Find Second largest element in an array

Given an array of integers, our task is to write a program that efficiently finds the second largest element present in the array. 
Example:

Input: arr[] = {12, 35, 1, 10, 34, 1}
Output: The second largest element is 34.
Explanation: The largest element of the 
array is 35 and the second 
largest element is 34

Input: arr[] = {10, 5, 10}
Output: The second largest element is 5.
Explanation: The largest element of 
the array is 10 and the second 
largest element is 5

Input: arr[] = {10, 10, 10}
Output: The second largest does not exist.
Explanation: Largest element of the array 
is 10 there is no second largest element


Simple Solution 
Approach: The idea is to sort the array in descending order and then return the second element which is not equal to largest element from the sorted array.

C++14

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// C++ program to find second largest
// element in an array
  
#include <bits/stdc++.h>
using namespace std;
  
/* Function to print the second largest elements */
void print2largest(int arr[], int arr_size)
{
    int i, first, second;
  
    /* There should be atleast two elements */
    if (arr_size < 2) {
        printf(" Invalid Input ");
        return;
    }
  
    // sort the array
    sort(arr, arr + arr_size);
  
    // start from second last element
    // as the largest element is at last
    for (i = arr_size - 2; i >= 0; i--) {
        // if the element is not
        // equal to largest element
        if (arr[i] != arr[arr_size - 1]) {
            printf("The second largest element is %d\n", arr[i]);
            return;
        }
    }
  
    printf("There is no second largest element\n");
}
  
/* Driver program to test above function */
int main()
{
    int arr[] = { 12, 35, 1, 10, 34, 1 };
    int n = sizeof(arr) / sizeof(arr[0]);
    print2largest(arr, n);
    return 0;
}

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Output:

The second largest element is 34

Complexity Analysis:

  • Time Complexity: O(n log n). 
    Time required to sort the array is O(n log n).
  • Auxiliary space: O(1). 
    As no extra space is required.

Better Solution: 
Approach: The approach is to traverse the array twice. In the first traversal find the maximum element. In the second traversal find the greatest element less than the element obtained in first traversal.



C++14

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// C++ program to find second largest
// element in an array
  
#include <bits/stdc++.h>
using namespace std;
  
/* Function to print the second largest elements */
void print2largest(int arr[], int arr_size)
{
    int i, first, second;
  
    /* There should be atleast two elements */
    if (arr_size < 2) {
        printf(" Invalid Input ");
        return;
    }
  
    int largest = second = INT_MIN;
  
    // find the largest element
    for (int i = 0; i < arr_size; i++) {
        largest = max(largest, arr[i]);
    }
  
    // find the second largest element
    for (int i = 0; i < arr_size; i++) {
        if (arr[i] != largest)
            second = max(second, arr[i]);
    }
    if (second == INT_MIN)
        printf("There is no second largest element\n");
    else
        printf("The second largest element is %d\n", second);
}
  
/* Driver program to test above function */
int main()
{
    int arr[] = { 12, 35, 1, 10, 34, 1 };
    int n = sizeof(arr) / sizeof(arr[0]);
    print2largest(arr, n);
    return 0;
}

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Java

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// Java program to find second largest
// element in an array
class GFG{
  
// Function to print the second largest elements 
static void print2largest(int arr[], int arr_size)
{
    int i, first, second;
  
    // There should be atleast two elements
    if (arr_size < 2)
    {
        System.out.printf(" Invalid Input ");
        return;
    }
  
    int largest = second = Integer.MIN_VALUE;
  
    // Find the largest element
    for(i = 0; i < arr_size; i++)
    {
        largest = Math.max(largest, arr[i]);
    }
  
    // Find the second largest element
    for(i = 0; i < arr_size; i++)
    {
        if (arr[i] != largest)
            second = Math.max(second, arr[i]);
    }
    if (second == Integer.MIN_VALUE)
        System.out.printf("There is no second " +
                          "largest element\n");
    else
        System.out.printf("The second largest " +
                          "element is %d\n", second);
}
  
// Driver code
public static void main(String[] args)
{
    int arr[] = { 12, 35, 1, 10, 34, 1 };
    int n = arr.length;
      
    print2largest(arr, n);
}
}
  
// This code is contributed by Amit Katiyar

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C#

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// C# program to find second largest
// element in an array
using System;
  
class GFG{
  
// Function to print the second largest elements 
static void print2largest(int []arr, int arr_size)
{
    // int first;
    int i, second;
  
    // There should be atleast two elements
    if (arr_size < 2)
    {
        Console.Write(" Invalid Input ");
        return;
    }
  
    int largest = second = int.MinValue;
  
    // Find the largest element
    for(i = 0; i < arr_size; i++)
    {
        largest = Math.Max(largest, arr[i]);
    }
  
    // Find the second largest element
    for(i = 0; i < arr_size; i++)
    {
        if (arr[i] != largest)
            second = Math.Max(second, arr[i]);
    }
      
    if (second == int.MinValue)
        Console.Write("There is no second " +
                      "largest element\n");
    else
        Console.Write("The second largest " +
                      "element is {0}\n", second);
}
  
// Driver code
public static void Main(String[] args)
{
    int []arr = { 12, 35, 1, 10, 34, 1 };
    int n = arr.Length;
      
    print2largest(arr, n);
}
  
// This code is contributed by Amit Katiyar

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Output:

The second largest element is 34

Complexity Analysis:

  • Time Complexity: O(n). 
    Two traversals of the array is needed.
  • Auxiliary space: O(1). 
    As no extra space is required.

Efficient Solution 
Approach: Find the second largest element in a single traversal. 
Below is the complete algorithm for doing this: 
 

1) Initialize two variables first and second to INT_MIN as
   first = second = INT_MIN
2) Start traversing the array,
   a) If the current element in array say arr[i] is greater
      than first. Then update first and second as,
      second = first
      first = arr[i]
   b) If the current element is in between first and second,
      then update second to store the value of current variable as
      second = arr[i]
3) Return the value stored in second.


C++

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// C++ program to find second largest
// element in an array
#include <bits/stdc++.h>
using namespace std;
  
// Function to print the second 
// largest elements
void print2largest(int arr[], int arr_size)
{
    int i, first, second;
  
    // There should be atleast two elements
    if (arr_size < 2)
    {
        cout << " Invalid Input ";
        return;
    }
  
    first = second = INT_MIN;
    for(i = 0; i < arr_size; i++)
    {
          
       // If current element is greater 
       // than first then update both 
       // first and second 
       if (arr[i] > first)
       {
           second = first;
           first = arr[i];
       }
         
       // If arr[i] is in between first 
       // and second then update second 
       else if (arr[i] > second &&
                arr[i] != first)
       {
           second = arr[i];
       }
    }
    if (second == INT_MIN)
        cout << "There is no second largest"
                "element\n";
    else
        cout << "The second largest element is "
             << second;
}
  
// Driver code
int main()
{
    int arr[] = { 12, 35, 1, 10, 34, 1 };
    int n = sizeof(arr) / sizeof(arr[0]);
      
    print2largest(arr, n);
    return 0;
}
  
// This code is contributed by shivanisinghss2110

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C

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// C program to find second largest
// element in an array
  
#include <limits.h>
#include <stdio.h>
  
/* Function to print the second largest elements */
void print2largest(int arr[], int arr_size)
{
    int i, first, second;
  
    /* There should be atleast two elements */
    if (arr_size < 2) {
        printf(" Invalid Input ");
        return;
    }
  
    first = second = INT_MIN;
    for (i = 0; i < arr_size; i++) {
        /* If current element is greater than first
           then update both first and second */
        if (arr[i] > first) {
            second = first;
            first = arr[i];
        }
  
        /* If arr[i] is in between first and 
           second then update second  */
        else if (arr[i] > second && arr[i] != first)
            second = arr[i];
    }
    if (second == INT_MIN)
        printf("There is no second largest element\n");
    else
        printf("The second largest element is %dn", second);
}
  
/* Driver program to test above function */
int main()
{
    int arr[] = { 12, 35, 1, 10, 34, 1 };
    int n = sizeof(arr) / sizeof(arr[0]);
    print2largest(arr, n);
    return 0;
}

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Java

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// JAVA Code for Find Second largest
// element in an array
class GFG {
  
    /* Function to print the second largest
    elements */
    public static void print2largest(int arr[],
                                     int arr_size)
    {
        int i, first, second;
  
        /* There should be atleast two elements */
        if (arr_size < 2) {
            System.out.print(" Invalid Input ");
            return;
        }
  
        first = second = Integer.MIN_VALUE;
        for (i = 0; i < arr_size; i++) {
            /* If current element is smaller than 
            first then update both first and second */
            if (arr[i] > first) {
                second = first;
                first = arr[i];
            }
  
            /* If arr[i] is in between first and 
               second then update second  */
            else if (arr[i] > second && arr[i] != first)
                second = arr[i];
        }
  
        if (second == Integer.MIN_VALUE)
            System.out.print("There is no second largest"
                             + " element\n");
        else
            System.out.print("The second largest element"
                             + " is " + second);
    }
  
    /* Driver program to test above function */
    public static void main(String[] args)
    {
        int arr[] = { 12, 35, 1, 10, 34, 1 };
        int n = arr.length;
        print2largest(arr, n);
    }
}
// This code is contributed by Arnav Kr. Mandal.

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Python3

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# Python program to
# find second largest 
# element in an array
  
  
# Function to print the
# second largest elements 
def print2largest(arr, arr_size):
  
    # There should be atleast
        # two elements 
    if (arr_size < 2):
      
        print(" Invalid Input ")
        return
      
  
    first = second = -2147483648
    for i in range(arr_size):
      
        # If current element is
                # smaller than first
        # then update both
                # first and second 
        if (arr[i] > first):
          
            second = first
            first = arr[i]
          
  
        # If arr[i] is in
                # between first and 
        # second then update second 
        elif (arr[i] > second and arr[i] != first):
            second = arr[i]
      
    if (second == -2147483648):
        print("There is no second largest element")
    else:
        print("The second largest element is", second)
  
  
# Driver program to test
# above function 
arr = [12, 35, 1, 10, 34, 1]
n = len(arr)
  
print2largest(arr, n)
  
# This code is contributed
# by Anant Agarwal.

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C#

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// C# Code for Find Second largest
// element in an array
using System;
  
class GFG {
  
    // Function to print the
    // second largest elements
    public static void print2largest(int[] arr,
                                     int arr_size)
    {
        int i, first, second;
  
        // There should be atleast two elements
        if (arr_size < 2) {
            Console.WriteLine(" Invalid Input ");
            return;
        }
  
        first = second = int.MinValue;
        for (i = 0; i < arr_size; i++) {
            // If current element is smaller than
            // first then update both first and second
            if (arr[i] > first) {
                second = first;
                first = arr[i];
            }
  
            // If arr[i] is in between first
            // and second then update second
            else if (arr[i] > second && arr[i] != first)
                second = arr[i];
        }
  
        if (second == int.MinValue)
            Console.Write("There is no second largest"
                          + " element\n");
        else
            Console.Write("The second largest element"
                          + " is " + second);
    }
  
    // Driver Code
    public static void Main(String[] args)
    {
        int[] arr = { 12, 35, 1, 10, 34, 1 };
        int n = arr.Length;
        print2largest(arr, n);
    }
}
  
// This code is contributed by Parashar.

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PHP

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<?php
// PHP program to find second largest 
// element in an array
  
// Function to print the 
// second largest elements
function print2largest($arr, $arr_size)
{
  
    // There should be atleast 
    // two elements 
    if ($arr_size < 2)
    {
        echo(" Invalid Input ");
        return;
    }
  
    $first = $second = PHP_INT_MIN;
    for ($i = 0; $i < $arr_size ; $i++)
    {
          
        // If current element is
        // smaller than first
        // then update both 
        // first and second 
        if ($arr[$i] > $first)
        {
            $second = $first;
            $first = $arr[$i];
        }
  
        // If arr[i] is in 
        // between first and 
        // second then update 
        // second 
        else if ($arr[$i] > $second &&
                 $arr[$i] != $first)
            $second = $arr[$i];
    }
    if ($second == PHP_INT_MIN)
        echo("There is no second largest element\n");
    else
        echo("The second largest element is " . $second . "\n");
}
  
// Driver Code
$arr = array(12, 35, 1, 10, 34, 1);
$n = sizeof($arr);
print2largest($arr, $n);
  
// This code is contributed by Ajit.
?>

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Output:

The second largest element is 34

Complexity Analysis:

  • Time Complexity: O(n). 
    Only one traversal of the array is needed.
  • Auxiliary space: O(1). 
    As no extra space is required.

Related Article
Smallest and second smallest element in an array
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