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A number maze is a k ×k grid of positive integers. A token starts in the upper left corner and your goal is to move the token to the lower-right corner. On each turn, you are allowed to move the token up, down, left, or right; the distance you may move the

A number maze is a k ×k grid of positive integers. A token starts in the upper left corner and your goal is to move the token to the lower-right corner. On each turn, you are allowed to move the token up, down, left, or right; the distance you may move the

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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A number maze is a k ×k grid of positive integers. A token starts in the upper left corner and your goal is to move the token to the lower-right corner. On each turn, you are allowed to move the token up, down, left, or right; the distance you may move the token is determined by the number on its current square. For example, if the token is on a square labeled 3, then you may move the token exactly three steps up, three steps down, three steps left, or three steps right. However, you are never allowed to move the token off the edge of the board. Design and analyze an algorithm that in O(k2) time determines if there is a way to move the token in the given number maze or not.

 

Example: Given the number maze in the following figure, your algorithm should return Yes. 3 5 7 4 35 6 5 3 1 5 3- 2 8. 3 4 8. 3| 1 4 45 72 3 4 2 3 3132|* 3 Figure 1: A 5 × 5 maze with the answer Yes. Hint: Think of graph reductions this problem is not that different from the fill coloring problem after all.
Transcribed Image Text:Example: Given the number maze in the following figure, your algorithm should return Yes. 3 5 7 4 35 6 5 3 1 5 3- 2 8. 3 4 8. 3| 1 4 45 72 3 4 2 3 3132|* 3 Figure 1: A 5 × 5 maze with the answer Yes. Hint: Think of graph reductions this problem is not that different from the fill coloring problem after all.
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