted subsequence of size 3
def find3Numbers(arr, n):
  
    # Initializing small and large(second smaller)
    # by INT_MAX
    small = +2147483647
    large = +2147483647
      
    for i in range(n):
      
        # Update small for smallest value of array
        if (arr[i] <= small):
            small = arr[i]
  
        # Update large for second smallest value of
        # array after occurrence of small
        elif (arr[i] <= large):
            large = arr[i]
  
        # If we reach here, we found 3 numbers in
        # increasing order : small, large and arr[i]
        else:
            break
  
    if (i == n):
      
        print("No such triplet found")
        return
      
    # last and second last will be same, but
    # first element can be updated retrieving 
    # first element by looping upto i
    for j in range(i + 1):
      
        if (arr[j] < large):
          
            small = arr[j]
            break
  
    print(small," ",large," ",arr[i])
    return
  
# Driver program
arr= [5, 7, 4, 8]
n = len(arr)
find3Numbers(arr, n)
  
# This code is contributed by Anant Agarwal.

chevron_right


C#

filter_none

edit
close

play_arrow

link
brightness_4
code

// C# program to find a sorted subsequence of
// size 3 using constant space
using System;
  
class GFG {
      
    // A function to fund a sorted subsequence
    // of size 3
    static void find3Numbers(int []arr, int n)
    {
          
        // Initializing small and large(second smaller)
        // by INT_MAX
        int small = +2147483647, large = +2147483647;
        int i;
        for (i = 0; i < n; i++)
        {
              
            // Update small for smallest value of array
            if (arr[i] <= small)
                small = arr[i];
      
            // Update large for second smallest value of
            // array after occurrence of small
            else if (arr[i] <= large)
                large = arr[i];
      
            // If we reach here, we found 3 numbers in
            // increasing order : small, large and arr[i]
            else
                break;
        }
      
        if (i == n)
        {
            Console.Write("No such triplet found");
            return;
        }
      
        // last and second last will be same, but first
        // element can be updated retrieving first element
        // by looping upto i
        for (int j = 0; j <= i; j++)
        {
            if (arr[j] < large)
            {
                small = arr[j];
                break;
            }
        }
      
        Console.Write(small + " " + large + " " + arr[i]);
        return;
    }
      
    // Driver program
    public static void Main()
    {
        int []arr = {5, 7, 4, 8};
        int n = arr.Length;
        find3Numbers(arr, n);
    }
}
  
// This code is contributed by nitin mittal

chevron_right


PHP

filter_none

edit
close

play_arrow

link
brightness_4
code

<?php
// PHP program to find a sorted 
// subsequence of size 3 using 
// constant space
  
// A function to fund a sorted
// subsequence of size 3
function find3Numbers($arr, $n)
{
      
    // Initializing small and 
    // large(second smaller)
    // by INT_MAX
    $small = PHP_INT_MAX; 
    $large = PHP_INT_MAX;
    $i;
    for($i = 0; $i < $n; $i++)
    {
        // Update small for smallest
        // value of array
        if ($arr[$i] <= $small)
            $small = $arr[$i];
  
        // Update large for second
        // smallest value of after 
        // occurrence of small
        else if ($arr[$i] <= $large)
            $large = $arr[$i];
  
        // If we reach here, we 
        // found 3 numbers in
        // increasing order : 
        // small, large and arr[i]
        else
            break;
    }
  
    if ($i == $n)
    {
        echo "No such triplet found";
        return;
    }
  
    // last and second last will
    // be same, but first
    // element can be updated 
    // retrieving first element
    // by looping upto i
    for($j = 0; $j <= $i; $j++)
    {
        if ($arr[$j] < $large)
        {
            $small = $arr[$j];
            break;
        }
    }
  
    echo $small," ", $large," ", $arr[$i];
    return;
}
  
    // Driver Code
    $arr = array(5, 7, 4, 8);
    $n = count($arr);
    find3Numbers($arr, $n);
  
// This code is contributed by anuj_67.
?>

chevron_right



Output:

5 7 8

This article is contributed by Utkarsh Trivedi. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.



My Personal Notes arrow_drop_up

Improved By : nitin mittal, vt_m



Article Tags :
Practice Tags :


2


Please write to us at contribute@geeksforgeeks.org to report any issue with the above content.