q16DungeonCrossingTimeMin

solutions.q16DungeonCrossingTimeMin

Question 16

There’s a dungeon arranged as a grid of \(N\times M\) rectangular rooms.

\(T\in\mathbb{Z}^{N\times M}\) represents for each room \((i,j)\), a threshold of minimum time \(t_{ij}\) starting from which a move into it may be initiated.

Move is allowed only between two adjacent rooms that share a common vertical or horizontal wall, and each move takes 1 unit time duration.

WAP to start from room \((0,0)\) and finally determine the minimum time required to reach the room \((N-1,M-1)\).

Examples

1. \(T=[[0,4],[4,4]]\)
   Result: \(6\)
   Explanation:
   \(t=4: (0,0)\to(1,0)\);
   \(t=5: (1,0)\to(1,1)\).
2. \(T=[[0,0,0],[0,0,0]]\)
   Result: \(3\)
   Explanation:
   \(t=0: (0,0)\to(1,0)\);
   \(t=1: (1,0)\to(1,1)\);
   \(t=1: (1,1)\to(1,1)\).
3. \(T=[[0,1],[1,2]]\)
   Result: \(3\)
   Explanation:
   \(t=1: (0,0)\to(1,0)\);
   \(t=2: (1,0)\to(1,1)\).

Functions:

Name	Description
q16DungeonCrossingTimeMin	Args:

q16DungeonCrossingTimeMin(T)

Parameters:

Name	Type	Description	Default
T	List[List[int]]	A list of \(N\) lists of \(M\) integer values each representing threshold time at room \((i,j)\).	required