Practice Paths to (i,j) - 2.1.1 | 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

How do you calculate the number of paths to (2,1) from (0,0)?

💡 Hint: Count the ways to get to the first point and then to the second.

Question 2

Easy

What is the value of paths(0,0)?

💡 Hint: Think about staying in one spot.

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 key method used to calculate paths(i,j) in a grid?

  • By moving only right
  • By moving only up
  • From neighbors on left or below

💡 Hint: Think about the movement options on a grid.

Question 2

True or False: If there is a hole at (2,1), paths(2,1) would be zero.

  • True
  • False

💡 Hint: Consider how holes affect calculations.

Solve 1 more question and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

Design a 5x5 grid with multiple holes. Calculate paths to (4,4) considering obstacles dynamically and using memoization. Discuss the efficiencies and pitfalls of each method.

💡 Hint: Document steps as you fill in the grid, then analyze results.

Question 2

Create a real-life application for pathfinding similar to this grid setup. How would obstacles affect routing?

💡 Hint: Think algorithms used in GPS applications or logistics.

Challenge and get performance evaluation