Is Count Monobit Integers easy or hard?

Count Monobit Integers is considered an easy problem. The core idea is recognizing that numbers with exactly one set bit are powers of two and can be detected using a standard bit manipulation trick.

Count Monobit Integers Python/Java solution

The implementation in Python, Java, C++, Go, or TypeScript follows the same logic: loop through numbers and check if x & (x - 1) == 0. If true, increment a counter. The code stays short and runs in O(n) time with constant memory.

How to solve Count Monobit Integers in O(n)?

Iterate through every integer in the range and apply the bit trick x & (x - 1). If the result equals zero and the number is positive, it contains exactly one set bit. Count all numbers satisfying this condition to obtain the result in linear time.

What is the best approach for Count Monobit Integers?

The most efficient approach iterates through the numbers and checks whether each value has exactly one set bit using the expression x & (x - 1) == 0. This works because only powers of two satisfy this property. The algorithm runs in O(n) time with O(1) extra space.

Is Count Monobit Integers asked at Google/Amazon/Meta?

Bit manipulation questions involving power-of-two checks and set-bit properties frequently appear in interviews at companies like Google, Amazon, and Meta. Variations of this problem are commonly used to test understanding of binary operations and bit tricks.

What data structure is used in Count Monobit Integers?

No complex data structure is required. The solution relies on bitwise operations and simple iteration. The key concept comes from bit manipulation rather than arrays, trees, or hash maps.

What is the time complexity of Count Monobit Integers?

The optimal solution runs in O(n) time where n is the number of integers examined in the range. Each integer is checked once using a constant-time bit manipulation operation. Space complexity remains O(1) because only a counter variable is required.

Description Hints 1 Solution Video 4:05

3827. Count Monobit Integers

Easy66.0% acceptance1 company

You are given an integer n.

An integer is called Monobit if all bits in its binary representation are the same.

Return the count of Monobit integers in the range [0, n] (inclusive).

Example 1:

Input: n = 1

Output: 2

Explanation:

The integers in the range [0, 1] have binary representations "0" and "1".
Each representation consists of identical bits. Thus, the answer is 2.

Example 2:

Input: n = 4

Output: 3

Explanation:

The integers in the range [0, 4] include binaries "0", "1", "10", "11", and "100".
Only 0, 1 and 3 satisfy the Monobit condition. Thus, the answer is 3.

Constraints:

0 <= n <= 1000

Asked at 1 company

Zoho

Topics

Bit Manipulation Enumeration

Hints open one at a time

Hint 1

Go through all the integers in the range [0, n] and count the monobit integers

4:05

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2    def countMonobit(self, n: int) -> int:
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