Start from room (0, 0) at time 0 and track each move considering the alternating 1-second and 2-second costs. Use a priority queue to propagate the earliest reachable time to each room while respecting moveTime constraints. This approach ensures the minimum total time is calculated efficiently even in large grids.
Problem Statement
You are in a dungeon represented as an n x m grid of rooms. Each room move has alternating travel times: moving once costs 1 second, then the next move costs 2 seconds, and this pattern repeats. You are given moveTime[i][j], the earliest time you can start moving into room (i, j). Starting at room (0, 0) at time 0, determine how quickly you can reach the last room.
Return the minimum time required to reach room (n - 1, m - 1). You may only move to adjacent rooms (up, down, left, right). Use the alternating movement pattern and moveTime constraints to find the optimal path, combining array traversal and graph shortest path strategies to handle the state of odd or even moves.
Examples
Example 1
Input: moveTime = [[0,4],[4,4]]
Output: 7
The minimum time required is 7 seconds.
Example 2
Input: moveTime = [[0,0,0,0],[0,0,0,0]]
Output: 6
The minimum time required is 6 seconds.
Example 3
Input: moveTime = [[0,1],[1,2]]
Output: 4
Example details omitted.
Constraints
- 2 <= n == moveTime.length <= 750
- 2 <= m == moveTime[i].length <= 750
- 0 <= moveTime[i][j] <= 109
Solution Approach
Model as Shortest Path with State
Treat each room as a node in a graph and include the parity of the last move (odd or even) as part of the state. This allows tracking whether the next move costs 1 or 2 seconds. Update each reachable neighbor using the maximum of current time plus move cost and moveTime constraint.
Use Priority Queue for Efficient Propagation
Implement a min-heap to always process the room with the earliest arrival time. Push neighbors with updated times and state into the heap. This ensures that the first time you reach the target room is the minimum possible time.
Handle MoveTime Constraints
For each neighbor, compute the next possible start time by comparing the calculated arrival time with moveTime[i][j]. If the current time is less than moveTime[i][j], wait until moveTime[i][j] before moving. This prevents illegal early moves and ensures correctness.
Complexity Analysis
| Metric | Value |
|---|---|
| Time | O(nm \log(nm)) |
| Space | O(nm) |
Time complexity is O(nm log(nm)) because each room state is processed once in a priority queue. Space complexity is O(nm) to store earliest reachable times for each room and move parity.
What Interviewers Usually Probe
- Expect you to notice alternating move costs and track state accordingly.
- Hinting at using a priority queue suggests shortest path with state propagation.
- Ask why naive BFS without parity fails for certain moveTime patterns.
Common Pitfalls or Variants
Common pitfalls
- Ignoring the odd/even move cost alternation leads to incorrect minimum times.
- Failing to wait until moveTime[i][j] for each move can produce invalid paths.
- Not tracking separate states for each parity may overestimate or underestimate total time.
Follow-up variants
- Allow diagonal moves in addition to cardinal directions, requiring updated state transitions.
- Change move costs to a repeating pattern beyond 1 and 2 seconds, adjusting state tracking.
- Introduce obstacles with infinite moveTime to test unreachable paths.
How GhostInterview Helps
- Automatically tracks earliest times per room with alternating move costs to avoid manual state errors.
- Simulates priority queue propagation to highlight optimal paths efficiently.
- Flags common mistakes like ignoring moveTime constraints or move parity.
Topic Pages
Related GhostInterview Pages
- LeetCode Interview Copilot - Use GhostInterview as a live solver when you want direct help with LeetCode-style coding questions.
- Coding Interview Assistant - See how GhostInterview supports array, string, linked list, graph, and tree interview workflows.
- How GhostInterview Works - Review the screenshot, reasoning, and answer flow before using the solver in a live interview.
FAQ
What is the main pattern to use in Find Minimum Time to Reach Last Room II?
The problem is an array plus graph pattern where each node carries state for move parity to handle alternating move times.
Can I move diagonally in this problem?
No, you can only move to adjacent rooms up, down, left, or right; diagonals are not allowed in the base problem.
Why does a simple BFS fail?
Simple BFS ignores the alternating move costs and moveTime constraints, producing incorrect minimum arrival times.
What data structure is recommended for efficiency?
A min-heap or priority queue is recommended to always process the room with the earliest reachable time.
How large can the grid be?
Grids can be up to 750 x 750 rooms, so an efficient O(nm log(nm)) solution is necessary to avoid timeouts.
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Find Minimum Time to Reach Last Room I challenges you to determine the minimum time to travel in a dungeon with a grid layout.
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