Majority Element Moore's Voting Algorithm in DSA C# - Time & Space Complexity

Time Complexity: Majority Element Moore's Voting Algorithm

O(n)

Understanding Time Complexity

We want to understand how the time needed to find the majority element grows as the list gets bigger.

Specifically, how many steps does the Moore's Voting Algorithm take to find the majority element?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

int FindMajorityElement(int[] nums) {
    int count = 0, candidate = 0;
    foreach (int num in nums) {
        if (count == 0) {
            candidate = num;
        }
        count += (num == candidate) ? 1 : -1;
    }
    return candidate;
}
    

This code finds the majority element by tracking a candidate and adjusting a count as it scans the array once.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: One loop that goes through each element of the array exactly once.
• How many times: The loop runs n times, where n is the number of elements in the array.

How Execution Grows With Input

As the input size grows, the number of steps grows directly with it.

Input Size (n)	Approx. Operations
10	About 10 steps
100	About 100 steps
1000	About 1000 steps

Pattern observation: The steps increase in a straight line as the input size increases.

Final Time Complexity

Time Complexity: O(n)

This means the time to find the majority element grows directly with the size of the input list.

Common Mistake

[X] Wrong: "Because there is a loop inside a conditional, the time complexity is more than linear."

[OK] Correct: The loop runs only once through the array, and the conditional inside does not add extra loops, so the time grows linearly.

Interview Connect

Understanding this linear time solution shows you can find efficient answers without extra space, a skill valued in real coding challenges.

Self-Check

"What if we added a second pass to verify the candidate's count? How would the time complexity change?"

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 time

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

   The algorithm is designed to find the majority element, which is the element that appears more than half the time in the array.

2. Step 2: Compare with other options

   Sorting, finding smallest element, or counting unique elements are not the goals of this algorithm.

3. Final Answer:

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

4. Quick Check:

   Majority element = element with >50% frequency [OK]

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

Common Mistakes:

• Thinking it sorts the array
• Confusing majority with most frequent element without >50%
• Assuming it finds smallest or unique counts

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

easy

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

B. int candidate; int count = 1;

C. int candidate = 0; int count = 0;

D. int candidate = 0; int count = 1;

Solution

1. Step 1: Understand initialization requirements

   Candidate should start with a default value (like 0) and count should start at 0 before processing the array.

2. Step 2: Check each option

   int candidate = 0; int count = 0; initializes candidate to 0 and count to 0, which is standard. int candidate; int count = 1; leaves candidate uninitialized. int candidate = -1; int count = 0; uses -1 which may be valid but less common. int candidate = 0; int count = 1; starts count at 1 which is incorrect before any element is processed.

3. Final Answer:

   int candidate = 0; int count = 0; -> Option C

4. Quick Check:

   Initialize candidate=0 and count=0 before loop [OK]

Hint: Start count at zero before scanning array [OK]

Common Mistakes:

• Leaving candidate uninitialized
• Starting count at 1 before processing
• Using invalid default candidate values

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

int[] nums = {2, 2, 1, 1, 1, 2, 2};
int candidate = 0, count = 0;
foreach (int num in nums) {
  if (count == 0) candidate = num;
  count += (num == candidate) ? 1 : -1;
}
Console.WriteLine(candidate);

medium

A. 1

B. 2

C. 0

D. Error

Solution

1. Step 1: Trace the candidate and count updates

   Start with candidate=0, count=0. Iterate nums:
   - num=2: count=0, candidate=2, count=1
   - num=2: same candidate, count=2
   - num=1: different, count=1
   - num=1: different, count=0
   - num=1: count=0, candidate=1, count=1
   - num=2: different, count=0
   - num=2: count=0, candidate=2, count=1

2. Step 2: Final candidate after loop

   The final candidate is 2 after processing all elements.

3. Final Answer:

   2 -> Option B

4. Quick Check:

   Final candidate = 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
• Ignoring count increments and decrements

4. Identify the error in the following C# implementation of Moore's Voting Algorithm:

int[] nums = {3, 3, 4, 2, 4, 4, 2, 4, 4};
int candidate = 0, count = 0;
foreach (int num in nums) {
  if (count == 0) candidate = num;
  if (num == candidate) count++;
  else count++;
}
Console.WriteLine(candidate);

medium

A. Count is incremented in both if and else, should decrement in else

B. Candidate is not updated when count is zero

C. Candidate should be initialized to -1

D. The array nums is empty

Solution

1. Step 1: Analyze count updates in loop

   Count is incremented in both if and else branches, so count never decreases. This breaks the algorithm logic.

2. Step 2: Correct the else branch

   In Moore's Voting Algorithm, count should decrement when current number is not the candidate.

3. Final Answer:

   Count is incremented in both if and else, should decrement in else -> Option A

4. Quick Check:

   Count must decrease when num != candidate [OK]

Hint: Count decreases when element differs from candidate [OK]

Common Mistakes:

• Incrementing count in else instead of decrementing
• Not updating candidate when count is zero
• Assuming candidate initialization causes error

5. Given an array int[] nums = {1, 2, 3, 2, 2, 2, 5, 2, 2}, how can you verify after Moore's Voting Algorithm that the candidate is actually the majority element?

hard

A. Sort the array and pick the middle element

B. Assume candidate is majority without verification

C. Check if candidate is the first element in the array

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

Solution

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

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

2. Step 2: Verify candidate by counting occurrences

   Count how many times candidate appears and compare with half the array length to confirm majority.

3. Final Answer:

   Count the occurrences of candidate in the array and check if it is more than half the array length -> Option D

4. Quick Check:

   Verify candidate count > n/2 after algorithm [OK]

Hint: Always verify candidate count > half array length [OK]

Common Mistakes:

• Skipping verification step
• Assuming candidate is always majority
• Using sorting instead of counting