Determine the number of character comparisons made by the brute-force algorithm in searching for the pattern GANDHI in the text THERE_IS_MORE_TO_LIFE_THAN_INCREASI NG_ITS_SPEED
(Assume that the length of the text-it is 47 characters long- is known before the search starts).

Total number of character comparison = 43

Explanation:

Using the Brute force algorithm

The string of n characters is known as text, and the string of m characters is known as the pattern.

From the given information:

The text (n)=THERE_IS_MORE_TO_LIFE_THAN_INCREASING_ITS_SPEED

The pattern (m) = GANDHI

The total no of characters that we have in the text = 47

The total number of characters in pattern = 6

For a brute force algorithm;

Since; the first character of the pattern does not exist in the text, then the number of trials made can be attempted can be expressed as = n – m + 1

= 47 – 6 + 1

= 47 – 5

= 42

Thus; the algorithm will attempt the trial 42 times.

Now, for loop in the algorithm to run 42 times, the G in the pattern will have to align against the for T in the text, and in the last case, it will be aligned against the last space.

On each attempted trial, the algorithm will make one unsuccessful comparison.

However, at the trial at which the G in the pattern Is aligned with the G in the text, there will be two successful comparisons.

Hence, we can calculate the total number of character comparison as follows:

Total number of character comparison =

Total number of character comparison = ( (( 42 – 1) × 1 ) + ( 1 × 2) )

Total number of character comparison = 41 + 2

Total number of character comparison = 43

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