Boyer-Moore Majority Vote Algorithm

April 28, 2023

Boyer-Moore Majority Vote Algorithm

On this page we will discuss about Boyer–Moore majority vote algorithm in Java. The Boyer-Moore Majority Vote Algorithm is an efficient algorithm for finding the majority element in an array, which refers to an element that occurs more than half of the time in the array. So lets see this in detail with code in Java.

Boyer-Moore Majority Vote Algorithm in Java

The Boyer-Moore Majority Vote Algorithm is an efficient algorithm for finding the majority element in an array, which is an element that appears more than n/2 times, where n is the length of the array. The algorithm was proposed by Robert S. Boyer and J Strother Moore in 1980 and is widely used in various applications, such as data analysis, voting systems, and image processing.

The Boyer-Moore Majority Vote Algorithm operates in linear time complexity, which makes it efficient for large arrays, and uses constant space. The basic idea of the algorithm is to maintain a counter that starts from zero and iterates through the array, incrementing the counter for each occurrence of a candidate element, and decrementing it for each occurrence of a different element. The algorithm identifies the majority element as the candidate element with the highest count after scanning through the array.

Note The algorithm works in O(n) time complexity and O(1) space complexity, which makes it very efficient for large arrays.

Example:

Input: k = 6,  arr = [ 1, 2, 5, 2, 2, 2 ]

Output: Majority Element is 2

Introduction to Arrays

Introduction to 2-D Arrays

Array Rotation

Reverse an Array or String

Sort the array in Waveform

Algorithm :

Iterate through the array from the beginning to the end.
For each element in the array:
- If the count is 0, set the current element as the candidate.
- If the current element is the same as the candidate, increment the count.
- If the current element is different from the candidate, decrement the count.
After the first pass, the candidate is the potential majority element.
Reset the count to 0.
Iterate through the array again.
Count the occurrences of the candidate element.
If the candidate occurs more than half of the time, it is the majority element.
If the candidate occurs more than half of the time, return it as the majority element.
If the candidate occurs less than or equal to half of the time, there is no majority element.

Java Code

Run

import java.util.*;

public class Main
{
    public static int majorityElement(int [] nums)
    {
        int candidate = 0;
        int count = 0;
        
        for(int num : nums)
        {
            if(count == 0)
            {
                candidate = num;
            }
            count += (num == candidate)? 1 : -1;
        }
        
        count = 0;
        for(int num : nums)
        {
            if(num == candidate)
            {
                count++;
            }
        }
        
        if(count > nums.length/2)
        {
            return candidate;
        }
        else
        {
            return -1;
        }
    }
    
	public static void main(String[] args) 
	{
		int [] nums = { 1, 2, 2, 2, 3, 2, 4, 2, 5 };
		int majority = majorityElement(nums);
		if(majority != -1)
		{
		    System.out.print("The majority element is: " + majority);
		}
		else
		{
		    System.out.print("There is no majority element.");
		}
	}
}

Output

The majority element is: 2

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