Lecture 5 - KMP

Question 1

What does KMP stand for?

Answer 1

Knuth Morris Pratt (algorithm)

Question 2

What kind of an algorithm is KMP? hint : on

Answer 2

An online algorithm, this means it has no need to back up in the text. It instead involves preprocessing of the border table.

Question 3

What is a border table?

Answer 3

an array b with entry b[j] for each position j of the string

Question 4

What happens if we get a mismatch?

Answer 4

we remain on the current text character and compare it to a character which is determined by the border table

Question 5

What is a suffix?

Answer 5

substring that ends at n-1 of string

Question 6

What is a prefix?

Answer 6

substring that begins at position 0

Question 7

What is the border of the table?

Answer 7

A border of the string s is a substring that is both a prefix and a suffix, but it cannot be the string itself

Question 8

What are the borders of acac gat acac?

Answer 8

ac and acac are both borders. acac being the longest one

Question 9

What is the border of an empty string?

Answer 9

an empty string itself is the border (length 0)

Question 10

What is the size of the border table

Answer 10

Same size as the string we are looking for.

Question 11

What is b[j] of the border table?

Answer 11

It holds the longest border of substring 0 to j-1

Question 12

What is b[0] always set to ?

Answer 12

0, as this refers to a substring of size 0 i.e. sub[0..0]

Question 13

fill in the border table of ababaca

Answer 13

0 0 0 1 2 3 0

Question 14

After mismatch what happens in the KMP algorithm visually?

Answer 14

the string s gets shifted left until the characters to the left of i (current position in t) match the characters of s to the left of i. This essentially determines what j becomes (j is the index of the string )

Question 15

Is it often that border tables of strings can be created?

Answer 15

NO

Question 16

What happens if we cannot get a border match after a mismatch?

Answer 16

We need to reset j to 0 (start checking from the beginning of the string), while i will remain unchanged.

EDGE CASE if j is already 0 , i.e. first char of string, then instead increment i by 1.

Question 17

What is the complexity of the KMP algorithm?

Answer 17

O(n) in the worst case, as the number of the interations of the loop is at most 2n, this is because i and k always increase.

-> refer to slides
-> this is O(m+n) when combined with algorithm to create border table (the efficient one)

Question 18

Why is KMP better than the brute force approach?

Answer 18

As we avoid matching characters we know will match.

Question 19

What is the complexity of creating the border table?

Answer 19

O(j^2) to evaluate each length, then O(m) to evaluate all chars
hence O(m^3) overall

-> there are better approaches, refer to live lecture from week 5

Question 20

LOOK OVER THE COMPLEXITY FOR BORDER TABLE CREATION