Leetcode #1997: First Day Where You Have Been in All the Rooms
In this guide, we solve Leetcode #1997 First Day Where You Have Been in All the Rooms 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
There are n rooms you need to visit, labeled from 0 to n - 1. Each day is labeled, starting from 0.
Quick Facts
- Difficulty: Medium
- Premium: No
- Tags: Array, Dynamic Programming
Intuition
The problem breaks into overlapping subproblems, so caching results prevents exponential repetition.
A carefully chosen DP state captures exactly what we need to build the final answer.
Approach
Define the DP state and recurrence, then compute states in the correct order.
Optionally compress space once the recurrence is clear.
Steps:
- Choose a DP state definition.
- Write the recurrence and base cases.
- Compute states in the correct order.
Example
Input: nextVisit = [0,0]
Output: 2
Explanation:
- On day 0, you visit room 0. The total times you have been in room 0 is 1, which is odd.
On the next day you will visit room nextVisit[0] = 0
- On day 1, you visit room 0, The total times you have been in room 0 is 2, which is even.
On the next day you will visit room (0 + 1) mod 2 = 1
- On day 2, you visit room 1. This is the first day where you have been in all the rooms.
Python Solution
class Solution:
def firstDayBeenInAllRooms(self, nextVisit: List[int]) -> int:
n = len(nextVisit)
f = [0] * n
mod = 10**9 + 7
for i in range(1, n):
f[i] = (f[i - 1] + 1 + f[i - 1] - f[nextVisit[i - 1]] + 1) % mod
return f[-1]
Complexity
The time complexity is , and the space complexity is , where is the number of rooms. The space complexity is , where is the number of rooms.
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.