Find the largest three elements in an array

Given an array with all distinct elements, find the largest three elements. Expected time complexity is O(n) and extra space is O(1).

Examples :

Input: arr[] = {10, 4, 3, 50, 23, 90}
Output: 90, 50, 23

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Below is algorithm:

1) Initialize the largest three elements as minus infinite.
    first = second = third = -∞

2) Iterate through all elements of array.
   a) Let current array element be x.
   b) If (x > first)
      {
          // This order of assignment is important
          third = second
          second = first
          first = x   
       }
   c)  Else if (x > second)
      {
          third = second
          second = x 
      }
   d)  Else if (x > third)
      {
          third = x  
      }

3) Print first, second and third.

Below is the implementation of above algorithm.

C

#include <stdio.h> 
#include <limits.h> /* For INT_MIN */ 
   
/* Function to print three largest elements */
void print2largest(int arr[], int arr_size) 
{ 
    int i, first, second, third; 
   
    /* There should be atleast two elements */
    if (arr_size < 3) 
    { 
        printf(" Invalid Input "); 
        return; 
    } 
   
    third = first = second = INT_MIN; 
    for (i = 0; i < arr_size ; i ++) 
    { 
        /* If current element is smaller than first*/
        if (arr[i] > first) 
        { 
            third = second; 
            second = first; 
            first = arr[i]; 
        } 
   
        /* If arr[i] is in between first and second then update second  */
        else if (arr[i] > second) 
        { 
            third = second; 
            second = arr[i]; 
        } 
   
        else if (arr[i] > third) 
            third = arr[i]; 
    } 
   
    printf("Three largest elements are %d %d %d\n", first, second, third); 
} 
   
   
/* Driver program to test above function */
int main() 
{ 
    int arr[] = {12, 13, 1, 10, 34, 1}; 
    int n = sizeof(arr)/sizeof(arr[0]); 
    print2largest(arr, n); 
    return 0; 
} 

Java

// Java code to find largest three elements 
// in an array 
  
class PrintLargest 
{ 
    /* Function to print three largest elements */
    static void print2largest(int arr[], int arr_size) 
    { 
        int i, first, second, third; 
    
        /* There should be atleast two elements */
        if (arr_size < 3) 
        { 
            System.out.print(" Invalid Input "); 
            return; 
        } 
        
        third = first = second = Integer.MIN_VALUE; 
        for (i = 0; i < arr_size ; i ++) 
        { 
            /* If current element is smaller than 
            first*/
            if (arr[i] > first) 
            { 
                third = second; 
                second = first; 
                first = arr[i]; 
            } 
        
            /* If arr[i] is in between first and 
            second then update second  */
            else if (arr[i] > second) 
            { 
                third = second; 
                second = arr[i]; 
            } 
        
            else if (arr[i] > third) 
                third = arr[i]; 
        } 
        
        System.out.println("Three largest elements are " + 
                       first + " " + second + " " + third); 
    } 
  
    /* Driver program to test above function*/
    public static void main (String[] args) 
    { 
        int arr[] = {12, 13, 1, 10, 34, 1}; 
        int n = arr.length; 
        print2largest(arr, n); 
    } 
} 
/*This code is contributed by Prakriti Gupta*/

Python3

# Python3 code to find largest three 
# elements in an array 
import sys 
  
# Function to print three largest  
# elements  
def print2largest(arr, arr_size): 
  
    # There should be atleast two 
    # elements  
    if (arr_size < 3): 
      
        print(" Invalid Input ") 
        return
      
    third = first = second = -sys.maxsize 
      
    for i in range(0, arr_size): 
      
        # If current element is smaller 
        # than first 
        if (arr[i] > first): 
          
            third = second 
            second = first 
            first = arr[i] 
          
  
        # If arr[i] is in between first 
        # and second then update second  
        elif (arr[i] > second): 
          
            third = second 
            second = arr[i] 
          
        elif (arr[i] > third): 
            third = arr[i] 
      
    print("Three largest elements are", 
                  first, second, third) 
  
# Driver program to test above function  
arr = [12, 13, 1, 10, 34, 1] 
n = len(arr) 
print2largest(arr, n) 
  
# This code is contributed by Smitha Dinesh Semwal 

C#

// C# code to find largest  
// three elements in an array 
using System; 
  
class PrintLargest 
{ 
      
    // Function to print three  
    // largest elements 
    static void print2largest(int[] arr, 
                              int arr_size) 
    { 
        int i, first, second, third; 
      
        // There should be atleast two elements 
        if (arr_size < 3) 
        { 
            Console.WriteLine("Invalid Input"); 
            return; 
        } 
          
        third = first = second = 000; 
        for (i = 0; i < arr_size ; i ++) 
        { 
            // If current element is  
            // smaller than first 
            if (arr[i] > first) 
            { 
                third = second; 
                second = first; 
                first = arr[i]; 
            } 
          
            // If arr[i] is in between first 
            // and second then update second 
            else if (arr[i] > second) 
            { 
                third = second; 
                second = arr[i]; 
            } 
          
            else if (arr[i] > third) 
                third = arr[i]; 
        } 
          
        Console.WriteLine("Three largest elements are " + 
                           first + " " + second + 
                           " " + third); 
    } 
  
    // Driver code 
    public static void Main () 
    { 
        int[] arr = new int[] {12, 13, 1, 10, 34, 1}; 
        int n = arr.Length; 
        print2largest(arr, n); 
    } 
} 
  
// This code is contributed by KRV.  

PHP

<?php 
// PHP code to find largest  
// three elements in an array 
  
// Function to print  
// three largest elements 
function print2largest($arr, $arr_size) 
{ 
    $i; $first; $second; $third; 
  
    // There should be atleast 
    // two elements  
    if ($arr_size < 3) 
    { 
        echo " Invalid Input "; 
        return; 
    } 
  
    $third = $first = $second = PHP_INT_MIN; 
    for ($i = 0; $i < $arr_size ; $i ++) 
    { 
        // If current element is 
        // smaller than first 
        if ($arr[$i] > $first) 
        { 
            $third = $second; 
            $second = $first; 
            $first = $arr[$i]; 
        } 
  
        // If arr[i] is in between first  
        // and second then update second  
        else if ($arr[$i] > $second) 
        { 
            $third = $second; 
            $second = $arr[$i]; 
        } 
  
        else if ($arr[$i] > $third) 
            $third = $arr[$i]; 
    } 
  
    echo "Three largest elements are ",  
       $first," ", $second," ", $third; 
} 
  
  
// Driver Code 
$arr = array(12, 13, 1,  
             10, 34, 1); 
$n = count($arr); 
print2largest($arr, $n); 
  
// This code is contributed by anuj_67. 
?> 

Output :

Three largest elements are 34 13 12

Another approach:An efficient way to solve this problem is to use any O(nLogn) sorting algorithm & simply returning the last 3 largest elements .

// Java code to find largest  
// three elements in an array 
  
  
import java.io.*; 
import java.util.Arrays; 
  
class GFG { 
     void find3largest(int[] arr) 
    { 
        Arrays.sort(arr); //It uses Tuned Quicksort with  
                         //avg. case Time complexity = O(nLogn) 
        int n = arr.length; 
        int check = 0, count = 1; 
          
        for(int i = 1; i <= n; i++){ 
              
            if(count<4){ 
                if(check!=arr[n-i])  
                {  
                   // to handle duplicate values 
                    System.out.print(arr[n-i]+" "); 
                    check = arr[n-i]; 
                    count++; 
                } 
            } 
             else 
                break; 
        } 
          
    } 
      
   // Driver code 
    public static void main(String[] args) 
    { 
        GFG obj = new GFG(); 
        int[] arr={12,45,1,-1,45,54,23,5,0,-10}; 
        obj.find3largest(arr); 
    } 
      
} 
//This code is contibuted by Prashant Malik 