Asked in: Meesho
Image of the Question
All Testcases Passed ✔
Solution
import heapq
def getMinJumps(grid):
n,m = len(grid), len(grid[0])
dist = [[float('inf') for i in range(m)] for j in range(n)]
// ... rest of solution available after purchaseExplanation
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To solve this problem, the goal is to determine the minimum number of valid jumps required to move from the start cell 'S' to the end cell 'E' on a 2D grid. Movement is constrained by rules about jump length and direction. Specifically, from any current position, a hacker can jump any positive integer distance `k` in any of the four cardinal directions (up, down, left, right), but with a catch: if a jump is made with `k > 1`, the next jump must continue in the same direction until a jump of length 1 resets the movement direction.
This unique constraint transforms what would normally be a straightforward grid traversal problem into one that requires additional state tracking: not just the current position on the grid, but also the direction of movement and whether the previous jump was of length greater than 1.
Let’s break this problem into key components and describe the conceptual approach to solving it.
1. **Grid Parsing and Setup**:
Begin by scanning the grid to identify the coordinates of the starting position 'S' and the ending position 'E'. This setup is essential before initiating any form of traversal. The grid itself is composed of open cells (`*`), blocked cells (`#`), and the start/end points. It’s also helpful to standardize these character values into a form that can be used programmatically, treating 'S' and 'E' as open cells for the purpose of movement.
2. **State Representation**:
Unlike typical shortest-path problems, the state here isn’t just a position `(x, y)` but includes additional components: the last direction of movement (if any) and a flag or counter to indicate whether the last jump was of length greater than 1. This is necessary because the allowed next moves depend on this state — you can only change direction if the previous jump was of length 1.
3. **Valid Move Calculation**:
From any given position, you can try to jump in all four directions. For each direction:
- Attempt jump lengths starting from 1 up to the maximum possible in that direction until a wall (`#`) or grid boundary is reached.
- For each jump, check if the destination cell is walkable (i.e., not blocked).
- If the jump is of length 1, mark that as a reset of directional constraint — you can now change direction on your next move.
- If the jump is longer than 1, you must continue moving in that direction in the next jump.
4. **Search Strategy**:
Since the problem asks for the minimum number of jumps, a Breadth-First Search (BFS) approach is most suitable. In BFS, you explore the grid level by level, which ensures that when you first reach the end cell 'E', you’ve done so using the minimal number of jumps.
In your BFS queue, each state should include:
- The current coordinates (x, y)
- The direction of movement (or `null` if none yet)
- A flag indicating whether the previous jump was of length greater than 1
- The current count of jumps made so far
You should also maintain a visited set or matrix to avoid revisiting the same state, taking into account not just position but direction and movement status.
5. **Handling Constraints**:
The challenge is primarily in respecting the movement constraint that after a jump of length > 1, direction must remain the same. This requires careful state propagation. Every time you make a move, ensure that you check whether changing direction is allowed based on your last jump.
6. **Termination and Result**:
As you perform BFS, the moment you reach the destination cell 'E', return the number of jumps taken to get there. If BFS completes without reaching 'E', return -1 indicating that there is no valid path from 'S' to 'E' under the given constraints.
7. **Efficiency Consideration**:
Since you might explore the same cell multiple times with different movement directions and jump histories, the visited structure must reflect all three components: position, direction, and jump continuity. Without this, you may either revisit too much or prune valid paths incorrectly.
This approach ensures that all valid paths are explored while adhering to the special directional constraints, and that the shortest path is selected thanks to the nature of BFS. By treating the movement rules as part of the state and traversing the grid accordingly, you can handle both simple and complex grid layouts effectively.
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