Is Nth Digit easy or hard?

Nth Digit is typically rated Medium because the implementation is short but the insight about digit blocks is not immediately obvious. Once the pattern of 1-digit, 2-digit, and 3-digit ranges is recognized, the solution becomes straightforward.

How to solve Nth Digit in O(log n)?

First determine the digit length group where the nth digit lies by subtracting digit blocks such as 9×1, 90×2, 900×3. After identifying the block, compute the target number with start + (n−1)/digits and find the digit index using (n−1)%digits. Extract the digit from the resulting number.

What is the best approach for Nth Digit?

The optimal approach counts digits in number-length blocks (1-digit, 2-digit, 3-digit, etc.). Subtract each block's total digit contribution until the remaining index falls within a block, then compute the exact number and digit using division and modulo. This runs in O(log n) time with O(1) space.

What data structure is used in Nth Digit?

No special data structures are required. The solution relies on arithmetic operations and integer math to identify the correct digit block and extract the target digit.

What is the time complexity of Nth Digit?

The standard solution runs in O(log n) time and O(1) space. The loop iterates through digit lengths (1-digit, 2-digit, 3-digit...), which grows logarithmically relative to n. No large strings or arrays are created.

Nth Digit Python or Java solution approach?

Both Python and Java implementations follow the same math logic: determine the digit-length block, compute the actual number containing the digit, and index into it. Python often converts the number to a string for extraction, while Java may use arithmetic or string conversion.

Is Nth Digit asked at Google, Amazon, or Meta?

Variants of digit indexing and number sequence math problems appear in interviews at companies like Google and Amazon. The question tests mathematical reasoning, handling large ranges, and avoiding brute-force string construction.

Description Solution Video 11:20

400. Nth Digit

Medium38.8% acceptance8 companies

Given an integer n, return the n^th digit of the infinite integer sequence [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, ...].

Example 1:

Input: n = 3
Output: 3

Example 2:

Input: n = 11
Output: 0
Explanation: The 11^th digit of the sequence 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, ... is a 0, which is part of the number 10.

Constraints:

1 <= n <= 2³¹ - 1

Asked at 8 companies

Accenture

Google Airbnb Tiktok Amazon Microsoft Meta Bloomberg

Topics

Binary Search Math

11:20

Still stuck?Read 3 approaches, or watch a walkthrough.

Open solution

LanguageLoading editor…

1class Solution:
2    def findNthDigit(self, n: int) -> int:
3        

Starter codePython 3Spaces: 4

Examples

Case 1Case 2

Input

Your code is saved on this device.Solution