Practice Handling Holes - 2.1.4 | 2. Inductive Formulation of the Grid Path | Design & Analysis of Algorithms - Vol 3
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Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

What is the number of paths to point (1,0) from (0,0)?

💡 Hint: Think of how you can only move from (0,0) to (1,0) directly.

Question 2

Easy

If a hole is placed at point (2,2), how many paths can go through it?

💡 Hint: Consider what happens when a point is obstructed.

Practice 4 more questions and get performance evaluation

Interactive Quizzes

Engage in quick quizzes to reinforce what you've learned and check your comprehension.

Question 1

What is the base case for paths(0,0)?

  • 0
  • 1
  • 2

💡 Hint: Consider what it means to be at the origin without moving.

Question 2

Can paths go through holes?

  • True
  • False

💡 Hint: Think about what a hole represents in terms of pathfinding.

Solve 2 more questions and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

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.

💡 Hint: Map out the valid paths while taking into consideration each hole's impact.

Question 2

Explain how the choice between using memoization versus dynamic programming can affect the performance of computing paths on a grid with multiple obstacles.

💡 Hint: Reflect on memory usage versus time efficiency.

Challenge and get performance evaluation