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

Time Complexity: Majority Element Moore's Voting Algorithm

O(n)

Understanding Time Complexity

We want to understand how fast the Moore's Voting Algorithm finds the majority element in a list.

How does the time needed grow as the list gets bigger?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

public int majorityElement(int[] nums) {
    int count = 0, candidate = 0;
    for (int num : 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: Single loop through the array elements.
• How many times: Exactly once for each element in the input array.

How Execution Grows With Input

As the input size grows, the algorithm checks each element once, so the work grows directly with the number of elements.

Input Size (n)	Approx. Operations
10	About 10 checks and updates
100	About 100 checks and updates
1000	About 1000 checks and updates

Pattern observation: The number of operations grows linearly with input size.

Final Time Complexity

Time Complexity: O(n)

This means the time to find the majority element grows in direct proportion to the number of elements.

Common Mistake

[X] Wrong: "The algorithm needs to check pairs or do nested loops, so it is slower than linear."

[OK] Correct: The algorithm only scans the list once, updating a count and candidate without nested loops, so it runs in linear time.

Interview Connect

Understanding this algorithm shows you can find efficient solutions by clever counting, a skill valued in problem solving and interviews.

Self-Check

"What if we needed to verify the candidate by counting its occurrences after the first pass? How would that affect the time complexity?"

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