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++



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    // 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;
    }

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    Java

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    // 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

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    Python3

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    # 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

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    C#

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    // 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

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    PHP

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    <?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
    ?>

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  • 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 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++

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    // 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;
    }

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    Java

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    // 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

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    Python3

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    # 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

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    C#

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    // 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

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    PHP

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    <?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
    ?>

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  • 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 the indices can be stored in constant space.
  • 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.

    Related Articles:

    1. Find the smallest and second smallest element in an array
    2. k largest(or smallest) elements in an array
    3. K’th Smallest/Largest Element in Unsorted Array | Set 3 (Worst Case Linear Time)

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