Leetcode #2549: Count Distinct Numbers on Board
In this guide, we solve Leetcode #2549 Count Distinct Numbers on Board in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
You are given a positive integer n, that is initially placed on a board. Every day, for 109 days, you perform the following procedure: For each number x present on the board, find all numbers 1 <= i <= n such that x % i == 1.
Quick Facts
- Difficulty: Easy
- Premium: No
- Tags: Array, Hash Table, Math, Simulation
Intuition
Fast membership checks and value lookups are the heart of this problem, which makes a hash map the natural choice.
By storing what we have already seen (or counts/indexes), we can answer the question in one pass without backtracking.
Approach
Scan the input once, using the map to detect when the condition is satisfied and to update state as you go.
This keeps the solution linear while remaining easy to explain in an interview setting.
Steps:
- Initialize a hash map for seen items or counts.
- Iterate through the input, querying/updating the map.
- Return the first valid result or the final computed value.
Example
Input: n = 5
Output: 4
Explanation: Initially, 5 is present on the board.
The next day, 2 and 4 will be added since 5 % 2 == 1 and 5 % 4 == 1.
After that day, 3 will be added to the board because 4 % 3 == 1.
At the end of a billion days, the distinct numbers on the board will be 2, 3, 4, and 5.
Python Solution
class Solution:
def distinctIntegers(self, n: int) -> int:
return max(1, n - 1)
Complexity
The time complexity is , and the space complexity is . The space complexity is .
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.