Third largest element in an array of distinct elements

1.6

Given an array of distinct elements, find third largest element in it.

Example :

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

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

Method 1 (Simple) Simplest way to solve this question is to first iterate through the array and find first maximum. Store this first maximum as well as its index. Now traverse the whole array finding the second max with the changed condition. Finally traverse the array third time and find the third largest element.

// 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;
}

Output :

The third Largest element is 13

Method 2 In this method, we need not to iterate array three times. We can find third largest in one traversal only.

  1. Initialize first = a[0] and second = -INF, third = -INF
  2. Iterate the array and compare each element with first.
    • If a[i] is greater than first then update all first, second and third:
      third = second
      second = first
      first = arr[i]
    • Else compare arr[i] with second, if its greater than second, then update:
      third = second
      second = arr[i]
    • Else compare arr[i] with third, if its greater than third, then update:
      third = arr[i]
  3. Return third
// 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;
}

Output :

The third Largest element is 13

Exercise :
Extend the above solution to find 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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