Majority Element Moore's Voting Algorithm in DSA C++ - Practice Problems & Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of Moore's Voting Algorithm on a given array

What is the output of the following C++ code that implements Moore's Voting Algorithm to find the majority element?

DSA C++

int findMajorityElement(int arr[], int n) {
    int count = 0, candidate = -1;
    for (int i = 0; i < n; i++) {
        if (count == 0) {
            candidate = arr[i];
            count = 1;
        } else if (arr[i] == candidate) {
            count++;
        } else {
            count--;
        }
    }
    // Verify candidate
    count = 0;
    for (int i = 0; i < n; i++) {
        if (arr[i] == candidate) count++;
    }
    if (count > n / 2) return candidate;
    return -1;
}

int main() {
    int arr[] = {2, 2, 1, 1, 1, 2, 2};
    int n = sizeof(arr) / sizeof(arr[0]);
    int result = findMajorityElement(arr, n);
    std::cout << result << std::endl;
    return 0;
}

A 2

B 1

C -1

D 3

💡 Hint

Remember Moore's Voting Algorithm finds the element that appears more than n/2 times if it exists.

The candidate selected by the algorithm is 2, which appears 4 times out of 7, more than half. So the output is 2.

🧠 Conceptual

intermediate

Understanding the candidate selection in Moore's Voting Algorithm

In Moore's Voting Algorithm, what does the 'candidate' variable represent during the iteration over the array?

A The last element seen in the array

B The element with the highest frequency counted so far

C The element currently considered as the potential majority element

D The element that appears exactly once in the array

💡 Hint

Think about how the algorithm updates the candidate when count reaches zero.

The candidate is the element currently considered as the potential majority element. It changes when count drops to zero.

🔧 Debug

advanced

Identify the error in this Moore's Voting Algorithm implementation

What error will this code produce when run, and why?

DSA C++

int findMajorityElement(int arr[], int n) {
    int count = 0, candidate;
    for (int i = 0; i < n; i++) {
        if (count == 0) {
            candidate = arr[i];
            count = 1;
        } else if (arr[i] == candidate) {
            count++;
        } else {
            count--;
        }
    }
    // Missing verification step
    return candidate;
}

int main() {
    int arr[] = {1, 2, 3, 4, 5};
    int n = sizeof(arr) / sizeof(arr[0]);
    int result = findMajorityElement(arr, n);
    std::cout << result << std::endl;
    return 0;
}

A It will always return -1

B It will cause a runtime error due to uninitialized variable

C It will cause a compilation error due to missing return statement

D It may return a candidate that is not a majority element

💡 Hint

Check if the candidate is verified before returning.

The code returns the candidate without verifying if it appears more than n/2 times, so it may return a wrong element.

❓ Predict Output

advanced

Output of Moore's Voting Algorithm on an array with no majority

What is the output of this code when the input array has no majority element?

DSA C++

int findMajorityElement(int arr[], int n) {
    int count = 0, candidate = -1;
    for (int i = 0; i < n; i++) {
        if (count == 0) {
            candidate = arr[i];
            count = 1;
        } else if (arr[i] == candidate) {
            count++;
        } else {
            count--;
        }
    }
    count = 0;
    for (int i = 0; i < n; i++) {
        if (arr[i] == candidate) count++;
    }
    if (count > n / 2) return candidate;
    return -1;
}

int main() {
    int arr[] = {1, 2, 3, 4};
    int n = sizeof(arr) / sizeof(arr[0]);
    int result = findMajorityElement(arr, n);
    std::cout << result << std::endl;
    return 0;
}

A 0

B -1

C 4

D 1

💡 Hint

If no element appears more than half the time, the function returns -1.

No element appears more than n/2 times, so the function returns -1.

🚀 Application

expert

Number of times the candidate changes in Moore's Voting Algorithm

Given the array [3, 3, 4, 2, 4, 4, 2, 4, 4], how many times does the candidate variable change its value during the execution of Moore's Voting Algorithm?

A 2

B 4

C 5

D 3

💡 Hint

Track candidate changes when count resets to zero.

Candidate changes occur at indices 0 (3) and 4 (4), totaling 2 changes.

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