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

Majority Element Moore's Voting Algorithm

📖 Scenario: Imagine you have a list of votes for candidates in a small election. You want to find out if there is a candidate who got more than half of the votes. This is called the majority element.

🎯 Goal: You will write a program in C to find the majority element in an array of integers using Moore's Voting Algorithm. If a majority element exists, print it; otherwise, print -1.

📋 What You'll Learn

Create an integer array called votes with the exact values: {2, 2, 1, 1, 1, 2, 2}

Create an integer variable called size and set it to the length of the votes array

Implement Moore's Voting Algorithm to find the candidate for majority element using variables candidate and count

Verify if the candidate is actually the majority element by counting its occurrences

Print the majority element if it exists, otherwise print -1

💡 Why This Matters

🌍 Real World

Finding a majority element is useful in elections, surveys, and data analysis where you want to identify the most common choice or value.

💼 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 votes array

Create an integer array called votes with the exact values {2, 2, 1, 1, 1, 2, 2}.

DSA C

# Your code here

Hint

Use int votes[] = {2, 2, 1, 1, 1, 2, 2}; to create the array.

2

Set the size variable

Create an integer variable called size and set it to the length of the votes array using sizeof(votes) / sizeof(votes[0]).

DSA C

int votes[] = {2, 2, 1, 1, 1, 2, 2};
# Your code here

Hint

Use int size = sizeof(votes) / sizeof(votes[0]); to get the array length.

3

Find the candidate using Moore's Voting Algorithm

Implement Moore's Voting Algorithm to find the candidate for majority element. Use integer variables candidate and count. Initialize candidate to votes[0] and count to 1. Then use a for loop from i = 1 to i < size to update candidate and count as per the algorithm.

DSA C

int votes[] = {2, 2, 1, 1, 1, 2, 2};
int size = sizeof(votes) / sizeof(votes[0]);
// Your code here

Hint

Use a loop to update candidate and count as you compare each vote.

4

Verify and print the majority element

Count how many times candidate appears in votes. If it appears more than size / 2, print candidate. Otherwise, print -1. Use a for loop with variable i to count occurrences, then use printf to print the result.

DSA C

int votes[] = {2, 2, 1, 1, 1, 2, 2};
int size = sizeof(votes) / sizeof(votes[0]);

int candidate = votes[0];
int count = 1;
for (int i = 1; i < size; i++) {
    if (votes[i] == candidate) {
        count++;
    } else {
        count--;
        if (count == 0) {
            candidate = votes[i];
            count = 1;
        }
    }
}
// Your code here

Hint

Count how many times candidate appears and print it if it is majority; else print -1.

Practice

1. What is the main purpose of Moore's Voting Algorithm in arrays?

easy

A. To sort the array in ascending order

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

C. To find the smallest element in the array

D. To reverse the array elements

Solution

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

   It 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 other options

   Sorting, finding smallest, or reversing are unrelated to majority element detection.

3. Final Answer:

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

4. Quick Check:

   Majority element = element with > n/2 occurrences [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 finds smallest or largest element

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

easy

A. int count = 0, candidate = -1;

B. int count = 1, candidate = 0;

C. int candidate = 0, count = 0;

D. int candidate = -1, count = 1;

Solution

1. Step 1: Identify correct variable initialization

   Moore's Voting Algorithm starts with count = 0 and candidate = -1 (or any invalid index) to indicate no candidate chosen yet.

2. Step 2: Check other options

   Other options start count or candidate incorrectly, which can cause logic errors.

3. Final Answer:

   int count = 0, candidate = -1; -> Option A

4. Quick Check:

   Start with no candidate and zero count [OK]

Hint: Initialize count=0 and candidate invalid (-1) [OK]

Common Mistakes:

• Starting count at 1 instead of 0
• Assigning candidate to 0 prematurely
• Swapping order of variables

3. What is the output of the following C code snippet using Moore's Voting Algorithm?

int arr[] = {2, 2, 1, 1, 1, 2, 2};
int n = 7;
int count = 0, candidate = -1;
for (int i = 0; i < n; i++) {
  if (count == 0) {
    candidate = arr[i];
  }
  if (arr[i] == candidate) {
    count++;
  } else {
    count--;
  }
}
printf("%d", candidate);

medium

A. 1

B. 0

C. 2

D. No majority element

Solution

1. Step 1: Trace the candidate and count updates

   Start count=0, candidate=-1
   i=0: count=0, candidate=2, count=1
   i=1: arr[i]=2 == candidate=2, count=2
   i=2: arr[i]=1 != candidate=2, count=1
   i=3: arr[i]=1 != candidate=2, count=0
   i=4: count=0, candidate=1, count=1
   i=5: arr[i]=2 != candidate=1, count=0
   i=6: count=0, candidate=2, count=1

2. Step 2: Final candidate after loop

   Candidate is 2 after loop ends.

3. Final Answer:

   2 -> Option C

4. Quick Check:

   Majority element found = 2 [OK]

Hint: Track count and candidate changes stepwise [OK]

Common Mistakes:

• Not resetting candidate when count hits zero
• Confusing candidate with last element
• Ignoring count decrement on mismatch

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

int count = 0, candidate = -1;
for (int i = 0; i < n; i++) {
  if (count == 0) {
    candidate = arr[i];
  }
  if (arr[i] != candidate) {
    count++;
  } else {
    count--;
  }
}

medium

A. Candidate initialized incorrectly

B. Candidate is not updated when count is zero

C. Loop does not run for all elements

D. Count increment and decrement conditions are reversed

Solution

1. Step 1: Check count update logic

   Correct logic: increment count if element equals candidate, decrement otherwise.
   Given code increments count when arr[i] != candidate, which is wrong.

2. Step 2: Confirm candidate update and loop correctness

   Candidate updates correctly when count == 0.
   Loop runs correctly for all elements.
   Candidate initialization is valid.

3. Final Answer:

   Count increment and decrement conditions are reversed -> Option D

4. Quick Check:

   Increment on match, decrement on mismatch [OK]

Hint: Increment count on match, decrement on mismatch [OK]

Common Mistakes:

• Swapping increment and decrement conditions
• Not updating candidate when count is zero
• Incorrect loop bounds

5. Given an array int arr[] = {3, 3, 4, 2, 4, 4, 2, 4, 4}, how can you verify if the candidate found by Moore's Voting Algorithm is actually a majority element?

hard

A. Count occurrences of candidate and check if it is more than n/2

B. Check if candidate is at the first position of the array

C. Verify if candidate is the maximum element in the array

D. No verification needed; candidate is always majority

Solution

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

   The algorithm finds a candidate but does not guarantee it is majority if none exists.

2. Step 2: Verify candidate by counting occurrences

   Count how many times candidate appears in array.
   If count > n/2, candidate is majority; else no majority element.

3. Final Answer:

   Count occurrences of candidate and check if it is more than n/2 -> Option A

4. Quick Check:

   Verify candidate count > n/2 to confirm majority [OK]

Hint: Always verify candidate count > n/2 after algorithm [OK]

Common Mistakes:

• Assuming candidate is always majority without check
• Checking candidate position instead of count
• Confusing majority with max element