Find Last Digit of a^b for Large Numbers

Third largest element in an array of distinct elements

Last Updated : 17 Feb, 2025

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Given an array of n integers, the task is to find the third largest element. All the elements in the array are distinct integers.

Examples :

Input: arr[] = {1, 14, 2, 16, 10, 20}
Output: 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: 16
Explanation: Largest element is 20, second largest element is 19 and third largest element is 16

[Naive Approach] Using Sorting – O(n * log n) time and O(1) space

The idea is to sort the array and return the third largest element in the array which will be present at (n-3)’th index.

C++

// C++ program to find the third largest
// element in an array.
#include <bits/stdc++.h>
using namespace std;

int thirdLargest(vector<int> &arr) {
    int n = arr.size();
    
    // Sort the array 
    sort(arr.begin(), arr.end());
    
    // Return the third largest element 
    return arr[n-3];
}

int main() {
    vector<int> arr = {1, 14, 2, 16, 10, 20};
    cout << thirdLargest(arr) << endl;

    return 0;
}

Java

// Java program to find the third largest
// element in an array.
import java.util.*;

class GfG {
    static int thirdLargest(int[] arr) {
        int n = arr.length;
        
        // Sort the array 
        Arrays.sort(arr);
        
        // Return the third largest element 
        return arr[n - 3];
    }

    public static void main(String[] args) {
        int[] arr = {1, 14, 2, 16, 10, 20};
        System.out.println(thirdLargest(arr));
    }
}

Python

# Python program to find the third largest
# element in an array.

# Function to find the third largest element
def thirdLargest(arr):
    n = len(arr)
    
    # Sort the array 
    arr.sort()
    
    # Return the third largest element 
    return arr[n - 3]

if __name__ == "__main__":
    arr = [1, 14, 2, 16, 10, 20]
    print(thirdLargest(arr))

C#

// C# program to find the third largest
// element in an array.
using System;

class GfG {
    static int thirdLargest(int[] arr) {
        int n = arr.Length;
        
        // Sort the array 
        Array.Sort(arr);
        
        // Return the third largest element 
        return arr[n - 3];
    }

    static void Main() {
        int[] arr = {1, 14, 2, 16, 10, 20};
        Console.WriteLine(thirdLargest(arr));
    }
}

JavaScript

// JavaScript program to find the third largest
// element in an array.

// Function to find the third largest element
function thirdLargest(arr) {
    let n = arr.length;
    
    // Sort the array 
    arr.sort((a, b) => a - b);
    
    // Return the third largest element 
    return arr[n - 3];
}

let arr = [1, 14, 2, 16, 10, 20];
console.log(thirdLargest(arr));

Output

[Expected Approach – 1] Using Three Loops – O(n) time and O(1) space

The 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.

Step by step approach:

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 the third largest
// element in an array.
#include <bits/stdc++.h>
using namespace std;

int thirdLargest(vector<int> &arr) {
    int n = arr.size();
    
    // Find the first maximum element.
    int first = INT_MIN;
    for (int i=0; i<n; i++) {
        if (arr[i] > first) first = arr[i];
    }
    
    // Find the second max element.
    int second = INT_MIN;
    for (int i=0; i<n; i++) {
        if (arr[i] > second && arr[i] < first) {
            second = arr[i];
        }
    }
    
    // Find the third largest element.
    int third = INT_MIN;
    for (int i=0; i<n; i++) {
        if (arr[i] > third && arr[i] < second) {
            third = arr[i];
        }
    }
    
    // Return the third largest element 
    return third;
}

int main() {
    vector<int> arr = {1, 14, 2, 16, 10, 20};
    cout << thirdLargest(arr) << endl;

    return 0;
}

Java

// Java program to find the third largest
// element in an array.
import java.util.*;

class GfG {
    static int thirdLargest(int[] arr) {
        int n = arr.length;
        
        // Find the first maximum element.
        int first = Integer.MIN_VALUE;
        for (int i = 0; i < n; i++) {
            if (arr[i] > first) first = arr[i];
        }
        
        // Find the second max element.
        int second = Integer.MIN_VALUE;
        for (int i = 0; i < n; i++) {
            if (arr[i] > second && arr[i] < first) {
                second = arr[i];
            }
        }
        
        // Find the third largest element.
        int third = Integer.MIN_VALUE;
        for (int i = 0; i < n; i++) {
            if (arr[i] > third && arr[i] < second) {
                third = arr[i];
            }
        }
        
        // Return the third largest element 
        return third;
    }

    public static void main(String[] args) {
        int[] arr = {1, 14, 2, 16, 10, 20};
        System.out.println(thirdLargest(arr));
    }
}

Python

# Python program to find the third largest
# element in an array.

# Function to find the third largest element
def thirdLargest(arr):
    n = len(arr)
    
    # Find the first maximum element.
    first = float('-inf')
    for i in range(n):
        if arr[i] > first:
            first = arr[i]
    
    # Find the second max element.
    second = float('-inf')
    for i in range(n):
        if arr[i] > second and arr[i] < first:
            second = arr[i]
    
    # Find the third largest element.
    third = float('-inf')
    for i in range(n):
        if arr[i] > third and arr[i] < second:
            third = arr[i]
    
    # Return the third largest element 
    return third

if __name__ == "__main__":
    arr = [1, 14, 2, 16, 10, 20]
    print(thirdLargest(arr))

C#

// C# program to find the third largest
// element in an array.
using System;

class GfG {
    static int thirdLargest(int[] arr) {
        int n = arr.Length;
        
        // Find the first maximum element.
        int first = int.MinValue;
        for (int i = 0; i < n; i++) {
            if (arr[i] > first) first = arr[i];
        }
        
        // Find the second max element.
        int second = int.MinValue;
        for (int i = 0; i < n; i++) {
            if (arr[i] > second && arr[i] < first) {
                second = arr[i];
            }
        }
        
        // Find the third largest element.
        int third = int.MinValue;
        for (int i = 0; i < n; i++) {
            if (arr[i] > third && arr[i] < second) {
                third = arr[i];
            }
        }
        
        // Return the third largest element 
        return third;
    }

    static void Main() {
        int[] arr = {1, 14, 2, 16, 10, 20};
        Console.WriteLine(thirdLargest(arr));
    }
}

JavaScript

// JavaScript program to find the third largest
// element in an array.

// Function to find the third largest element
function thirdLargest(arr) {
    let n = arr.length;
    
    // Find the first maximum element.
    let first = -Infinity;
    for (let i = 0; i < n; i++) {
        if (arr[i] > first) first = arr[i];
    }
    
    // Find the second max element.
    let second = -Infinity;
    for (let i = 0; i < n; i++) {
        if (arr[i] > second && arr[i] < first) {
            second = arr[i];
        }
    }
    
    // Find the third largest element.
    let third = -Infinity;
    for (let i = 0; i < n; i++) {
        if (arr[i] > third && arr[i] < second) {
            third = arr[i];
        }
    }
    
    // Return the third largest element 
    return third;
}

let arr = [1, 14, 2, 16, 10, 20];
console.log(thirdLargest(arr));

Output

[Expected Approach – 2] Using Three variables – O(n) time and O(1) space

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.

Step by step approach:

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.

C++

// C++ program to find the third largest
// element in an array.
#include <bits/stdc++.h>
using namespace std;

int thirdLargest(vector<int> &arr) {
    int n = arr.size();
    
    int first = INT_MIN, second = INT_MIN,
    third = INT_MIN;
    
    for (int i=0; i<n; i++) {
        
        // If arr[i] is greater than first,
        // set third to second, second to 
        // first and first to arr[i].
        if (arr[i] > first) {
            third = second;
            second = first;
            first = arr[i];
        }
        
        // If arr[i] is greater than second, 
        // set third to second and second 
        // to arr[i].
        else if (arr[i] > second) {
            third = second;
            second = arr[i];
        }
        
        // If arr[i] is greater than third,
        // set third to arr[i].
        else if (arr[i] > third) {
            third = arr[i];
        }
    }
    
    // Return the third largest element 
    return third;
}

int main() {
    vector<int> arr = {1, 14, 2, 16, 10, 20};
    cout << thirdLargest(arr) << endl;

    return 0;
}

Java

// Java program to find the third largest
// element in an array.
import java.util.*;

class GfG {
    static int thirdLargest(int[] arr) {
        int n = arr.length;
        
        int first = Integer.MIN_VALUE, second = Integer.MIN_VALUE,
        third = Integer.MIN_VALUE;
        
        for (int i = 0; i < n; i++) {
            
            // If arr[i] is greater than first,
            // set third to second, second to 
            // first and first to arr[i].
            if (arr[i] > first) {
                third = second;
                second = first;
                first = arr[i];
            }
            
            // If arr[i] is greater than second, 
            // set third to second and second 
            // to arr[i].
            else if (arr[i] > second) {
                third = second;
                second = arr[i];
            }
            
            // If arr[i] is greater than third,
            // set third to arr[i].
            else if (arr[i] > third) {
                third = arr[i];
            }
        }
        
        // Return the third largest element 
        return third;
    }

    public static void main(String[] args) {
        int[] arr = {1, 14, 2, 16, 10, 20};
        System.out.println(thirdLargest(arr));
    }
}

Python

# Python program to find the third largest
# element in an array.

# Function to find the third largest element
def thirdLargest(arr):
    n = len(arr)
    
    first, second, third = float('-inf'), float('-inf'), float('-inf')
    
    for i in range(n):
        
        # If arr[i] is greater than first,
        # set third to second, second to 
        # first and first to arr[i].
        if arr[i] > first:
            third = second
            second = first
            first = arr[i]
        
        # If arr[i] is greater than second, 
        # set third to second and second 
        # to arr[i].
        elif arr[i] > second:
            third = second
            second = arr[i]
        
        # If arr[i] is greater than third,
        # set third to arr[i].
        elif arr[i] > third:
            third = arr[i]
    
    # Return the third largest element 
    return third

if __name__ == "__main__":
    arr = [1, 14, 2, 16, 10, 20]
    print(thirdLargest(arr))

C#

// C# program to find the third largest
// element in an array.
using System;

class GfG {
    static int thirdLargest(int[] arr) {
        int n = arr.Length;
        
        int first = int.MinValue, second = int.MinValue,
        third = int.MinValue;
        
        for (int i = 0; i < n; i++) {
            
            // If arr[i] is greater than first,
            // set third to second, second to 
            // first and first to arr[i].
            if (arr[i] > first) {
                third = second;
                second = first;
                first = arr[i];
            }
            
            // If arr[i] is greater than second, 
            // set third to second and second 
            // to arr[i].
            else if (arr[i] > second) {
                third = second;
                second = arr[i];
            }
            
            // If arr[i] is greater than third,
            // set third to arr[i].
            else if (arr[i] > third) {
                third = arr[i];
            }
        }
        
        // Return the third largest element 
        return third;
    }

    static void Main() {
        int[] arr = {1, 14, 2, 16, 10, 20};
        Console.WriteLine(thirdLargest(arr));
    }
}

JavaScript

// JavaScript program to find the third largest
// element in an array.

// Function to find the third largest element
function thirdLargest(arr) {
    let n = arr.length;
    
    let first = -Infinity, second = -Infinity,
    third = -Infinity;
    
    for (let i = 0; i < n; i++) {
        
        // If arr[i] is greater than first,
        // set third to second, second to 
        // first and first to arr[i].
        if (arr[i] > first) {
            third = second;
            second = first;
            first = arr[i];
        }
        
        // If arr[i] is greater than second, 
        // set third to second and second 
        // to arr[i].
        else if (arr[i] > second) {
            third = second;
            second = arr[i];
        }
        
        // If arr[i] is greater than third,
        // set third to arr[i].
        else if (arr[i] > third) {
            third = arr[i];
        }
    }
    
    // Return the third largest element 
    return third;
}

let arr = [1, 14, 2, 16, 10, 20];
console.log(thirdLargest(arr));

Output

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