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:
- First, iterate through the array and find maximum.
- Store this as first maximum along with its index.
- Now traverse the whole array finding the second max, excluding the maximum element.
- 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.
- Time Complexity: O(n).
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:
- 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).
- Move along the input array from start to the end.
- 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.
- Else if the element is larger than the second, then update the value of second,and the second largest element becomes third largest.
- If the previous two conditions fail, but the element is larger than the third, then update the third.
- 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.
- Time Complexity: O(n).
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)
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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:
- Find the smallest and second smallest element in an array
- k largest(or smallest) elements in an array
- K’th Smallest/Largest Element in Unsorted Array | Set 3 (Worst Case Linear Time)
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