Check if Number is Prime in DSA Rust - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to check if a number is less than 2, which means it is not prime.

DSA Rust

fn is_prime(n: u32) -> bool {
    if n [1] 2 {
        return false;
    }
    true
}

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

A==

B<

C>

D<=

Attempts:

3 left

💡 Hint

Common Mistakes

Using '>' instead of '<' causes wrong logic.

Checking for equality with 2 misses numbers less than 2.

If the number is less than 2, it is not prime. So we return false.

2fill in blank

medium

Complete the code to loop from 2 up to the square root of the number to check for divisors.

DSA Rust

fn is_prime(n: u32) -> bool {
    if n < 2 {
        return false;
    }
    let limit = (n as f64).sqrt() as u32;
    for i in 2..=[1] {
        if n % i == 0 {
            return false;
        }
    }
    true
}

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

A1

Bn

Cn/2

Dlimit

Attempts:

3 left

💡 Hint

Common Mistakes

Looping up to n is inefficient.

Using 'n/2' is more than needed.

We only need to check divisors up to the square root of n, stored in 'limit'.

3fill in blank

hard

Fix the error in the code to correctly return false if a divisor is found.

DSA Rust

fn is_prime(n: u32) -> bool {
    if n < 2 {
        return false;
    }
    let limit = (n as f64).sqrt() as u32;
    for i in 2..=limit {
        if n % i [1] 0 {
            return false;
        }
    }
    true
}

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

A==

B!=

C>

D<

Attempts:

3 left

💡 Hint

Common Mistakes

Using '!=' causes wrong logic.

Using '>' or '<' is incorrect for equality check.

We return false if n is divisible by i, which means n % i == 0.

4fill in blank

hard

Fill both blanks to complete the function that checks if a number is prime.

DSA Rust

fn is_prime(n: u32) -> bool {
    if n [1] 2 {
        return false;
    }
    let limit = (n as f64).sqrt() as u32;
    for i in 2..=[2] {
        if n % i == 0 {
            return false;
        }
    }
    true
}

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

A<

B>

Climit

Dn

Attempts:

3 left

💡 Hint

Common Mistakes

Using '>' instead of '<' in first blank.

Using 'n' instead of 'limit' in loop range.

The function returns false if n is less than 2, and loops up to 'limit' to check divisors.

5fill in blank

hard

Fill all three blanks to create a function that checks if a number is prime efficiently.

DSA Rust

fn is_prime(n: u32) -> bool {
    if n [1] 2 {
        return false;
    }
    let limit = (n as f64).[2]() as u32;
    for i in 2..=[3] {
        if n % i == 0 {
            return false;
        }
    }
    true
}

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

A<

Bsqrt

Climit

D>

Attempts:

3 left

💡 Hint

Common Mistakes

Using '>' instead of '<' in first blank.

Using 'pow' or other methods instead of 'sqrt'.

Using 'n' instead of 'limit' in loop.

The function returns false if n is less than 2, calculates the square root as 'limit', and loops up to 'limit' to check divisors.

Practice

1. What does it mean for a number to be prime?

easy

A. It has more than two divisors.

B. It is divisible by 2 only.

C. It is an even number greater than 2.

D. It has exactly two distinct positive divisors: 1 and itself.

Solution

1. Step 1: Understand the definition of prime number

   A prime number is a number greater than 1 that has no divisors other than 1 and itself.

2. Step 2: Compare options with definition

   Only It has exactly two distinct positive divisors: 1 and itself. correctly states this definition.

3. Final Answer:

   It has exactly two distinct positive divisors: 1 and itself. -> Option D

4. Quick Check:

   Prime = two divisors [OK]

Hint: Prime numbers have only 1 and itself as divisors [OK]

Common Mistakes:

• Thinking even numbers are always prime
• Confusing prime with odd numbers
• Assuming 1 is prime

2. Which of the following Rust code snippets correctly checks if a number n is prime?

easy

A. for i in 1..n { if n % i == 0 { return false; } } true

B. for i in 2..n { if n % i == 0 { return false; } } true

C. for i in 2..=n { if n % i == 0 { return false; } } true

D. for i in 2..n { if n % i != 0 { return false; } } true

Solution

1. Step 1: Analyze the loop range for divisor checking

   We check divisors from 2 up to n-1 (exclusive of n) to find if any divides n.

2. Step 2: Check each option's loop and condition

   for i in 2..n { if n % i == 0 { return false; } } true correctly loops from 2 to n-1 and returns false if divisor found; others have errors like including n or wrong condition.

3. Final Answer:

   for i in 2..n { if n % i == 0 { return false; } } true -> Option B

4. Quick Check:

   Loop 2 to n-1 and check divisibility [OK]

Hint: Loop from 2 to n-1 to check divisors [OK]

Common Mistakes:

• Including n in the loop range
• Starting loop from 1 instead of 2
• Using wrong condition for divisibility

3. What is the output of this Rust function call: is_prime(11)?

fn is_prime(n: u32) -> bool {
    if n <= 1 { return false; }
    for i in 2..n {
        if n % i == 0 {
            return false;
        }
    }
    true
}

medium

A. true

B. false

C. panic at runtime

D. compile error

Solution

1. Step 1: Check input and loop behavior for n=11

   11 is greater than 1, so the function proceeds to loop from 2 to 10 checking divisibility.

2. Step 2: Test divisibility of 11 by numbers 2 to 10

   11 is not divisible by any number between 2 and 10, so loop completes without returning false.

3. Final Answer:

   true -> Option A

4. Quick Check:

   11 is prime, so function returns true [OK]

Hint: Prime numbers return true after no divisors found [OK]

Common Mistakes:

• Assuming 11 is not prime
• Confusing loop range
• Expecting runtime errors incorrectly

4. Identify the bug in this Rust function that checks if a number is prime:

fn is_prime(n: u32) -> bool {
    if n < 2 { return false; }
    for i in 2..=n {
        if n % i == 0 {
            return false;
        }
    }
    true
}

medium

A. Missing return type in function signature

B. Condition should be n <= 1 instead of n < 2

C. Loop includes n, causing always false for n > 1

D. Loop should start from 1 instead of 2

Solution

1. Step 1: Analyze the loop range 2..=n

   The loop includes n itself, so n % n == 0 is always true, causing immediate false return.

2. Step 2: Understand correct loop range

   Loop should be 2..n (exclusive of n) to avoid checking n against itself.

3. Final Answer:

   Loop includes n, causing always false for n > 1 -> Option C

4. Quick Check:

   Loop must exclude n to avoid false negatives [OK]

Hint: Exclude n from divisor loop to avoid false negatives [OK]

Common Mistakes:

• Including n in divisor checks
• Wrong loop start index
• Misunderstanding return conditions

5. You want to optimize prime checking for large numbers by only checking divisors up to the square root of n. Which Rust code snippet correctly implements this?

hard

A. for i in 2..=((n as f64).sqrt() as u32) { if n % i == 0 { return false; } } true

B. for i in 2..n { if n % i == 0 { return false; } } true

C. for i in 2..=(n / 2) { if n % i == 0 { return false; } } true

D. for i in 1..=((n as f64).sqrt() as u32) { if n % i == 0 { return false; } } true

Solution

1. Step 1: Understand optimization using square root

   Checking divisors up to sqrt(n) is enough because larger factors pair with smaller ones.

2. Step 2: Analyze each option's loop range and correctness

   for i in 2..=((n as f64).sqrt() as u32) { if n % i == 0 { return false; } } true correctly casts n to float, computes sqrt, casts back to u32, and loops up to that value.

3. Final Answer:

   for i in 2..=((n as f64).sqrt() as u32) { if n % i == 0 { return false; } } true -> Option A

4. Quick Check:

   Loop up to sqrt(n) for efficient prime check [OK]

Hint: Check divisors only up to sqrt(n) for efficiency [OK]

Common Mistakes:

• Checking divisors beyond sqrt(n)
• Starting loop from 1 instead of 2
• Incorrect casting causing errors