Is Find Nth Smallest Integer With K One Bits easy or hard?

The problem is typically classified as Hard because it requires combining bit manipulation with combinatorial counting. Brute force solutions are straightforward but inefficient, while the optimal solution requires understanding how to count combinations and construct the result greedily.

Find Nth Smallest Integer With K One Bits Python/Java solution

Implement the greedy combinatorial approach. Iterate through bit positions from high to low, compute C(remaining_bits, remaining_ones), and decide whether to place a 0 or 1 at that position. The same logic works across Python, Java, C++, Go, and TypeScript with a helper function for binomial coefficients.

How to solve Find Nth Smallest Integer With K One Bits in O(log N)?

Build the number from the most significant bit downward. At each position, compute how many numbers exist if that bit remains 0 while distributing the remaining k ones among lower bits using C(remaining_bits, remaining_ones). If the count is less than n, subtract it and set the bit to 1. Otherwise keep it 0 and continue.

What is the best approach for Find Nth Smallest Integer With K One Bits?

The optimal approach uses combinatorics with greedy bit construction. For each bit position, compute how many numbers can be formed if the bit is 0 using binomial coefficients like C(n, k). If that count is smaller than the remaining index, subtract it and place a 1. This skips entire ranges of integers and runs in about O(log ans) time with O(1) space.

Is Find Nth Smallest Integer With K One Bits asked at Google/Amazon/Meta?

Variants of this problem appear in interviews at companies that emphasize combinatorics and bit manipulation, including Google, Amazon, and Meta. Interviewers use it to test understanding of binomial coefficients, greedy construction, and efficient bit-level reasoning rather than brute-force enumeration.

What data structure is used in Find Nth Smallest Integer With K One Bits?

The solution mainly relies on mathematical counting rather than complex data structures. It uses binary representation of integers, bit operations, and binomial coefficient calculations from combinatorics. Only constant extra variables are needed to track remaining bits and ones.

What is the time complexity of Find Nth Smallest Integer With K One Bits?

The optimal combinatorics + greedy solution runs in O(log ans) time because it processes each bit position once while computing combination counts. Space complexity is O(1). A naive brute force solution that checks every integer until the nth valid one appears can take roughly O(ans * log ans) time due to repeated popcount operations.

3821. Find Nth Smallest Integer With K One Bits - Practice Online

You are given two positive integers n and k.

Return an integer denoting the n^th smallest positive integer that has exactly k ones in its binary representation. It is guaranteed that the answer is strictly less than 2⁵⁰.

Example 1:

Input: n = 4, k = 2

Output: 9

Explanation:

The 4 smallest positive integers that have exactly k = 2 ones in their binary representations are:

3 = 11₂
5 = 101₂
6 = 110₂
9 = 1001₂

Example 2:

Input: n = 3, k = 1

Output: 4

Explanation:

The 3 smallest positive integers that have exactly k = 1 one in their binary representations are:

1 = 1₂
2 = 10₂
4 = 100₂

Constraints:

1 <= n <= 2⁵⁰
1 <= k <= 50
The answer is strictly less than 2⁵⁰.