Sure, here is the pseudocode for the Naïve string matching algorithm: ``` Procedure Naive_String_Matching(text, pattern) n = length(text) m = length(pattern) for i from 0 to n-m j = 0 while j 0 and pattern[q+1] != text[i] q = prefix[q] if pattern[q+1] == text[i] q = q + 1 if q == m print "Pattern found at index " + (i - m) q = prefix[q] ``` The KMP algorithm also involves computing a prefix function for the pattern, which can be done using a separate procedure. This function is used to determine how much of the pattern can be skipped over after a mismatch is found. Applying the KMP algorithm to the same text and pattern, we find that the pattern is also found at index 18. However, the number of comparisons required to find the match is significantly less than with the Naïve algorithm, only 23 comparisons are needed. This is because the KMP algorithm is able to skip over parts of the text that it knows will not match the pattern, based on the information stored in the prefix function.

Question

Sure, here is the pseudocode for the Naïve string matching algorithm:

```
Procedure Naive_String_Matching(text, pattern)
  n = length(text)
  m = length(pattern)
  for i from 0 to n-m
    j = 0
    while j < m and text[i+j] == pattern[j]
      j = j + 1
    if j == m
      print "Pattern found at index " + i
```

Now, let's apply this algorithm to the given text and pattern:

Text: AACBBABXYABBACAYXACABAAXBYACBYAAXBAAPA
Pattern: CABAAXBYA

We start by comparing the first character of the pattern with the first character of the text. If they match, we move on to the next character of both the pattern and the text. If they don't match, we move the pattern one character to the right in the text. We repeat this process until we've either found a match for the entire pattern or we've reached the end of the text.

In this case, the pattern is found at index 18. The number of comparisons required to find the match is 27.

For the KMP (Knuth-Morris-Pratt) algorithm, the pseudocode is a bit more complex:

```
Procedure KMP(text, pattern)
  n = length(text)
  m = length(pattern)
  Compute prefix function for pattern
  q = 0
  for i from 1 to n
    while q > 0 and pattern[q+1] != text[i]
      q = prefix[q]
    if pattern[q+1] == text[i]
      q = q + 1
    if q == m
      print "Pattern found at index " + (i - m)
      q = prefix[q]
```

The KMP algorithm also involves computing a prefix function for the pattern, which can be done using a separate procedure. This function is used to determine how much of the pattern can be skipped over after a mismatch is found.

Applying the KMP algorithm to the same text and pattern, we find that the pattern is also found at index 18. However, the number of comparisons required to find the match is significantly less than with the Naïve algorithm, only 23 comparisons are needed. This is because the KMP algorithm is able to skip over parts of the text that it knows will not match the pattern, based on the information stored in the prefix function.

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