Majority Element Challenge
Find the majority element in an array using Moore's Voting Algorithm. Learn efficient array algorithms and voting techniques.
Find Majority Element
Array:
🎯 Problem Statement
Given an array of integers, find the majority element. The majority element is the element that appears more than ⌊n/2⌋ times. You may assume that the array is non-empty and the majority element always exists in the array.
💡 Key Concepts
Moore's Voting Algorithm
An efficient algorithm that finds the majority element in O(n) time and O(1) space by using a voting mechanism.
Majority Property
If an element appears more than n/2 times, it will remain as the candidate even after canceling out with other elements.
📋 Algorithm Pseudo Code
function findMajorityElement(nums):
// Initialize candidate and count
candidate = nums[0]
count = 1
// First pass: Find potential candidate
for i from 1 to length(nums) - 1:
if count == 0:
// Reset candidate
candidate = nums[i]
count = 1
else if nums[i] == candidate:
// Increment count for same element
count += 1
else:
// Decrement count for different element
count -= 1
// Second pass: Verify the candidate
count = 0
for i from 0 to length(nums) - 1:
if nums[i] == candidate:
count += 1
// Check if candidate is majority
if count > length(nums) / 2:
return candidate
else:
return null // No majority element🔍 Step-by-Step Example
Input: nums = [3, 3, 4, 2, 4, 4, 2, 4, 4]
Step 1: candidate = 3, count = 1
Step 2: nums[1] = 3, count = 2
Step 3: nums[2] = 4, count = 1
Step 4: nums[3] = 2, count = 0, candidate = 2
Step 5: Continue until end, final candidate = 4
Verification: 4 appears 5 times > 9/2 = 4.5 ✓
📊 Voting Visualization
⏱️ Complexity Analysis
Time Complexity
O(n) - Two passes through the array
Space Complexity
O(1) - Only using a few variables
🔄 Alternative Approaches
Hash Map Approach
Count occurrences of each element using a hash map. Time: O(n), Space: O(n)
Sorting Approach
Sort the array and find the middle element. Time: O(n log n), Space: O(1)
Boyer-Moore Voting
The most efficient approach for guaranteed majority element. Time: O(n), Space: O(1)
⚠️ Edge Cases
No Majority Element
When no element appears more than n/2 times, the algorithm may return an incorrect result. Always verify!
Single Element Array
Array with one element is always the majority element.
All Same Elements
When all elements are the same, that element is the majority.
1. Click on numbers in the array to select them
2. Select enough numbers to analyze a potential majority
3. The majority element appears more than n/2 times
4. Use Moore\'s Voting Algorithm for efficiency
5. Complete all levels to win!