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4 cards from this section. Quick, good the night before a test.
What is the number of paths to point (1,0) from (0,0)?
Think of how you can only move from (0,0) to (1,0) directly.
If a hole is placed at point (2,2), how many paths can go through it?
Consider what happens when a point is obstructed.
What is the base case for paths(0,0)?
Consider what it means to be at the origin without moving.
Can paths go through holes?
Think about what a hole represents in terms of pathfinding.
Design a 5x5 grid with two holes and calculate the number of unique paths from (0,0) to (4,4). Provide a step-by-step explanation.
Map out the valid paths while taking into consideration each hole's impact.
Explain how the choice between using memoization versus dynamic programming can affect the performance of computing paths on a grid with multiple obstacles.
Reflect on memory usage versus time efficiency.
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