Majority Element Moore's Voting Algorithm in DSA Java - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the Majority Element in an array?

The Majority Element is the element that appears more than half the size of the array (more than n/2 times).

intermediate

What is the main idea behind Moore's Voting Algorithm?

Moore's Voting Algorithm finds the majority element by maintaining a candidate and a count. It increases the count when the same element appears and decreases it when a different element appears, resetting the candidate when count reaches zero.

intermediate

Why does Moore's Voting Algorithm work for finding the majority element?

Because the majority element appears more than half the time, it will remain as the candidate after canceling out all other elements with different values.

beginner

What are the two main steps in Moore's Voting Algorithm?

1. Find a candidate for majority element by counting and canceling out different elements.
2. Verify if the candidate is actually the majority by counting its occurrences.

beginner

What is the time complexity of Moore's Voting Algorithm?

The time complexity is O(n) because it scans the array twice: once to find the candidate and once to verify it.

What does Moore's Voting Algorithm use to keep track of the majority element candidate?

A Sorting the array first

B A hash map to count frequencies

C A stack to store elements

D A candidate variable and a count variable

Moore's Voting Algorithm maintains a candidate and a count to find the majority element efficiently.

What happens when the count reaches zero in Moore's Voting Algorithm?

A The candidate is reset to the current element

B The algorithm stops

C The count is doubled

D The candidate is removed permanently

When count reaches zero, the algorithm resets the candidate to the current element and count to 1.

Why do we need to verify the candidate after finding it in Moore's Voting Algorithm?

A To sort the array

B Because the candidate might not be the majority element

C To count all elements

D Verification is not needed

Verification ensures the candidate actually appears more than n/2 times.

What is the space complexity of Moore's Voting Algorithm?

A O(n)

B O(log n)

C O(1)

D O(n^2)

Moore's Voting Algorithm uses constant extra space, only a few variables.

If no element appears more than n/2 times, what will Moore's Voting Algorithm return?

A A candidate that may not be majority, so verification fails

B Null or error

C The first element always

D The last element always

The algorithm returns a candidate, but verification will show it is not a majority.

Explain how Moore's Voting Algorithm finds the majority element in an array.

Think about how the algorithm cancels out different elements.

Describe why Moore's Voting Algorithm is efficient compared to counting frequencies with a hash map.

Focus on space and time usage differences.

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