LC Hard 3286 Safe Walk Through a Grid Solving with Dijkstra's Algorithm🧩

Описание: Summary for [Finding Minimum Time to Reach the Last Room in a Dungeon Grid]
Solving a Dungeon Grid Problem: Calculating Minimum Time to Reach the Last Room with Alternating Move Costs

[00:04](   • LC 3342 Dungeon Grid Problem: Calculating ...  ) Find the minimum time to reach the last room in a dungeon grid.
The problem involves navigating a n x m grid with time constraints for moving between rooms.
Movement takes an alternating time of 1 second for odd moves and 2 seconds for even moves.

[01:31](   • LC 3342 Dungeon Grid Problem: Calculating ...  ) Calculating minimum time in a dungeon grid using algorithms.
The example demonstrates moving through a zero-value matrix with calculated time for each step, totaling 6 seconds.
To find minimum time, the Dijkstra algorithm will be implemented with a priority queue, considering time flags for movement.

[03:09](   • LC 3342 Dungeon Grid Problem: Calculating ...  ) Defining variables for time and coordinates in the dungeon grid.
Storing time, coordinates, and a flag to alternate between 1 and 2 seconds.
Initializing a minimum heap priority queue to track the minimum time to reach the last room.

[05:02](   • LC 3342 Dungeon Grid Problem: Calculating ...  ) Algorithm for determining valid movements in dungeon grid.
The algorithm checks if the next cell coordinates are within the grid bounds before proceeding.
A 2D array defines movement directions: left, right, up, and down for navigating the grid.

[06:50](   • LC 3342 Dungeon Grid Problem: Calculating ...  ) Explaining the calculation of move costs in a dungeon grid.
The move cost alternates between 1 and 2 seconds, determined by a flag.
Arrival time is calculated by adding the current time and the move cost based on the flag's value.

[08:45](   • LC 3342 Dungeon Grid Problem: Calculating ...  ) Implementing dynamic programming to optimize dungeon grid navigation.
Correcting errors related to move time calculations and double time handling in the grid.
Declaring a 3D DP vector to store values based on rows, columns, and a binary flag for state tracking.

[10:37](   • LC 3342 Dungeon Grid Problem: Calculating ...  ) Explains DP calculation for the dungeon grid movement over time.
Movement timing is alternating based on a flag, influencing the 3D vector representation.
Correcting errors involves ensuring that 'move time' remains unchanged while determining start time.

[12:32](   • LC 3342 Dungeon Grid Problem: Calculating ...  ) Debugging code for a dungeon grid movement algorithm.
The importance of setting the correct dbx5 flag value and ensuring proper timing conditions to avoid errors.
Adjusting movement and wait time calculations led to successful test case passes, but further debugging was required to refine the algorithm
Key Insights for [Finding Minimum Time to Reach the Last Room in a Dungeon Grid] c
*Movement Mechanics*
The first move from the starting position takes 1 second, the second move takes 2 seconds, and this pattern continues to alternate.
To successfully navigate the grid, players must account for both the move time associated with each cell and the alternating time cost.
The player must wait for the designated time in the starting cell before moving to any adjacent cell.

*Algorithmic Approach*
The solution employs a shortest path algorithm, specifically Dijkstra's algorithm, to efficiently find the minimum time to reach the destination.
A priority queue (min-heap) is used to manage the exploration of rooms based on their accumulated move time.
Each entry in the queue includes the current time, coordinates of the room, and a flag to indicate whether the next move will take 1 or 2 seconds.

*Implementation Details*
The algorithm initializes by pushing the starting position (0,0) with a wait time into the priority queue.
As rooms are processed, the algorithm checks all possible adjacent rooms (up, down, left, right) to determine their validity and the time to reach them.
The flag is updated after every move to alternate the time cost appropriately, and only valid moves (within grid boundaries) are considered.

*Dynamic Programming Enhancement*
A dynamic programming approach is introduced to handle the varying time costs associated with each cell and the alternating nature of movement.
A 3D vector is created to store the minimum time required to reach each cell with respect to the current move status (1 second or 2 seconds).
This ensures that previously computed values are reused efficiently, enhancing the overall performance of the algorithm.

*Challenges and Debugging*
The presenter discusses various challenges faced during coding, including handling edge cases and ensuring that the correct time values are stored and compared.
Errors related to incorrect time handling and priority queue management are addressed, leading to successful compilation and functioning of the algorithm.