Third largest element in an array of distinct elements

Given an array of n integers, find the third largest element. All the elements in the array are distinct integers. 
Example :

Input: arr[] = {1, 14, 2, 16, 10, 20}
Output: The third Largest element is 14

Explanation: Largest element is 20, second largest element is 16 
and third largest element is 14

Input: arr[] = {19, -10, 20, 14, 2, 16, 10}
Output: The third Largest element is 16

Explanation: Largest element is 20, second largest element is 19 
and third largest element is 16 

Naive Approach: The task is to first find the largest element, followed by the second-largest element and then excluding them both find the third-largest element. The basic idea is to iterate the array twice and mark the maximum and second maximum element and then excluding them both find the third maximum element, i.e the maximum element excluding the maximum and second maximum.

Algorithm:

1. First, iterate through the array and find maximum.
2. Store this as first maximum along with its index.
3. Now traverse the whole array finding the second max, excluding the maximum element.
4. Finally traverse the array the third time and find the third largest element i.e., excluding the maximum and second maximum.
   

C

// C program to find third Largest element in an array of
// distinct elements
#include <limits.h>
#include <stdio.h>

void thirdLargest(int arr[], int arr_size)
{
    /* There should be atleast three elements */
    if (arr_size < 3) {
        printf(" Invalid Input ");
        return;
    }

    // Find first largest element
    int first = arr[0];
    for (int i = 1; i < arr_size; i++)
        if (arr[i] > first)
            first = arr[i];

    // Find second largest element
    int second = INT_MIN;
    for (int i = 0; i < arr_size; i++)
        if (arr[i] > second && arr[i] < first)
            second = arr[i];

    // Find third largest element
    int third = INT_MIN;
    for (int i = 0; i < arr_size; i++)
        if (arr[i] > third && arr[i] < second)
            third = arr[i];

    printf("The third Largest element is %d\n", third);
}

/* Driver program to test above function */
int main()
{
    int arr[] = { 12, 13, 1, 10, 34, 16 };
    int n = sizeof(arr) / sizeof(arr[0]);
    thirdLargest(arr, n);
    return 0;
}

// This code is contributed by Aditya Kumar (adityakumar129)

C++

// C++ program to find third Largest
// element in an array of distinct elements
#include <bits/stdc++.h>

void thirdLargest(int arr[], int arr_size)
{
    /* There should be atleast three elements */
    if (arr_size < 3) {
        printf(" Invalid Input ");
        return;
    }

    // Find first largest element
    int first = arr[0];
    for (int i = 1; i < arr_size; i++)
        if (arr[i] > first)
            first = arr[i];

    // Find second largest element
    int second = INT_MIN;
    for (int i = 0; i < arr_size; i++)
        if (arr[i] > second && arr[i] < first)
            second = arr[i];

    // Find third largest element
    int third = INT_MIN;
    for (int i = 0; i < arr_size; i++)
        if (arr[i] > third && arr[i] < second)
            third = arr[i];

    printf("The third Largest element is %d\n", third);
}

/* Driver program to test above function */
int main()
{
    int arr[] = { 12, 13, 1, 10, 34, 16 };
    int n = sizeof(arr) / sizeof(arr[0]);
    thirdLargest(arr, n);
    return 0;
}

// This code is contributed by Aditya Kumar (adityakumar129)

Java

// Java program to find third
// Largest element in an array
// of distinct elements

class GFG
{
static void thirdLargest(int arr[],
                         int arr_size)
{
    /* There should be
    atleast three elements */
    if (arr_size < 3)
    {
        System.out.printf(" Invalid Input ");
        return;
    }

    // Find first
    // largest element
    int first = arr[0];
    for (int i = 1;
             i < arr_size ; i++)
        if (arr[i] > first)
            first = arr[i];

    // Find second
    // largest element
    int second = Integer.MIN_VALUE;
    for (int i = 0;
             i < arr_size ; i++)
        if (arr[i] > second &&
            arr[i] < first)
            second = arr[i];

    // Find third
    // largest element
    int third = Integer.MIN_VALUE;
    for (int i = 0;
             i < arr_size ; i++)
        if (arr[i] > third &&
            arr[i] < second)
            third = arr[i];

    System.out.printf("The third Largest " +
                  "element is %d\n", third);
}

// Driver code
public static void main(String []args)
{
    int arr[] = {12, 13, 1,
                 10, 34, 16};
    int n = arr.length;
    thirdLargest(arr, n);
}
}

// This code is contributed
// by Smitha

Python3

# Python 3 program to find
# third Largest element in
# an array of distinct elements
import sys
def thirdLargest(arr, arr_size):

    # There should be
    # atleast three elements
    if (arr_size < 3):

        print(" Invalid Input ")
        return


    # Find first
    # largest element
    first = arr[0]
    for i in range(1, arr_size):
        if (arr[i] > first):
            first = arr[i]

    # Find second
    # largest element
    second = -sys.maxsize
    for i in range(0, arr_size):
        if (arr[i] > second and
            arr[i] < first):
            second = arr[i]

    # Find third
    # largest element
    third = -sys.maxsize
    for i in range(0, arr_size):
        if (arr[i] > third and
            arr[i] < second):
            third = arr[i]

    print("The Third Largest",
          "element is", third)

# Driver Code
arr = [12, 13, 1,
       10, 34, 16]
n = len(arr)
thirdLargest(arr, n)

# This code is contributed
# by Smitha

Javascript

<script>

// JavaScript program to find third
// Largest element in an array
// of distinct elements

function thirdLargest(arr, arr_size)
{
    /* There should be
    atleast three elements */
    if (arr_size < 3)
    {
        document.write(" Invalid Input ");
        return;
    }

    // Find first
    // largest element
    let first = arr[0];
    for (let i = 1;
             i < arr_size ; i++)
        if (arr[i] > first)
            first = arr[i];

    // Find second
    // largest element
    let second = Number.MIN_VALUE;
    for (let i = 0;
             i < arr_size ; i++)
        if (arr[i] > second &&
            arr[i] < first)
            second = arr[i];

    // Find third
    // largest element
    let third = Number.MIN_VALUE;
    for (let i = 0;
             i < arr_size ; i++)
        if (arr[i] > third &&
            arr[i] < second)
            third = arr[i];

    document.write("The third Largest " +
                  "element is ", third);
}

// Driver Code

    let arr = [12, 13, 1,
                 10, 34, 16];
    let n = arr.length;
    thirdLargest(arr, n);

</script>

C#

// C# program to find third
// Largest element in an array
// of distinct elements
using System;

class GFG
{
static void thirdLargest(int []arr,
                         int arr_size)
{
    /* There should be
    atleast three elements */
    if (arr_size < 3)
    {
        Console.Write(" Invalid Input ");
        return;
    }

    // Find first
    // largest element
    int first = arr[0];
    for (int i = 1;
             i < arr_size ; i++)
        if (arr[i] > first)
            first = arr[i];

    // Find second
    // largest element
    int second = -int.MaxValue;
    for (int i = 0;
             i < arr_size ; i++)
        if (arr[i] > second &&
            arr[i] < first)
            second = arr[i];

    // Find third
    // largest element
    int third = -int.MaxValue;
    for (int i = 0;
             i < arr_size ; i++)
        if (arr[i] > third &&
            arr[i] < second)
            third = arr[i];

    Console.Write("The third Largest " +
                  "element is "+ third);
}

// Driver code
public static void Main()
{
    int []arr = {12, 13, 1,
                 10, 34, 16};
    int n = arr.Length;
    thirdLargest(arr, n);
}
}

// This code is contributed by Smitha

PHP

<?php
// PHP program to find third
// Largest element in an array
// of distinct elements

function thirdLargest($arr, $arr_size)
{
    /* There should be atleast
    three elements */
    if ($arr_size < 3)
    {
        echo " Invalid Input ";
        return;
    }

    // Find first largest element
    $first = $arr[0];
    for ($i = 1; $i < $arr_size ; $i++)
        if ($arr[$i] > $first)
            $first = $arr[$i];

    // Find second largest element
    $second = PHP_INT_MIN;
    for ($i = 0; $i < $arr_size ; $i++)
        if ($arr[$i] > $second &&
               $arr[$i] < $first)
            $second = $arr[$i];

    // Find third largest element
    $third = PHP_INT_MIN;
    for ($i = 0; $i < $arr_size ; $i++)
        if ($arr[$i] > $third &&
              $arr[$i] < $second)
            $third = $arr[$i];

    echo "The third Largest element is ",
                             $third,"\n";
}

// Driver Code
$arr = array(12, 13, 1,
             10, 34, 16);
$n = sizeof($arr);
thirdLargest($arr, $n);

// This code is contributed by m_kit
?>

Output

The third Largest element is 13

• Complexity Analysis:
  • Time Complexity: O(n). 
    As the array is iterated thrice and is done in a constant time
  • Space complexity: O(1). 
    No extra space is needed as the indices can be stored in constant space.

Efficient Approach: The problem deals with finding the third largest element in the array in a single traversal. The problem can be cracked by taking help of a similar problem- finding the second maximum element. So the idea is to traverse the array from start to end and to keep track of the three largest elements up to that index (stored in variables). So after traversing the whole array, the variables would have stored the indices (or value) of the three largest elements of the array.

Algorithm:

1. Create three variables, first, second, third, to store indices of three largest elements of the array. (Initially all of them are initialized to a minimum value).
2. Move along the input array from start to the end.
3. For every index check if the element is larger than first or not. Update the value of first, if the element is larger, and assign the value of first to second and second to third. So the largest element gets updated and the elements previously stored as largest becomes second largest, and the second largest element becomes third largest.
4. Else if the element is larger than the second, then update the value of second,and the second largest element becomes third largest.
5. If the previous two conditions fail, but the element is larger than the third, then update the third.
6. Print the value of third after traversing the array from start to end
   

C++

// C++ program to find third
// Largest element in an array
#include <bits/stdc++.h>

void thirdLargest(int arr[], int arr_size)
{
    /* There should be atleast three elements */
    if (arr_size < 3)
    {
        printf(" Invalid Input ");
        return;
    }

    // Initialize first, second and third Largest element
    int first = arr[0], second = INT_MIN, third = INT_MIN;

    // Traverse array elements to find the third Largest
    for (int i = 1; i < arr_size ; i ++)
    {
        /* If current element is greater than first,
           then update first, second and third */
        if (arr[i] > first)
        {
            third  = second;
            second = first;
            first  = arr[i];
        }

        /* If arr[i] is in between first and second */
        else if (arr[i] > second)
        {
            third = second;
            second = arr[i];
        }

        /* If arr[i] is in between second and third */
        else if (arr[i] > third)
            third = arr[i];
    }

    printf("The third Largest element is %d\n", third);
}

/* Driver program to test above function */
int main()
{
    int arr[] = {12, 13, 1, 10, 34, 16};
    int n = sizeof(arr)/sizeof(arr[0]);
    thirdLargest(arr, n);
    return 0;
}

Java

// Java program to find third Largest element in an array
class GFG {

    static void thirdLargest(int arr[], int arr_size) {
        /* There should be atleast three elements */
        if (arr_size < 3) {
            System.out.printf(" Invalid Input ");
            return;
        }

        // Initialize first, second and third Largest element
        int first = arr[0], second = Integer.MIN_VALUE,
                            third = Integer.MIN_VALUE;

        // Traverse array elements to find the third Largest
        for (int i = 1; i < arr_size; i++) {
            /* If current element is greater than first,
        then update first, second and third */
            if (arr[i] > first) {
                third = second;
                second = first;
                first = arr[i];
            } /* If arr[i] is in between first and second */
            else if (arr[i] > second) {
                third = second;
                second = arr[i];
            } /* If arr[i] is in between second and third */
            else if (arr[i] > third) {
                third = arr[i];
            }
        }

        System.out.printf("The third Largest element is %d\n", third);
    }

    /* Driver program to test above function */
    public static void main(String []args) {
        int arr[] = {12, 13, 1, 10, 34, 16};
        int n = arr.length;
        thirdLargest(arr, n);
    }
}
//This code is contributed by 29AjayKumar

Python3

# Python3 program to find
# third Largest element in
# an array
import sys
def thirdLargest(arr, arr_size):

    # There should be
    # atleast three elements
    if (arr_size < 3):

        print(" Invalid Input ")
        return

    # Initialize first, second
    # and third Largest element
    first = arr[0]
    second = -sys.maxsize
    third = -sys.maxsize

    # Traverse array elements
    # to find the third Largest
    for i in range(1, arr_size):

        # If current element is
        # greater than first,
        # then update first,
        # second and third
        if (arr[i] > first):

            third = second
            second = first
            first = arr[i]


        # If arr[i] is in between
        # first and second
        elif (arr[i] > second):

            third = second
            second = arr[i]

        # If arr[i] is in between
        # second and third
        elif (arr[i] > third):
            third = arr[i]

    print("The third Largest" ,
                  "element is", third)

# Driver Code
arr = [12, 13, 1,
       10, 34, 16]
n = len(arr)
thirdLargest(arr, n)

# This code is contributed
# by Smitha

Javascript

<script>

// JavaScript program to find third
// Largest element in an array

function thirdLargest(arr, arr_size)
{
    /* There should be atleast three elements */
    if (arr_size < 3)
    {
        document.write(" Invalid Input ");
        return;
    }

    // Initialize first, second and third Largest element
    var first = arr[0], second = -1000000000, third = -1000000000;

    // Traverse array elements to find the third Largest
    for (var i = 1; i < arr_size ; i ++)
    {
        /* If current element is greater than first,
        then update first, second and third */
        if (arr[i] > first)
        {
            third = second;
            second = first;
            first = arr[i];
        }

        /* If arr[i] is in between first and second */
        else if (arr[i] > second)
        {
            third = second;
            second = arr[i];
        }

        /* If arr[i] is in between second and third */
        else if (arr[i] > third)
            third = arr[i];
    }

    document.write("The third Largest element is "+ third);
}

/* Driver program to test above function */
var arr = [12, 13, 1, 10, 34, 16];
var n = arr.length;
thirdLargest(arr, n);

</script>

C#

// C# program to find third Largest element in an array
using System;
class GFG {

static void thirdLargest(int[] arr, int arr_size)
{
    /* There should be atleast three elements */
    if (arr_size < 3)
    {
        Console.Write(" Invalid Input ");
        return;

    }

    // Initialize first, second and third Largest element
    int first = arr[0], second = int.MinValue,
                            third = int.MinValue;

    // Traverse array elements to find the third Largest
    for (int i = 1; i < arr_size; i++)
    {
        /* If current element is greater than first,
        then update first, second and third */
        if (arr[i] > first) {
            third = second;
            second = first;
            first = arr[i];
        }

        /* If arr[i] is in between first and second */
        else if (arr[i] > second) {
            third = second;
            second = arr[i];
        }
        /* If arr[i] is in between second and third */
        else if (arr[i] > third) {
            third = arr[i];
        }
    }

    Console.Write("The third Largest element is "+ third);
}

/* Driver program to test above function */
public static void Main() {
        int[] arr = {12, 13, 1, 10, 34, 16};
        int n = arr.Length;
        thirdLargest(arr, n);
    }
}

// This code is contributed
// by Ita_c

PHP

<?php
// PHP program to find third
// Largest element in an array

function thirdLargest($arr, $arr_size)
{
    /* There should be atleast
       three elements */
    if ($arr_size < 3)
    {
        echo " Invalid Input ";
        return;
    }

    // Initialize first, second and
    // third Largest element
    $first = $arr[0];
    $second = PHP_INT_MIN;
    $third = PHP_INT_MIN;

    // Traverse array elements to
    // find the third Largest
    for ($i = 1; $i < $arr_size ; $i ++)
    {
        /* If current element is greater
        than first, then update first,
        second and third */
        if ($arr[$i] > $first)
        {
            $third = $second;
            $second = $first;
            $first = $arr[$i];
        }

        /* If arr[i] is in between
        first and second */
        else if ($arr[$i] > $second)
        {
            $third = $second;
            $second = $arr[$i];
        }

        /* If arr[i] is in between
        second and third */
        else if ($arr[$i] > $third)
            $third = $arr[$i];
    }

    echo "The third Largest element is ",
                                  $third;
}

// Driver Code
$arr = array (12, 13, 1,
              10, 34, 16);
$n = sizeof($arr);
thirdLargest($arr, $n);

// This code is contributed by jit_t
?>

Output

The third Largest element is 13

• Complexity Analysis:
  • Time Complexity: O(n). 
    As the array is iterated once and is done in a constant time
  • Space complexity: O(1). 
    No extra space is needed as the indices can be stored in constant space.

Another method: Using Slicing

Here, we are using slicing method, to extract 3rd largest number.

First we will sort the array then we will extract the 3rd largest element using slicing. 

C++

#include <bits/stdc++.h>
using namespace std;

int thirdLargest(int arr[], int arr_size)
{
  // if array size is less than 3,
  // then it will give invalid input
  if (arr_size < 3)
  {
        cout<<" Invalid Input"<<endl;
        return 0;
  }
  else
  {
     // here we are sorting the array
     // return 3rd largest element
     sort(arr,arr+arr_size);
    return arr[arr_size-3];
  }
}

/* Driver program to test above function */
int main()
{
    int arr[] = {12, 13, 1, 10, 34, 16};
    int n = sizeof(arr)/sizeof(arr[0]);
    cout<<thirdLargest(arr, n)<<endl;
    return 0;
}

Java

// Java implementation
import java.util.Arrays;

class Main {

    public static int thirdLargest(int[] arr)
    {
        int arr_size = arr.length;
        // if array size is less than 3,
        // then it will give invalid input
        if (arr_size < 3) {
            System.out.println("Invalid Input");
            return 0;
        }
        else {
            // here we are sorting the array
            // return 3rd largest element
            Arrays.sort(arr);
            return arr[arr_size - 3];
        }
    }

    /* Driver program to test above function */
    public static void main(String[] args)
    {

        // Input taken
        int[] arr = { 12, 13, 1, 10, 34, 16 };
        System.out.println(thirdLargest(arr));
    }
}

Python3

# Python3 program to find
# third Largest element in
# an array
def thirdLargest(arr, arr_size):
  if (arr_size < 3):                   #if array size is less than 3,
                                       #then it will give invalid input
        print(" Invalid Input ")
        return
  else:
    arr= sorted(arr)                 #here we are sorting the array
    return arr[-3]                   #return 3rd largest element




# Driver Code
arr = [12, 13, 1, 10, 34, 16]
arr_size = len(arr)
print(thirdLargest(arr, arr_size))

C#

using System;

class MainClass {
    public static int thirdLargest(int[] arr)
    {
        int arr_size = arr.Length;
        // if array size is less than 3,
        // then it will give invalid input
        if (arr_size < 3) {
            Console.WriteLine("Invalid Input");
            return 0;
        }
        else {
            // here we are sorting the array
            // return 3rd largest element
            Array.Sort(arr);
            return arr[arr_size - 3];
        }
    }

    /* Driver program to test above function */
    public static void Main(string[] args)
    {

        // Input taken
        int[] arr = { 12, 13, 1, 10, 34, 16 };
        Console.WriteLine(thirdLargest(arr));
    }
}

Javascript

function thirdLargest(arr) {
    let arr_size = arr.length;

    // if array size is less than 3,
    // then it will give invalid input
    if (arr_size < 3) {
        console.log("Invalid Input");
        return 0;
    }
    else
    {

        // here we are sorting the array
        // return 3rd largest element
        arr.sort(function(a, b) {
            return a - b;
        });
        return arr[arr_size - 3];
    }
}

// Driver program to test above function
let arr = [12, 13, 1, 10, 34, 16];
console.log(thirdLargest(arr));

Output

13

Time complexity: O(nlogn). where n is the length of the array.
Auxiliary space: O(1)

?list=PLqM7alHXFySEQDk2MDfbwEdjd2svVJH9p

Exercise Problem: Extend the above solution to find the third largest when array may have duplicates. For example, if the input array is {10, 5, 15, 5, 15, 10, 1, 1}, then output should be 5. The extended solution should also work in one traversal.