Consider the following problem on a dictionary of n words, W1 ... Wn, each with exactly k characters. You can transform a word W; into word W;if they differ in at most d

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
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Consider the following problem on a dictionary of n words, W1... Wn, each with
exactly k characters. You can transform a word W; into word W;if they differ in at
most d <k characters. (both d and k are specified as part of the input, along with
n and the words) For example, if the dictionary is W1 = 'hiť, W2 = 'cog', W3= 'hot',
W4 = 'dot', Ws = 'dog', W6 = 'lot, W7 = 'log', and d = 1, one way to change 'hiť to
'cog' is: 'hit' → 'hot → 'dot → 'dog' → 'cog'. We want to find the fewest number
of steps to transform Wito W2.
5a. Formulate this problem as a shortest path problem.
5b. Describe an algorithm for finding the minimum number of steps (you only
need to describe how to find the number of steps, not the sequence of
transformations). estimate the time efficiency.
Transcribed Image Text:Consider the following problem on a dictionary of n words, W1... Wn, each with exactly k characters. You can transform a word W; into word W;if they differ in at most d <k characters. (both d and k are specified as part of the input, along with n and the words) For example, if the dictionary is W1 = 'hiť, W2 = 'cog', W3= 'hot', W4 = 'dot', Ws = 'dog', W6 = 'lot, W7 = 'log', and d = 1, one way to change 'hiť to 'cog' is: 'hit' → 'hot → 'dot → 'dog' → 'cog'. We want to find the fewest number of steps to transform Wito W2. 5a. Formulate this problem as a shortest path problem. 5b. Describe an algorithm for finding the minimum number of steps (you only need to describe how to find the number of steps, not the sequence of transformations). estimate the time efficiency.
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