Unit 11 Session 1 Standard (Click for link to problem statements)
Unit 11 Session 1 Advanced (Click for link to problem statements)
Understand what the interviewer is asking for by using test cases and questions about the problem.
- Established a set (2-3) of test cases to verify their own solution later.
- Established a set (1-2) of edge cases to verify their solution handles complexities.
- Have fully understood the problem and have no clarifying questions.
- Have you verified any Time/Space Constraints for this problem?
False immediately if the start or target zone is unsafe.HAPPY CASE
Input: position = (0, 0), grid = [
[1, 0, 1, 1, 0],
[1, 1, 1, 1, 0],
[0, 0, 1, 1, 0],
[1, 0, 1, 1, 1]
]
Output: True
Explanation: There exists a safe path to the bottom-right corner.
EDGE CASE
Input: position = (0, 1), grid = [
[1, 0, 1, 1, 0],
[1, 1, 1, 1, 0],
[0, 0, 1, 1, 0],
[1, 0, 1, 1, 1]
]
Output: False
Explanation: The start position is unsafe, so we cannot move.Match what this problem looks like to known categories of problems, e.g. Linked List or Dynamic Programming, and strategies or patterns in those categories.
For Grid Traversal problems, we want to consider the following approaches:
Plan the solution with appropriate visualizations and pseudocode.
General Idea: Start from the initial position and explore the grid using DFS, ensuring you only move to adjacent safe zones. Keep track of visited zones to avoid cycles and unnecessary reprocessing.
1) Define a helper function `next_moves` that returns all valid adjacent safe zones that haven't been visited.
2) Initialize a set `visited` to keep track of previously visited zones.
3) Use DFS to recursively explore the grid from the starting position:
a) If the current position is the target, return True.
b) Mark the current position as visited.
c) Explore all valid adjacent positions by calling the helper function.
d) If any recursive call returns True, propagate the result upward.
4) If no path to the target exists, return False.⚠️ Common Mistakes
Implement the code to solve the algorithm.
# Helper function to find valid next moves
def next_moves(position, grid, visited):
row, col = position
rows = len(grid)
cols = len(grid[0])
# Define directions for moving up, down, left, and right
directions = [(-1, 0), (1, 0), (0, -1), (0, 1)]
# List to hold the valid next moves
valid_moves = []
# Check each direction
for d_row, d_col in directions:
new_row, new_col = row + d_row, col + d_col
# Ensure new position is within the grid bounds, is safe (grid[new_row][new_col] == 1),
# and has not been visited
if 0 <= new_row < rows and 0 <= new_col < cols and grid[new_row][new_col] == 1 and (new_row, new_col) not in visited:
valid_moves.append((new_row, new_col))
return valid_moves
# Main function to determine if the safe haven can be reached
def can_move_safely(position, grid):
rows, cols = len(grid), len(grid[0])
start_row, start_col = position
target = (rows - 1, cols - 1)
# If starting or target position is unsafe, return False immediately
if grid[start_row][start_col] == 0 or grid[rows - 1][cols - 1] == 0:
return False
# Initialize the visited set
visited = set()
# DFS function to explore the grid
def dfs(row, col):
if (row, col) == target:
return True
visited.add((row, col))
# Get valid next moves from the current position using the helper function
for next_move in next_moves((row, col), grid, visited):
if dfs(next_move[0], next_move[1]):
return True
return False
# Start DFS from the initial position
return dfs(start_row, start_col)Review the code by running specific example(s) and recording values (watchlist) of your code's variables along the way.
Example 1:
next_move in each DFS iteration?Evaluate the performance of your algorithm and state any strong/weak or future potential work.
Assume m is the number of rows and n is the number of columns in the grid.
O(m * n) because, in the worst case, we might need to visit every cell in the grid.O(m * n) due to the recursive call stack and the visited set.