First Day Where You Have Been in All the Rooms - Problem
Imagine you're a security guard tasked with visiting n rooms numbered from 0 to n-1 in a building. Each day, starting from day 0, you must visit exactly one room following specific rules.
Starting Point: On day 0, you visit room 0.
Visit Rules: When you're in room i:
- If this is an odd-numbered visit to room
i(1st, 3rd, 5th time, etc.), tomorrow you'll visit roomnextVisit[i]wherenextVisit[i] ≤ i - If this is an even-numbered visit to room
i(2nd, 4th, 6th time, etc.), tomorrow you'll visit room(i + 1) % n
Goal: Find the first day when you've visited all rooms at least once. Since the answer can be very large, return it modulo 109 + 7.
Example: With rooms [0,1,2] and nextVisit = [0,0,2], you might visit: Day 0→Room 0 (1st visit), Day 1→Room 0 (2nd visit), Day 2→Room 1 (1st visit), Day 3→Room 0 (3rd visit), Day 4→Room 0 (4th visit), Day 5→Room 1 (2nd visit), Day 6→Room 2 (1st visit). Answer: Day 6.
Input & Output
example_1.py — Small Building
$
Input:
nextVisit = [0, 0]
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Output:
2
💡 Note:
Day 0: Visit room 0 (1st time) → Next: room nextVisit[0]=0. Day 1: Visit room 0 (2nd time) → Next: room (0+1)%2=1. Day 2: Visit room 1 (1st time) → All rooms visited!
example_2.py — Medium Building
$
Input:
nextVisit = [0, 0, 2]
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Output:
6
💡 Note:
Day 0→Room 0 (1st), Day 1→Room 0 (2nd), Day 2→Room 1 (1st), Day 3→Room 0 (3rd), Day 4→Room 0 (4th), Day 5→Room 1 (2nd), Day 6→Room 2 (1st). All rooms visited by day 6.
example_3.py — Single Room
$
Input:
nextVisit = [0]
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Output:
0
💡 Note:
Only one room (room 0), and we start there on day 0. All rooms are visited immediately, so the answer is 0.
Constraints
- n == nextVisit.length
- 1 ≤ n ≤ 104
- 0 ≤ nextVisit[i] ≤ i
- Important: The answer is guaranteed to exist and may be very large (use modulo 109 + 7)
Visualization
Tap to expand
Understanding the Visualization
1
Pattern Recognition
Notice that reaching room i depends on time to reach room i-1 plus escape time
2
Mathematical Formula
Derive: dp[i] = 2×dp[i-1] - dp[nextVisit[i-1]] + 2
3
Sequential Calculation
Compute dp[1], dp[2], ..., dp[n-1] using the formula
4
Final Answer
dp[n-1] gives the day when all rooms are first visited
Key Takeaway
🎯 Key Insight: Mathematical analysis reveals that room visiting follows a predictable pattern, allowing us to skip the expensive simulation and directly calculate when each room is first reached using dynamic programming.
💡
Explanation
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