Sieve of Eratosthenes Find All Primes in DSA Javascript - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to create an array of boolean values initialized to true.

DSA Javascript

const sieve = new Array(n + 1).fill([1]);

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

Atrue

Bfalse

Cnull

D0

Attempts:

3 left

💡 Hint

Common Mistakes

Using false instead of true will mark all numbers as non-prime initially.

Using 0 or null will not correctly represent prime status.

We fill the array with true because initially we assume all numbers are prime.

2fill in blank

medium

Complete the code to start crossing out multiples from the square of the current prime candidate.

DSA Javascript

for (let j = [1]; j <= n; j += i) {
  sieve[j] = false;
}

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

Ai + i

Bi - 1

C2 * i

Di * i

Attempts:

3 left

💡 Hint

Common Mistakes

Starting from i + i crosses out some numbers multiple times.

Starting from i - 1 or 2 * i is incorrect for the sieve algorithm.

We start crossing out multiples from i squared because smaller multiples were already crossed out by smaller primes.

3fill in blank

hard

Fix the error in the loop condition to only check up to the square root of n.

DSA Javascript

for (let i = 2; i <= [1]; i++) {

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

An / 2

BMath.sqrt(n)

Cn

Dn * n

Attempts:

3 left

💡 Hint

Common Mistakes

Using n or n/2 causes unnecessary checks and slows down the algorithm.

Using n * n is incorrect and causes errors.

We only need to check up to the square root of n because any composite number must have a factor less than or equal to its square root.

4fill in blank

hard

Fill both blanks to collect all prime numbers from the sieve array.

DSA Javascript

const primes = [];
for (let i = 2; i <= n; i++) {
  if (sieve[[1]]) {
    primes.push([2]);
  }
}

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

Ai

Cn

Dtrue

Attempts:

3 left

💡 Hint

Common Mistakes

Using n instead of i causes wrong indexing or adding wrong numbers.

Using true instead of i in push adds a boolean instead of the prime number.

We check sieve[i] to see if i is prime, and if so, add i to the primes list.

5fill in blank

hard

Fill all three blanks to complete the Sieve of Eratosthenes function that returns all primes up to n.

DSA Javascript

function sieveOfEratosthenes(n) {
  const sieve = new Array(n + 1).fill([1]);
  sieve[0] = false;
  sieve[1] = false;
  for (let i = 2; i <= [2]; i++) {
    if (sieve[i]) {
      for (let j = i * i; j <= [3]; j += i) {
        sieve[j] = false;
      }
    }
  }
  const primes = [];
  for (let i = 2; i <= n; i++) {
    if (sieve[i]) primes.push(i);
  }
  return primes;
}

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

Atrue

BMath.sqrt(n)

Cfalse

Dn

Attempts:

3 left

💡 Hint

Common Mistakes

Initializing sieve with false causes no primes to be found.

Looping up to n instead of square root of n is inefficient.

Using false in the inner loop condition causes logic errors.

We initialize sieve with true, loop up to square root of n, and use n in the inner loop condition.

Practice

1. What is the main purpose of the Sieve of Eratosthenes algorithm?

easy

A. To find all prime numbers up to a given limit

B. To sort an array of numbers

C. To find the greatest common divisor of two numbers

D. To reverse a string

Solution

1. Step 1: Understand the algorithm's goal

   The Sieve of Eratosthenes is designed to identify prime numbers efficiently.

2. Step 2: Recognize the output

   It marks multiples of primes as non-prime to find all primes up to a limit.

3. Final Answer:

   To find all prime numbers up to a given limit -> Option A

4. Quick Check:

   Sieve of Eratosthenes = Find primes [OK]

Hint: Remember: sieve filters out non-primes to find primes [OK]

Common Mistakes:

• Confusing it with sorting algorithms
• Thinking it finds factors instead of primes
• Assuming it works on strings

2. Which of the following JavaScript code snippets correctly initializes the sieve array for numbers up to n?

easy

A. const sieve = Array(n).fill(true); sieve[0] = sieve[1] = true;

B. const sieve = new Array(n).fill(false); sieve[0] = sieve[1] = true;

C. const sieve = new Array(n + 1).fill(true); sieve[0] = sieve[1] = false;

D. const sieve = new Array(n + 1).fill(false); sieve[0] = sieve[1] = false;

Solution

1. Step 1: Understand sieve initialization

   The sieve array should mark all numbers as true initially, except 0 and 1 which are not prime.

2. Step 2: Check each option

   const sieve = new Array(n + 1).fill(true); sieve[0] = sieve[1] = false; correctly creates an array of size n+1 filled with true, then sets 0 and 1 to false.

3. Final Answer:

   const sieve = new Array(n + 1).fill(true); sieve[0] = sieve[1] = false; -> Option C

4. Quick Check:

   Initialize sieve with true, except 0 and 1 false [OK]

Hint: Sieve size is n+1; 0 and 1 are not prime [OK]

Common Mistakes:

• Using size n instead of n+1
• Filling with false instead of true
• Marking 0 and 1 as true

3. What will be the output of the following code snippet?

function sieve(n) {
  const sieve = new Array(n + 1).fill(true);
  sieve[0] = sieve[1] = false;
  for (let i = 2; i * i <= n; i++) {
    if (sieve[i]) {
      for (let j = i * i; j <= n; j += i) {
        sieve[j] = false;
      }
    }
  }
  return sieve.map((val, idx) => val ? idx : null).filter(x => x);
}
console.log(sieve(10));

medium

A. [1, 2, 3, 5, 7]

B. [2, 3, 5, 7]

C. [2, 3, 4, 5, 7]

D. [2, 3, 5, 7, 9]

Solution

1. Step 1: Understand sieve marking

   The code marks multiples of primes as false, starting from i*i, up to n=10.

2. Step 2: Identify primes up to 10

   Primes are 2, 3, 5, 7. Numbers 1, 4, 6, 8, 9, 10 are marked false.

3. Final Answer:

   [2, 3, 5, 7] -> Option B

4. Quick Check:

   Primes up to 10 = [2, 3, 5, 7] [OK]

Hint: Primes under 10 are 2,3,5,7 only [OK]

Common Mistakes:

• Including 1 as prime
• Including non-primes like 4 or 9
• Off-by-one errors in loops

4. Identify the error in the following Sieve of Eratosthenes implementation:

function sieve(n) {
  const sieve = new Array(n).fill(true);
  sieve[0] = sieve[1] = false;
  for (let i = 2; i <= n; i++) {
    if (sieve[i]) {
      for (let j = i * 2; j < n; j += i) {
        sieve[j] = false;
      }
    }
  }
  return sieve.map((val, idx) => val ? idx : null).filter(x => x);
}

medium

A. Array size should be n+1 to include number n

B. Inner loop should start from i*3 instead of i*2

C. Outer loop should run only up to sqrt(n)

D. sieve[0] and sieve[1] should be true

Solution

1. Step 1: Check array size

   The array is created with size n, so index n is out of range and not included.

2. Step 2: Understand loop bounds

   To include number n, array size must be n+1; otherwise, sieve[n] is undefined.

3. Final Answer:

   Array size should be n+1 to include number n -> Option A

4. Quick Check:

   Array size = n+1 to cover all numbers [OK]

Hint: Array size must cover all indices up to n [OK]

Common Mistakes:

• Using array size n instead of n+1
• Looping outer loop beyond sqrt(n)
• Starting inner loop from i*3 incorrectly

5. You want to find all prime numbers between 50 and 100 using the Sieve of Eratosthenes. Which approach is correct?

hard

A. Run sieve up to 150 and ignore primes below 50

B. Run sieve only from 50 to 100 directly

C. Run sieve up to 50, then add primes from 51 to 100 manually

D. Run sieve up to 100, then filter primes >= 50 from the result

Solution

1. Step 1: Understand sieve range requirement

   The sieve finds primes from 2 up to the limit; partial ranges are not supported directly.

2. Step 2: Filter primes after full sieve

   Run sieve up to 100, then select primes >= 50 from the result for correct output.

3. Final Answer:

   Run sieve up to 100, then filter primes >= 50 from the result -> Option D

4. Quick Check:

   Sieve full range, then filter needed primes [OK]

Hint: Sieve full range, then filter start point [OK]

Common Mistakes:

• Trying to sieve partial ranges directly
• Ignoring primes below 50 without full sieve
• Manually adding primes without verification