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

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of Moore's Voting Algorithm on given array

What is the output of the following Java code that uses Moore's Voting Algorithm to find the majority element?

DSA Java

public class MajorityElement {
    public static int findMajority(int[] nums) {
        int count = 0, candidate = -1;
        for (int num : nums) {
            if (count == 0) {
                candidate = num;
            }
            count += (num == candidate) ? 1 : -1;
        }
        return candidate;
    }

    public static void main(String[] args) {
        int[] arr = {2, 2, 1, 1, 1, 2, 2};
        System.out.println(findMajority(arr));
    }
}

A 1

B 2

C 0

D Runtime Error

💡 Hint

The majority element is the one that appears more than half the times in the array.

The algorithm picks a candidate and counts its occurrences against others. Here, 2 appears 4 times out of 7, which is more than half, so the output is 2.

🧠 Conceptual

intermediate

Understanding the count variable in Moore's Voting Algorithm

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

A The number of times the current candidate has appeared minus the number of times other elements have appeared

B The total number of elements processed so far

C The sum of all elements processed so far

D The index of the current candidate in the array

💡 Hint

Think about how the algorithm balances the candidate's count against other elements.

The count increases when the current element matches the candidate and decreases otherwise, effectively tracking the difference between candidate occurrences and others.

🔧 Debug

advanced

Identify the error in this Moore's Voting Algorithm implementation

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

DSA Java

public class MajorityElement {
    public static int findMajority(int[] nums) {
        int count = 0, candidate = 0;
        for (int num : nums) {
            if (count == 0) {
                candidate = num;
            }
            if (num == candidate) {
                count++;
            } else {
                count--;
            }
        }
        return candidate;
    }

    public static void main(String[] args) {
        int[] arr = {};
        System.out.println(findMajority(arr));
    }
}

A Throws NullPointerException

B Throws ArrayIndexOutOfBoundsException

C Returns 0 without error

D Returns incorrect majority element

💡 Hint

Consider what happens when the input array is empty.

The code returns 0 because candidate is initialized to 0 and the loop does not run. No exception is thrown.

🚀 Application

advanced

Using Moore's Voting Algorithm to verify majority element

After finding a candidate using Moore's Voting Algorithm, what additional step is necessary to confirm it is truly the majority element?

A Count the occurrences of the candidate in the array and check if it is more than half the array length

B Return the candidate immediately as majority element

C Sort the array and check the middle element

D Check if candidate is the first element of the array

💡 Hint

The algorithm finds a candidate but does not guarantee it is majority without verification.

Moore's Voting Algorithm finds a candidate that might be majority. To confirm, count its occurrences and verify it exceeds half the array size.

❓ Predict Output

expert

Output of Moore's Voting Algorithm with no majority element

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

DSA Java

public class MajorityElement {
    public static int findMajority(int[] nums) {
        int count = 0, candidate = -1;
        for (int num : nums) {
            if (count == 0) {
                candidate = num;
            }
            count += (num == candidate) ? 1 : -1;
        }
        return candidate;
    }

    public static void main(String[] args) {
        int[] arr = {1, 2, 3, 4, 3, 6};
        System.out.println(findMajority(arr));
    }
}

A -1

B 6

C No majority element

D 3

💡 Hint

The algorithm returns a candidate but does not guarantee majority if none exists.

The algorithm returns 3 as candidate after processing, but since no element appears more than half, it is not a true majority.

Practice

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

easy

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

B. To sort the array in ascending order

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

   The algorithm 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 with other options

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

3. Final Answer:

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

4. Quick Check:

   Majority element = element appearing > n/2 times [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 Java code snippets correctly initializes the count variable for Moore's Voting Algorithm?

easy

A. int count = null;

B. int count = -1;

C. int count = 0;

D. int count = 1;

Solution

1. Step 1: Check valid initialization for count

   Count starts at 1 because the first candidate is chosen and has one vote initially.

2. Step 2: Validate each option

   - -1 is invalid as count should not start negative.
   - 0 is incorrect because the first candidate is already counted once.
   - null is invalid for int type in Java.

3. Final Answer:

   int count = 1; -> Option D

4. Quick Check:

   Count starts at one for the first candidate [OK]

Hint: Count starts at one for the first candidate [OK]

Common Mistakes:

• Initializing count with 0 instead of 1
• Using null for primitive int
• Starting count negative

3. What will be the output of the following Java code using Moore's Voting Algorithm?

int[] arr = {2, 2, 1, 1, 1, 2, 2};
int candidate = arr[0];
int count = 1;
for (int i = 1; i < arr.length; i++) {
  if (arr[i] == candidate) count++;
  else count--;
  if (count == 0) {
    candidate = arr[i];
    count = 1;
  }
}
System.out.println(candidate);

medium

A. 2

B. 1

C. 0

D. Runtime Error

Solution

1. Step 1: Trace the candidate and count changes

   Start candidate=2, count=1
   i=1: arr[1]=2 equals candidate, count=2
   i=2: arr[2]=1 not equal, count=1
   i=3: arr[3]=1 not equal, count=0 -> reset candidate=1, count=1
   i=4: arr[4]=1 equals candidate, count=2
   i=5: arr[5]=2 not equal, count=1
   i=6: arr[6]=2 not equal, count=0 -> reset candidate=2, count=1

2. Step 2: Final candidate after loop

   Candidate is 2 after last iteration.

3. Final Answer:

   2 -> Option A

4. Quick Check:

   Final candidate = 2 [OK]

Hint: Track count changes to find final candidate [OK]

Common Mistakes:

• Not resetting candidate when count hits zero
• Confusing candidate value after last iteration
• Assuming output is the first element

4. Identify the error in this Moore's Voting Algorithm Java code snippet:

int candidate = 0;
int count = 0;
for (int num : arr) {
  if (count == 0) candidate = num;
  if (num == candidate) count++;
  else count = 0;
}
System.out.println(candidate);

medium

A. Printing candidate before loop ends

B. Candidate initialization outside loop

C. Resetting count to 0 instead of decrementing

D. Using enhanced for loop instead of index loop

Solution

1. Step 1: Analyze count update logic

   Count should decrement when current number is not candidate, but code resets count to 0.

2. Step 2: Effect of resetting count to 0

   This causes the algorithm to lose track of votes incorrectly, breaking the logic.

3. Final Answer:

   Resetting count to 0 instead of decrementing -> Option C

4. Quick Check:

   Count must decrement, not reset to zero [OK]

Hint: Decrement count when different element found [OK]

Common Mistakes:

• Resetting count to zero instead of decrementing
• Misunderstanding candidate update timing
• Confusing loop types as error

5. Given an array where no element appears more than half the time, what will Moore's Voting Algorithm return?
Example: int[] arr = {1, 2, 3, 4, 5, 6};

hard

A. The algorithm returns the element with highest frequency

B. The algorithm returns an incorrect candidate without verification

C. The algorithm throws an exception

D. The algorithm returns null

Solution

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

   The algorithm assumes a majority element exists (more than half the array).

2. Step 2: Behavior when no majority element exists

   It returns a candidate but this candidate may not actually be majority without a verification step.

3. Step 3: Verification necessity

   To confirm majority, a second pass counting candidate occurrences is needed.

4. Final Answer:

   The algorithm returns an incorrect candidate without verification -> Option B

5. Quick Check:

   No majority means candidate may be wrong [OK]

Hint: Verify candidate count if no guaranteed majority [OK]

Common Mistakes:

• Assuming algorithm throws error if no majority
• Thinking it returns null automatically
• Believing it always returns highest frequency element