Practice Handling Holes in Computation - 2.2.3 | 2. Inductive Formulation of the Grid Path | Design & Analysis of Algorithms - Vol 3
K12 Students

Academics

AI-Powered learning for Grades 8–12, aligned with major Indian and international curricula.

Professionals

Professional Courses

Industry-relevant training in Business, Technology, and Design to help professionals and graduates upskill for real-world careers.

Games

Interactive Games

Fun, engaging games to boost memory, math fluency, typing speed, and English skills—perfect for learners of all ages.

Typing
Memory
Math
English Adventures
Knowledge

2.2.3 - Handling Holes in Computation

Enroll to start learning

You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.

Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

What is the formula for calculating the number of paths to a point (i, j) on the grid?

💡 Hint: Think about where you can come from to reach (i, j).

Question 2

Easy

If there's a hole at (2, 2), what is the value of Paths(2, 2)?

💡 Hint: What does a hole represent in terms of path counts?

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 value do we assign to paths when there's a hole in the grid?

  • 1
  • 0
  • infinity

💡 Hint: Recall the definition of a hole in the context of paths.

Question 2

True or False: Dynamic programming only calculates necessary paths as needed.

  • True
  • False

💡 Hint: Consider how each method approaches problem-solving.

Solve 1 more question and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

You have a grid of size 6x6 with holes at (2, 2), (3, 3), and (1, 5). Calculate the number of unique paths from (0, 0) to (5, 5). What strategies will you employ?

💡 Hint: Focus on filling values in a structured manner and adjust according to hole placements.

Question 2

Compare the efficiency of dynamic programming versus memoization in a scenario where 70% of the grid is filled with holes. Discuss any trade-offs.

💡 Hint: Analyze how the structure of the grid and placement of holes contribute to each method’s computational efficiency.

Challenge and get performance evaluation