MAJORITY ELEMENT IN AN ARRAY

Majority Element in an Array – Moore’s Voting Algorithm

Introduction

The majority element in an array is the element that appears more than n/2 times, where n is the size of the array.

This problem can be solved in multiple ways, but the most efficient one is Moore’s Voting Algorithm, which works in linear time and constant space.

Problem Statement

Given an array arr[], find the majority element:

  • If an element appears more than n/2 times = return it

  • Otherwise = return -1

Example

Input:

arr = [1, 1, 2, 1, 3, 5, 1]

Output:

1

Solution Code

class Solution:
    def majorityElement(self, arr):
        
        candidate = None
        count = 0

        for num in arr:
            if count == 0:
                candidate = num
                count = 1
            elif num == candidate:
                count += 1
            else:
                count -= 1

        
        count = 0
        for num in arr:
            if num == candidate:
                count += 1

        if count > len(arr) // 2:
            return candidate
        else:
            return -1

Approach Used: Moore’s Voting Algorithm

Idea

We try to find a candidate that could be the majority element by canceling out different elements.

How It Works

Step 1: Find Candidate

  • Traverse the array:

    • If count == 0 => pick a new candidate

    • If same as candidate => increase count

    • Else => decrease count

This “cancels out” different elements

Step 2: Verify Candidate

  • Count how many times the candidate appears

  • Check if it is more than n/2

Why This Approach Was Chosen

  • Works in O(n) time

  • Uses O(1) space

  • Much better than counting using maps

Alternative Approaches

  • HashMap / Dictionary
     Easy to implement
     Uses extra space

  • Sorting
     Majority will be at middle
     Time Complexity: O(n log n)

Why Moore’s Algorithm?
Because it is the most optimized solution

Time and Space Complexity

  • Time Complexity: O(n)

  • Space Complexity: O(1)

Important Observation

  • Majority element cancels out all other elements

  • If it exists, it will always remain as the final candidate

Edge Cases

  • Single element = always majority

  • No majority = return -1

  • All elements same

Conclusion

Moore’s Voting Algorithm is an efficient and elegant solution for finding the majority element. By canceling out non-majority elements, it ensures that the correct candidate emerges, making it one of the best approaches for this problem.

 

Comments

Post a Comment

Popular posts from this blog

THE DELIVERY MAN

  The Delivery Man – Python List Operations  Introduction Lists in Python are used to store multiple items in a single variable. They are flexible, allowing us to add, remove, update, and manipulate elements easily. In this task, different list operations are performed to simulate a delivery man's workflow. 1. Creating a list and accessing an item items = ["Notebook", "Pencil", "Eraser", "Ruler", "Marker"] print(items[2]) Approach: Indexing Why: Lists use zero-based indexing, so the third item is accessed using index 2. 2. Adding a new item items.append("Glue Stick") print(items) Approach: append() method Why: It adds an item at the end of the list, which is ideal for adding new deliveries. 3. Inserting an item items.insert(2, "Highlighter") print(items) Approach: insert() method Why: Used when we need to add an item at a specific position instead of the end. 4. Removing an item items.remove("Ruler...
Read more

EC2 LAUNCHING

  EC2 Step 1: Launch EC2 Instance Go to: AWS Console --> EC2 --> Launch Instance Configure: Name : my-web-server AMI : Amazon Linux 2 (easy for beginners) Instance Type : t2.micro (free tier) Step 2: Key Pair Create or select a key pair. Step 3: Network Settings  Allow these: SSH (port 22) --> for login  HTTP (port 80) --> for web access Step 4: Launch Instance Click Launch Instance Step 5: Connect to Instance Use: EC2 --> Connect --> EC2 Instance Connect (easiest) OR via terminal: with this command. for this you have to download the pem files while selecting the key pair.  ssh -i your-key.pem ec2-user@<public-ip> Step 6: Install Web Server For Amazon Linux: sudo yum update -y sudo yum install httpd -y Step 7: Start Web Server sudo systemctl start httpd sudo systemctl enable httpd Step 8: Add a Web Page echo "Hello from EC2" | sudo tee /var/www/html/index.html Step 9: Get Public IP Go to EC2 d...
Read more

SORT A LINKED LIST USING MERGE SORT

  Sort a Linked List using Merge Sort Introduction Sorting a linked list efficiently is a common problem in data structures. Unlike arrays, linked lists do not allow direct access to elements, so algorithms like quicksort are not ideal. Merge Sort is the best choice for linked lists because: It does not require random access It works efficiently with node-based structures Problem Statement Given the head of a linked list: Sort the list in ascending order Return the sorted linked list Example Input: 10 -> 30 -> 20 -> 40 -> 60 -> 50 Output: 10 -> 20 -> 30 -> 40 -> 50 -> 60 Solution Code class Solution: def mergeSort(self, head): if not head or not head.next: return head mid = self.getMiddle(head) next_to_mid = mid.next mid.next = None left = self.mergeSort(head) right = self.mergeSort(next_to_mid) return self.merge(left, right) def getMiddle(self,...
Read more