Majority Element Moore's Voting Algorithm in DSA Rust - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to initialize the candidate variable.

DSA Rust

let mut candidate = [1];

Drag options to blanks, or click blank then click option'

Avec![]

B0

CNone

D1

Attempts:

3 left

💡 Hint

Common Mistakes

Using None instead of a number

Using a vector instead of a number

The candidate starts as 0 to hold the potential majority element.

2fill in blank

medium

Complete the code to update the count when the current number matches the candidate.

DSA Rust

if num == candidate {
    count [1] 1;
}

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A+=

B/=

C*=

D-=

Attempts:

3 left

💡 Hint

Common Mistakes

Using -= instead of +=

Using multiplication or division operators

We add 1 to count when the current number matches the candidate.

3fill in blank

hard

Fix the error in resetting the candidate and count when count reaches zero.

DSA Rust

if count == 0 {
    candidate = [1];
    count = [2];
}

Drag options to blanks, or click blank then click option'

Anum

B0

C1

Dcandidate

Attempts:

3 left

💡 Hint

Common Mistakes

Resetting count to 0 instead of 1

Setting candidate to old candidate instead of current number

When count is zero, we reset candidate to current number and count to 1.

4fill in blank

hard

Fill both blanks to correctly decrease count when the current number differs from candidate.

DSA Rust

if num != candidate {
    count [1] 1;
}

Drag options to blanks, or click blank then click option'

A*=

B+=

C-=

D/=

Attempts:

3 left

💡 Hint

Common Mistakes

Using += instead of -=

Using multiplication or division operators

We subtract 1 from count when the current number is different from candidate.

5fill in blank

hard

Fill all three blanks to complete the function that returns the majority element.

DSA Rust

fn majority_element(nums: Vec<i32>) -> i32 {
    let mut candidate = [1];
    let mut count = 0;
    for num in nums {
        if count == 0 {
            candidate = num;
            count = [2];
        }
        if num == candidate {
            count [3] 1;
        } else {
            count -= 1;
        }
    }
    candidate
}

Drag options to blanks, or click blank then click option'

A0

B1

C+=

D-=

Attempts:

3 left

💡 Hint

Common Mistakes

Using wrong operators for count update

Incorrect initial candidate value

The candidate starts at 0, count resets to 1 when candidate changes, and count increases by 1 when num matches candidate.

Practice

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

easy

A. To sort the array in ascending order

B. To find the element that appears more than half the times in the array

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 an array.

2. Step 2: Compare with other options

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

3. Final Answer:

   To find the element that appears more than half the times in the array -> Option B

4. Quick Check:

   Majority element = element with > n/2 occurrences [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 Rust code snippets correctly initializes the variables for Moore's Voting Algorithm?

easy

A. let count = None; let candidate = None;

B. let count = 0; let candidate = 0;

C. let mut count = None; let mut candidate = 0;

D. let mut count = 0; let mut candidate = 0;

Solution

1. Step 1: Identify correct variable types and mutability

   Moore's Voting Algorithm requires mutable count and candidate variables. Candidate starts as 0 (sentinel value), count as 0.

2. Step 2: Check each option

   let mut count = 0; let mut candidate = 0; correctly uses mutable variables with candidate as 0 and count as 0. Others either lack mutability or wrong types.

3. Final Answer:

   let mut count = 0; let mut candidate = 0; -> Option D

4. Quick Check:

   Mutable count=0 and candidate=0 initialization [OK]

Hint: Candidate starts 0, count starts 0, both mutable [OK]

Common Mistakes:

• Not using mutable variables
• Initializing candidate with None instead of 0
• Using None for count variable

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

fn majority_element(nums: &[i32]) -> i32 {
    let mut count = 0;
    let mut candidate = 0;
    for &num in nums {
        if count == 0 {
            candidate = num;
        }
        if num == candidate {
            count += 1;
        } else {
            count -= 1;
        }
    }
    candidate
}

fn main() {
    let arr = [2, 2, 1, 1, 1, 2, 2];
    println!("{}", majority_element(&arr));
}

medium

A. 2

B. 1

C. 0

D. Compilation error

Solution

1. Step 1: Trace the algorithm with given array

   Array: [2, 2, 1, 1, 1, 2, 2]. Candidate and count update as follows:
   - Start: count=0, candidate=0
   - num=2, count=0 -> candidate=2, count=1
   - num=2 == candidate -> count=2
   - num=1 != candidate -> count=1
   - num=1 != candidate -> count=0
   - num=1, count=0 -> candidate=1, count=1
   - num=2 != candidate -> count=0
   - num=2, count=0 -> candidate=2, count=1

2. Step 2: Final candidate is 2

   After loop, candidate is 2, which is the majority element.

3. Final Answer:

   2 -> Option A

4. Quick Check:

   Majority element found = 2 [OK]

Hint: Track candidate and count changes stepwise [OK]

Common Mistakes:

• Not updating candidate when count is zero
• Miscounting increments and decrements
• Assuming first element is always majority

4. Identify the bug in this Rust implementation of Moore's Voting Algorithm:

fn majority_element(nums: &[i32]) -> i32 {
    let mut count = 0;
    let mut candidate = 0;
    for &num in nums {
        if count == 0 {
            candidate = num;
        }
        if num != candidate {
            count += 1;
        } else {
            count -= 1;
        }
    }
    candidate
}

medium

A. The count increment and decrement conditions are reversed

B. Candidate should be initialized to None

C. Loop should iterate over mutable references

D. Function should return Option<i32> instead of i32

Solution

1. Step 1: Analyze count update logic

   In Moore's Voting Algorithm, count increases when current number equals candidate, and decreases otherwise. Here, conditions are reversed.

2. Step 2: Identify correct logic

   Correct logic: if num == candidate { count += 1 } else { count -= 1 }.

3. Final Answer:

   The count increment and decrement conditions are reversed -> Option A

4. Quick Check:

   Count updates reversed cause wrong majority [OK]

Hint: Count++ if equal candidate, else count-- [OK]

Common Mistakes:

• Swapping increment and decrement conditions
• Not resetting candidate when count is zero
• Ignoring mutability of variables

5. Given an array where no element appears more than half the time, what will Moore's Voting Algorithm return?
Example: [1, 2, 3, 4]
How can you modify the algorithm to correctly handle this case?

hard

A. It returns zero; change candidate initialization to -1

B. It returns None automatically; no modification needed

C. It returns a candidate anyway; add a verification step counting candidate occurrences

D. It panics at runtime; wrap code in Result to handle errors

Solution

1. Step 1: Understand algorithm behavior without majority

   Moore's Voting Algorithm always returns a candidate even if no majority exists, because it only finds a potential majority.

2. Step 2: Modify algorithm to verify candidate

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

3. Final Answer:

   It returns a candidate anyway; add a verification step counting candidate occurrences -> Option C

4. Quick Check:

   Verification step needed to confirm majority [OK]

Hint: Verify candidate count after algorithm completes [OK]

Common Mistakes:

• Assuming algorithm returns None if no majority
• Not verifying candidate count after selection
• Expecting runtime errors for no majority