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Find the largest three distinct elements in an array
  • Difficulty Level : Easy
  • Last Updated : 23 Feb, 2021

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

Method 1 – 
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 the above algorithm.

C++




// C++ program for find the largest
// three elements in an array
#include <bits/stdc++.h>
using namespace std;
 
// Function to print three largest elements
void print3largest(int arr[], int arr_size)
{
    int first, second, third;
 
    // There should be atleast three elements
    if (arr_size < 3)
    {
        cout << " Invalid Input ";
        return;
    }
 
    third = first = second = INT_MIN;
    for(int i = 0; i < arr_size; i++)
    {
         
        // If current element is
        // greater 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];
    }
 
    cout << "Three largest elements are "
        << first << " " << second << " "
        << third << endl;
}
 
// Driver code
int main()
{
    int arr[] = { 12, 13, 1, 10, 34, 1 };
    int n = sizeof(arr) / sizeof(arr[0]);
     
    print3largest(arr, n);
    return 0;
}
 
// This code is contributed by Anjali_Chauhan


C




// C program for find the largest
// three elements in an array
#include <limits.h> /* For INT_MIN */
#include <stdio.h>
 
/* Function to print three largest elements */
void print3largest(int arr[], int arr_size)
{
    int i, first, second, third;
 
    /* There should be atleast three 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 greater 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]);
    print3largest(arr, n);
    return 0;
}
/*This code is edited by Ayush Singla(@ayusin51)*/


Java




// Java code to find largest three elements
// in an array
 
class PrintLargest {
    /* Function to print three largest elements */
    static void print3largest(int arr[], int arr_size)
    {
        int i, first, second, third;
 
        /* There should be atleast three 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 greater 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;
        print3largest(arr, n);
    }
}
/*This code is contributed by Prakriti Gupta
and edited by Ayush Singla(@ayusin51)*/


Python3




# Python3 code to find largest three
# elements in an array
import sys
 
# Function to print three largest
# elements
def print3largest(arr, arr_size):
 
    # There should be atleast three
    # 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 greater
        # 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)
print3largest(arr, n)
 
# This code is contributed by Smitha Dinesh Semwal
# and edited by Ayush Singla(@ayusin51).


C#




// C# code to find largest
// three elements in an array
using System;
 
class PrintLargest {
 
    // Function to print three
    // largest elements
    static void print3largest(int[] arr,
                              int arr_size)
    {
        int i, first, second, third;
 
        // There should be atleast three 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
            // greater 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;
        print3largest(arr, n);
    }
}
 
// This code is contributed by KRV and edited by Ayush Singla(@ayusin51).


PHP




<?php
// PHP code to find largest
// three elements in an array
 
// Function to print
// three largest elements
function print3largest($arr, $arr_size)
{
    $i; $first; $second; $third;
 
    // There should be atleast
    // three elements
    if ($arr_size < 3)
    {
        echo " Invalid Input ";
        return;
    }
 
    $third = $first = $second = PHP_INT_MIN;
    for ($i = 0; $i < $arr_size ; $i ++)
    {
        // If current element is
        // greater than first
        if ($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);
print3largest($arr, $n);
 
// This code is contributed by anuj_67 and edited by Ayush Singla(@ayusin51).
?>


Output : 

Three largest elements are 34 13 12

Method 2 
An efficient way to solve this problem is to use any O(nLogn) sorting algorithm & simply returning the last 3 largest elements.



C++




// C++ code to find largest
// three elements in an array
#include <bits/stdc++.h>
using namespace std;
 
void find3largest(int arr[], int n)
{
    sort(arr, arr + n); // It uses Tuned Quicksort with
    // avg. case Time complexity = O(nLogn)
 
    int check = 0, count = 1;
 
    for (int i = 1; i <= n; i++) {
 
        if (count < 4) {
            if (check != arr[n - i]) {
                // to handle duplicate values
                cout << arr[n - i] << " ";
                check = arr[n - i];
                count++;
            }
        }
        else
            break;
    }
}
 
// Driver code
int main()
{
    int arr[] = { 12, 45, 1, -1, 45, 54, 23, 5, 0, -10 };
    int n = sizeof(arr) / sizeof(arr[0]);
    find3largest(arr, n);
}
 
// This code is contibuted by Rajput-Ji


Java




// 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


Python3




# Python3 code to find largest
# three elements in an array
def find3largest(arr, n):
    arr = sorted(arr) # It uses Tuned Quicksort with
                      # avg. case Time complexity = O(nLogn)
 
    check = 0
    count = 1
 
    for i in range(1, n + 1):
 
        if(count < 4):
            if(check != arr[n - i]):
                 
                # to handle duplicate values
                print(arr[n - i], end = " ")
                check = arr[n - i]
                count += 1
        else:
            break
 
# Driver code
arr = [12, 45, 1, -1, 45,
       54, 23, 5, 0, -10]
n = len(arr)
find3largest(arr, n)
 
# This code is contibuted by mohit kumar


C#




// C# code to find largest
// three elements in an array
using System;
 
class GFG {
    void find3largest(int[] arr)
    {
        Array.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
                    Console.Write(arr[n - i] + " ");
                    check = arr[n - i];
                    count++;
                }
            }
            else
                break;
        }
    }
 
    // Driver code
    public static void Main()
    {
        GFG obj = new GFG();
        int[] arr = { 12, 45, 1, -1, 45,
                      54, 23, 5, 0, -10 };
        obj.find3largest(arr);
    }
}
 
// This code is contibuted by Code_Mech


Javascript




<script>
 
// JavaScript code to find largest
// three elements in an array
 
     function find3largest(arr) {
        arr.sort((a,b)=>a-b); // It uses Tuned Quicksort with
        // avg. case Time complexity = O(nLogn)
  
        let check = 0, count = 1;
  
        for (let i = 1; i <= arr.length; i++) {
  
            if (count < 4) {
                if (check != arr[arr.length - i]) {
                    // to handle duplicate values
                    document.write(arr[arr.length - i] + " ");
                    check = arr[arr.length - i];
                    count++;
                }
            }
            else
                break;
        }
    }
  
    // Driver code
 
    let arr = [ 12, 45, 1, -1, 45, 54, 23, 5, 0, -10 ];
    find3largest(arr);
  
// This code is contributed by Surbhi Tyagi
 
</script>


Output : 

 54 45 23

Method 3 – 
We can use Partial Sort of C++ STL. partial_sort uses Heapselect, which provides better performance than Quickselect for small M. As a side effect, the end state of Heapselect leaves you with a heap, which means that you get the first half of the Heapsort algorithm “for free”. The complexity is “approximately” O(N log(M)), where M is distance(middle-first).

C++




#include <bits/stdc++.h>
using namespace std;
int main()
{
    vector<int> V = { 11, 65, 193, 36, 209, 664, 32 };
    partial_sort(V.begin(), V.begin() + 3, V.end(), greater<int>());
 
    cout << "first = " << V[0] << "\n";
    cout << "second = " << V[1] << "\n";
    cout << "third = " << V[2] << "\n";
    return 0;
}


Output :

first = 664
second = 209
third = 193

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

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