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Majority Element II

Certification: Intermediate Level Accuracy: 0% Submissions: 0 Points: 15

Write a C program to find all elements that appear more than ⌊n/3⌋ times in an array, where n is the length of the array. The algorithm should run in linear time and use only constant extra space. There can be at most 2 such elements in any array.

Example 1
    
      
  • Input: nums = [3,2,3]
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  • Output: [3]
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  • Explanation: 
    • Array length n = 3, so ⌊n/3⌋ = 1. 
    • Element 3 appears 2 times, which is > 1. 
    • Element 2 appears 1 time, which is not > 1. 
    • Therefore, only [3] appears more than ⌊n/3⌋ times.
    •
Example 2
    
      
  • Input: nums = [1]
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  • Output: [1]
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  • Explanation: 
    • Array length n = 1, so ⌊n/3⌋ = 0. 
    • Element 1 appears 1 time, which is > 0. 
    • Therefore, [1] appears more than ⌊n/3⌋ times.
    •
Constraints
    
      
  • 1 ≤ nums.length ≤ 5 * 10^4
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  • -10^9 ≤ nums[i] ≤ 10^9
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  • Time Complexity: O(n)
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  • Space Complexity: O(1)
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  • At most 2 elements can appear more than ⌊n/3⌋ times
    •
ArraysAlgorithmsIBMEY
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Solution

Solution Hints

    
      
  • Use Boyer-Moore Majority Vote algorithm extended for finding 2 candidates
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  • Maintain two candidates and their respective counts
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  • In the first pass, find potential candidates using voting mechanism
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  • In the second pass, verify if candidates actually appear more than n/3 times
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  • If a number matches candidate1, increment count1; if matches candidate2, increment count2
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  • If neither matches and both counts > 0, decrement both counts
    •

Steps to solve by this approach:

 Step 1: Initialize two candidate variables and their respective count variables to 0
 Step 2: First pass through array - use voting mechanism to find potential candidates
 Step 3: If current element matches candidate1, increment count1; if matches candidate2, increment count2
 Step 4: If no match and count1 is 0, set candidate1 to current element; if count2 is 0, set candidate2
 Step 5: If no match and both counts > 0, decrement both counts (voting mechanism)
 Step 6: Second pass through array - count actual occurrences of both candidates
 Step 7: Add candidates to result array only if their count exceeds n/3 threshold

Submitted Code :