Majority Element Moore's Voting Algorithm in DSA Python - Build from Scratch

Majority Element using Moore's Voting Algorithm

📖 Scenario: Imagine you have a list of votes from a group of people choosing their favorite fruit. You want to find out which fruit got more than half of the votes, if any.

🎯 Goal: Build a program that uses Moore's Voting Algorithm to find the majority element (the fruit that appears more than half the time) in a list of votes.

📋 What You'll Learn

Create a list called votes with the exact values: ['apple', 'banana', 'apple', 'apple', 'orange', 'banana', 'apple']

Create a variable called count and set it to 0

Use a variable called candidate to store the current majority candidate

Use a for loop with variable vote to iterate over votes

Implement Moore's Voting Algorithm logic inside the loop

Print the final majority element stored in candidate

💡 Why This Matters

🌍 Real World

Finding the majority element is useful in voting systems, surveys, and data analysis where you want to identify the most common choice quickly.

💼 Career

Understanding Moore's Voting Algorithm helps in roles involving data processing, algorithm design, and software development where efficient majority detection is needed.

1

Create the list of votes

Create a list called votes with these exact values: ['apple', 'banana', 'apple', 'apple', 'orange', 'banana', 'apple']

DSA Python

# Create the list of votes
# Your code here

Hint

Use square brackets [] to create a list and separate items with commas.

2

Initialize count and candidate

Create a variable called count and set it to 0. Create a variable called candidate and set it to None.

DSA Python

votes = ['apple', 'banana', 'apple', 'apple', 'orange', 'banana', 'apple']
# Initialize count and candidate
# Your code here

Hint

Set count to zero and candidate to None before starting the loop.

3

Implement Moore's Voting Algorithm loop

Use a for loop with variable vote to iterate over votes. Inside the loop, if count is zero, set candidate to vote. If vote equals candidate, increase count by 1, else decrease count by 1.

DSA Python

votes = ['apple', 'banana', 'apple', 'apple', 'orange', 'banana', 'apple']
count = 0
candidate = None
# Implement Moore's Voting Algorithm loop
# Your code here

Hint

Follow the steps of Moore's Voting Algorithm carefully inside the loop.

4

Print the majority element

Print the value of the variable candidate.

DSA Python

votes = ['apple', 'banana', 'apple', 'apple', 'orange', 'banana', 'apple']
count = 0
candidate = None
for vote in votes:
    if count == 0:
        candidate = vote
    if vote == candidate:
        count += 1
    else:
        count -= 1
# Print the majority element
# Your code here

Hint

Use print(candidate) to show the majority element.

Practice

1. What is the main purpose of Moore's Voting Algorithm in an array of numbers?

easy

A. To find the element that appears more than half the time

B. To sort the array in ascending order

C. To find the smallest element in the array

D. To count the total number of unique elements

Solution

1. Step 1: Understand the problem Moore's Voting Algorithm solves

   The algorithm is designed to find the majority element, which is the element that appears more than half the time in the array.

2. Step 2: Compare with other options

   Sorting, finding smallest element, or counting unique elements are not the goals of this algorithm.

3. Final Answer:

   To find the element that appears more than half the time -> Option A

4. Quick Check:

   Majority element = element with >50% frequency [OK]

Hint: Majority element appears more than half times [OK]

Common Mistakes:

• Confusing majority element with most frequent element
• Thinking it sorts the array
• Assuming it counts unique elements

2. Which of the following is the correct initialization step in Moore's Voting Algorithm in Python?

easy

A. count = 0; candidate = 0

B. count = 1; candidate = 0

C. count = None; candidate = 0

D. count = 0; candidate = None

Solution

1. Step 1: Recall initialization in Moore's Voting Algorithm

   We start with count = 0 and candidate = None to indicate no candidate chosen yet.

2. Step 2: Check other options for correctness

   Starting count at 1 or candidate at 0 without context is incorrect; None is used to indicate no candidate.

3. Final Answer:

   count = 0; candidate = None -> Option D

4. Quick Check:

   Initialize count=0 and candidate=None [OK]

Hint: Start count at 0 and candidate as None [OK]

Common Mistakes:

• Starting count at 1 instead of 0
• Assigning candidate to 0 prematurely
• Using None for count instead of candidate

3. What will be the output of the following code snippet?

def majority_element(nums):
    count = 0
    candidate = None
    for num in nums:
        if count == 0:
            candidate = num
        count += (1 if num == candidate else -1)
    return candidate

print(majority_element([2,2,1,1,1,2,2]))

medium

A. 2

B. 1

C. None

D. Error

Solution

1. Step 1: Trace the candidate and count updates

   Start with count=0, candidate=None. Iterate: 2 (count=0->1, candidate=2), 2 (count=2), 1 (count=1), 1 (count=0), 1 (count=1, candidate=1), 2 (count=0), 2 (count=1, candidate=2).

2. Step 2: Final candidate after iteration

   The candidate ends as 2 after the loop finishes.

3. Final Answer:

   2 -> Option A

4. Quick Check:

   Majority element in [2,2,1,1,1,2,2] is 2 [OK]

Hint: Track candidate changes when count hits zero [OK]

Common Mistakes:

• Not updating candidate when count is zero
• Confusing candidate with last element
• Assuming candidate is None if count resets

4. Identify the bug in this Moore's Voting Algorithm implementation:

def majority_element(nums):
    count = 0
    candidate = None
    for num in nums:
        if count == 0:
            candidate = num
        if num == candidate:
            count += 1
        else:
            count -= 1
    return candidate

print(majority_element([3,3,4]))

medium

A. Count increment/decrement logic is reversed

B. No bug, code works correctly

C. Candidate not updated when count is zero

D. Function does not handle empty list

Solution

1. Step 1: Analyze candidate update and count logic

   Candidate updates when count is zero. Count increments if current num equals candidate, else decrements.

2. Step 2: Test with input [3,3,4]

   Iteration: 3 (count=1, candidate=3), 3 (count=2), 4 (count=1). Returns candidate 3 correctly.

3. Final Answer:

   No bug, code works correctly -> Option B

4. Quick Check:

   Code correctly finds majority element [OK]

Hint: Check candidate update and count changes carefully [OK]

Common Mistakes:

• Thinking candidate is not updated when count is zero
• Confusing increment and decrement logic
• Ignoring empty list edge case

5. Given an array where no element appears more than half the time, what will Moore's Voting Algorithm return?
Example: [1,2,3,4]

hard

A. Error or exception

B. The element with highest frequency

C. None or incorrect candidate

D. The first element of the array

Solution

1. Step 1: Understand Moore's Voting Algorithm assumption

   The algorithm assumes a majority element exists (more than half the array). If none exists, it still returns a candidate but it may be incorrect.

2. Step 2: Apply to example [1,2,3,4]

   No element appears more than 2 times (half of 4). The algorithm returns a candidate but it is not a true majority.

3. Final Answer:

   None or incorrect candidate -> Option C

4. Quick Check:

   No majority means candidate may be wrong [OK]

Hint: Algorithm assumes majority exists; else candidate may be wrong [OK]

Common Mistakes:

• Assuming algorithm returns error if no majority
• Thinking it returns highest frequency element always
• Believing it returns first element by default