Majority Element Moore's Voting Algorithm in DSA Go - 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 paired with different elements.

beginner

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

The time complexity is O(n), where n is the number of elements in the array, because it makes a single pass through the array.

beginner

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

The space complexity is O(1) because it uses only a few variables to keep track of the candidate and count, regardless of input size.

What does Moore's Voting Algorithm maintain while scanning the array?

A A stack of elements

B A candidate element and a count

C A hash map of element frequencies

D A sorted copy of the array

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

When does Moore's Voting Algorithm reset the candidate element?

A When count reaches zero

B When a new element is found

C At the start of the array

D When the array is sorted

The candidate is reset when the count drops to zero, meaning the previous candidate is canceled out.

What is the minimum number of times the majority element appears in the array?

A More than n/2 times

B Exactly n/2 times

C Less than n/2 times

D At least once

The majority element appears more than half the size of the array, i.e., more than n/2 times.

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

A O(1)

B O(n log n)

C O(n^2)

D O(n)

The algorithm scans the array once, so it runs in linear time O(n).

Which of these is NOT required by Moore's Voting Algorithm?

A A count variable

B A candidate variable

C Extra space proportional to input size

D Single pass through the array

Moore's Voting Algorithm uses constant extra space, so it does not require extra space proportional to input size.

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

Think about how the algorithm cancels out pairs of different elements.

Describe the time and space complexity of Moore's Voting Algorithm and why it is efficient.

Focus on how many times the array is scanned and how much memory is used.

Practice

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

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 count the total number of unique 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 times in the array.

2. Step 2: Compare with other options

   Sorting, finding smallest element, or counting unique elements are not the algorithm's purpose.

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 the array length [OK]

Common Mistakes:

• Confusing majority element with most frequent element
• Thinking it sorts the array
• Assuming it finds smallest or unique elements

2. Which of the following Go code snippets correctly initializes the variables needed for Moore's Voting Algorithm?

easy

A. count := 0; candidate := 0

B. var count int = 1; var candidate int = -1

C. count := 0; candidate := ''

D. var count string = '0'; var candidate int = 0

Solution

1. Step 1: Identify correct variable types and initialization

   Moore's Voting Algorithm uses an integer count starting at 0 and an integer candidate initialized to 0 or any valid integer.

2. Step 2: Check each option for type correctness

   count := 0; candidate := 0 uses count and candidate as integers with proper initialization. var count int = 1; var candidate int = -1 initializes count to 1 which is not standard start. count := 0; candidate := '' uses empty string for candidate which is wrong type. var count string = '0'; var candidate int = 0 uses string type for count which is incorrect.

3. Final Answer:

   count := 0; candidate := 0 -> Option A

4. Quick Check:

   Integer count and candidate initialized to 0 [OK]

Hint: Count starts at 0, candidate is integer zero [OK]

Common Mistakes:

• Using wrong data types for count or candidate
• Starting count at 1 instead of 0
• Initializing candidate with empty string

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

arr := []int{2, 2, 1, 1, 1, 2, 2}
count := 0
candidate := 0
for _, num := range arr {
  if count == 0 {
    candidate = num
  }
  if num == candidate {
    count++
  } else {
    count--
  }
}
fmt.Println(candidate)

medium

A. 1

B. 0

C. 2

D. 3

Solution

1. Step 1: Trace the loop to find candidate

   Start with count=0, candidate=0.
   Iteration 1: count=0, candidate=2, count=1
   Iteration 2: num=2 == candidate=2, count=2
   Iteration 3: num=1 != candidate=2, count=1
   Iteration 4: num=1 != candidate=2, count=0
   Iteration 5: count=0, candidate=1, count=1
   Iteration 6: num=2 != candidate=1, count=0
   Iteration 7: count=0, candidate=2, count=1

2. Step 2: Final candidate after loop

   The candidate after the loop ends is 2.

3. Final Answer:

   2 -> Option C

4. Quick Check:

   Majority element found = 2 [OK]

Hint: Track count changes; candidate updates when count hits zero [OK]

Common Mistakes:

• Not updating candidate when count is zero
• Confusing candidate with last element
• Miscounting increments and decrements

4. Identify the bug in this Go code implementing Moore's Voting Algorithm:

arr := []int{3, 3, 4, 2, 4, 4, 2, 4, 4}
count := 0
candidate := 0
for i := 0; i < len(arr); i++ {
  if count == 0 {
    candidate = arr[i]
  }
  if arr[i] == candidate {
    count--
  } else {
    count++
  }
}
fmt.Println(candidate)

medium

A. Candidate is not updated when count is zero

B. Candidate initialized incorrectly

C. Loop index goes out of range

D. Count increments and decrements are reversed

Solution

1. Step 1: Analyze count update logic

   The algorithm should increase count when current element equals candidate, and decrease count otherwise.

2. Step 2: Identify the bug in code

   Here, count is decreased when arr[i] == candidate and increased otherwise, which is reversed.

3. Final Answer:

   Count increments and decrements are reversed -> Option D

4. Quick Check:

   Correct count update: increment if equal, decrement if not [OK]

Hint: Increment count if equal, decrement if different [OK]

Common Mistakes:

• Swapping increment and decrement operations
• Not updating candidate when count is zero
• Incorrect loop bounds causing runtime errors

5. Given an array where no element appears more than half the time, how can Moore's Voting Algorithm be adapted to confirm the absence of a majority element?

hard

A. Return the candidate directly without verification

B. Run the algorithm to find a candidate, then verify its count exceeds half the array length

C. Sort the array and pick the middle element

D. Count all elements and pick the one with maximum frequency without verification

Solution

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

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

2. Step 2: Adaptation to confirm majority

   After finding candidate, count its occurrences in the array. If count > n/2, candidate is majority; else no majority element exists.

3. Final Answer:

   Run the algorithm to find a candidate, then verify its count exceeds half the array length -> Option B

4. Quick Check:

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

Hint: Verify candidate count after algorithm to confirm majority [OK]

Common Mistakes:

• Assuming candidate is always majority without verification
• Using sorting instead of Moore's Voting Algorithm
• Picking max frequency without checking majority condition