Is Find the Count of Numbers Which Are Not Special easy or hard?

The problem is rated Medium because the brute force interpretation looks expensive, but the correct solution relies on recognizing a number theory pattern. Once you realize special numbers must be squares of primes, the implementation becomes straightforward.

Find the Count of Numbers Which Are Not Special Python/Java solution

In Python, iterate p from 2 to sqrt(r) and check if p is prime, counting cases where p*p lies within [l, r]. In Java or C++, the same idea is often implemented with a sieve array to generate primes efficiently before checking their squares.

How to solve Find the Count of Numbers Which Are Not Special in O(sqrt(n))?

Compute the square root bounds of the range: low = ceil(sqrt(l)) and high = floor(sqrt(r)). Every integer p in this range whose value is prime contributes one special number because p^2 lies inside the range. Count those primes and subtract the result from the total number of integers in the interval.

What is the best approach for Find the Count of Numbers Which Are Not Special?

The optimal approach is to recognize that special numbers are exactly the squares of prime numbers. Instead of scanning every number in the range, compute primes up to sqrt(r) and check which of their squares fall inside [l, r]. This reduces the problem to counting prime squares and subtracting them from the total range size.

Is Find the Count of Numbers Which Are Not Special asked at Google/Amazon/Meta?

Problems involving prime detection, divisor counting, and mathematical reduction frequently appear in interviews at companies like Amazon, Google, and fintech startups. This specific pattern—reducing a divisor condition to prime squares—is a common number theory trick used in coding interviews.

What data structure is used in Find the Count of Numbers Which Are Not Special?

Most optimized implementations use an array-based Sieve of Eratosthenes to precompute primes up to sqrt(r). Aside from that, the solution mainly relies on mathematical reasoning rather than complex data structures.

What is the time complexity of Find the Count of Numbers Which Are Not Special?

The optimized solution runs in O(sqrt(r)) time if you perform primality checks for numbers up to sqrt(r). Using the Sieve of Eratosthenes changes the complexity to O(sqrt(r) log log r) with O(sqrt(r)) space, which is still efficient for large ranges.

Description Hints 3 Solution Video 12:01

3233. Find the Count of Numbers Which Are Not Special

Medium28.3% acceptance1 company

You are given 2 positive integers l and r. For any number x, all positive divisors of x except x are called the proper divisors of x.

A number is called special if it has exactly 2 proper divisors. For example:

The number 4 is special because it has proper divisors 1 and 2.
The number 6 is not special because it has proper divisors 1, 2, and 3.

Return the count of numbers in the range [l, r] that are not special.

Example 1:

Input: l = 5, r = 7

Output: 3

Explanation:

There are no special numbers in the range [5, 7].

Example 2:

Input: l = 4, r = 16

Output: 11

Explanation:

The special numbers in the range [4, 16] are 4 and 9.

Constraints:

1 <= l <= r <= 10⁹

Asked at 1 company

Microsoft

Topics

Hints open one at a time

Hint 1

A special number must be a square of a prime number.

Hint 2

We need to find all primes in the range [sqrt(l), sqrt(r)].

Hint 3

Use sieve to find primes till sqrt(10⁹).

12:01

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