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

Majority Element Moore's Voting Algorithm

📖 Scenario: You are analyzing survey data collected from a group of people. The data is a list of numbers representing their favorite colors coded as integers. You want to find the color that more than half of the people chose, if any.

🎯 Goal: Build a program that uses Moore's Voting Algorithm to find the majority element in the list of favorite colors.

📋 What You'll Learn

Create a vector called colors with the exact values: {2, 2, 1, 1, 1, 2, 2}

Create an integer variable called candidate to store the potential majority element

Create an integer variable called count to keep track of the count for the candidate

Use a for loop with variable color to iterate over colors

Implement Moore's Voting Algorithm logic inside the loop

Print the value of candidate after processing all elements

💡 Why This Matters

🌍 Real World

Finding the majority element is useful in surveys, voting systems, 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 required.

1

Create the data vector

Create a vector of integers called colors with these exact values: {2, 2, 1, 1, 1, 2, 2}

DSA C++

#include 
#include 

int main() {
    // Create vector colors with values {2, 2, 1, 1, 1, 2, 2}
    // Your code here

    return 0;
}

Hint

Use std::vector<int> and initialize it with the given values.

2

Initialize candidate and count

Create an integer variable called candidate and set it to -1. Create an integer variable called count and set it to 0.

DSA C++

#include 
#include 

int main() {
    std::vector colors = {2, 2, 1, 1, 1, 2, 2};
    // Create candidate and count variables
    // Your code here

    return 0;
}

Hint

Initialize candidate to -1 and count to 0 before the loop.

3

Implement Moore's Voting Algorithm loop

Use a for loop with variable color to iterate over colors. Inside the loop, if count is 0, set candidate to color. If color equals candidate, increment count. Otherwise, decrement count.

DSA C++

#include 
#include 

int main() {
    std::vector colors = {2, 2, 1, 1, 1, 2, 2};
    int candidate = -1;
    int count = 0;

    // Implement Moore's Voting Algorithm loop
    // Your code here

    return 0;
}

Hint

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

4

Print the majority element candidate

Print the value of candidate using std::cout.

DSA C++

#include 
#include 

int main() {
    std::vector colors = {2, 2, 1, 1, 1, 2, 2};
    int candidate = -1;
    int count = 0;

    for (int color : colors) {
        if (count == 0) {
            candidate = color;
        }
        if (color == candidate) {
            count++;
        } else {
            count--;
        }
    }

    // Print candidate
    // Your code here

    return 0;
}

Hint

Use std::cout << candidate << std::endl; to print the candidate.

Practice

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

easy

A. To count the total number of unique elements

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

C. To find the smallest element in the array

D. To sort the array in ascending order

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 times in the array.

2. Step 2: Compare other options

   Sorting, finding smallest element, or counting unique elements are unrelated to Moore's Voting Algorithm's goal.

3. Final Answer:

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

4. Quick Check:

   Majority element = element with > n/2 occurrences [OK]

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

Common Mistakes:

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

2. Which of the following is the correct syntax to initialize the candidate and count variables for Moore's Voting Algorithm in C++?

easy

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

B. int candidate, count = 1;

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

D. int candidate = 0; int count;

Solution

1. Step 1: Check initialization for candidate and count

   Candidate is usually initialized to an invalid value like -1 or first element, count starts at 0.

2. Step 2: Validate options

   int candidate = -1, count = 0; initializes candidate to -1 and count to 0, which is standard and safe before iteration.

3. Final Answer:

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

4. Quick Check:

   Candidate = -1, Count = 0 initialization [OK]

Hint: Initialize candidate to -1 and count to 0 before loop [OK]

Common Mistakes:

• Not initializing count to 0
• Setting count to negative value
• Leaving candidate uninitialized

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 candidate = -1, count = 0;
for (int i = 0; i < 7; i++) {
  if (count == 0) candidate = arr[i];
  if (arr[i] == candidate) count++;
  else count--;
}
std::cout << candidate << std::endl;

medium

A. 1

B. No output

C. 0

D. 2

Solution

1. Step 1: Trace the loop and update candidate and count

   Start with candidate=-1, count=0.
   i=0: count=0, candidate=2, arr[0]=2 matches candidate, count=1
   i=1: arr[1]=2 matches candidate, count=2
   i=2: arr[2]=1 not match, count=1
   i=3: arr[3]=1 not match, count=0
   i=4: count=0, candidate=1, arr[4]=1 matches candidate, count=1
   i=5: arr[5]=2 not match, count=0
   i=6: count=0, candidate=2, arr[6]=2 matches candidate, count=1

2. Step 2: Final candidate after loop

   The candidate is 2 after the loop ends.

3. Final Answer:

   2 -> Option D

4. Quick Check:

   Final candidate = 2 [OK]

Hint: Update candidate when count is zero, increment/decrement count [OK]

Common Mistakes:

• Not updating candidate when count is zero
• Confusing increment and decrement conditions
• Assuming candidate is last element always

4. Identify the error in the following Moore's Voting Algorithm implementation snippet:

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

medium

A. Candidate update should happen before count increment/decrement

B. Count should never be decremented

C. Candidate should be initialized to -1

D. Loop should run from i = 1 to n

Solution

1. Step 1: Analyze order of candidate update and count changes

   The candidate must be updated when count is zero before comparing arr[i] with candidate to decide increment or decrement.

2. Step 2: Identify the error in code order

   Here, count is changed before candidate update, which causes wrong counting because candidate may be outdated.

3. Final Answer:

   Candidate update should happen before count increment/decrement -> Option A

4. Quick Check:

   Update candidate first when count=0 [OK]

Hint: Update candidate before count changes when count is zero [OK]

Common Mistakes:

• Updating candidate after changing count
• Initializing candidate incorrectly
• Wrong loop range

5. Given an array arr = {3, 3, 4, 2, 4, 4, 2, 4, 4}, apply Moore's Voting Algorithm to find the majority element. What is the correct majority element and why?

hard

A. 2, because it appears twice

B. 3, because it appears first in the array

C. 4, because it appears 5 times which is more than half of 9

D. No majority element exists

Solution

1. Step 1: Apply Moore's Voting Algorithm to find candidate

   Start candidate=-1, count=0.
   i=0: count=0, candidate=3, arr[0]=3 matches candidate, count=1
   i=1: arr[1]=3 matches candidate, count=2
   i=2: arr[2]=4 not match, count=1
   i=3: arr[3]=2 not match, count=0
   i=4: count=0, candidate=4, arr[4]=4 matches candidate, count=1
   i=5: arr[5]=4 matches candidate, count=2
   i=6: arr[6]=2 not match, count=1
   i=7: arr[7]=4 matches candidate, count=2
   i=8: arr[8]=4 matches candidate, count=3

2. Step 2: Verify candidate frequency

   Candidate is 4. Count occurrences of 4 in array: 5 times.
   Since 5 > 9/2 (4.5), 4 is majority element.

3. Final Answer:

   4, because it appears 5 times which is more than half of 9 -> Option C

4. Quick Check:

   Count(4) = 5 > 9/2 [OK]

Hint: Count candidate frequency after algorithm to confirm majority [OK]

Common Mistakes:

• Assuming first element is majority
• Not verifying candidate frequency
• Ignoring that majority must be > n/2