Practice Initial Conditions - 2.1.3 | 2. Inductive Formulation of the Grid Path | Design & Analysis of Algorithms - Vol 3
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Initial Conditions

2.1.3 - Initial Conditions

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Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

How many paths are there to the point (0,0)?

💡 Hint: Consider your starting point.

Question 2 Easy

What happens to the path count if there’s a hole at (2,3)?

💡 Hint: Think about the implications of obstacles.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the path count from (0,0) to (0,0)?

0
1
More than 1

💡 Hint: Think about movement options.

Question 2

Paths to a point with a hole are counted as?

True
False

💡 Hint: Remember the role of obstacles.

2 more questions available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

In a 6x6 grid with holes at (2,2) and (3,3), compute the number of paths to (5,5) through dynamic programming and illustrate your table.

💡 Hint: Start with your base cases and fill each cell considering blockage from holes.

Challenge 2 Hard

Construct a comprehensive table showing both memoized and dynamically programmed solutions for a 5x5 grid with four holes randomly distributed.

💡 Hint: Use both methods to fill the same grid and compare the resulting path counts, especially noting differences in efficiency.

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Reference links

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