1. String Processing

2. Basic String Techniques
Storing strings
Reading text input by line
Concatenating strings
Checking for matching string at beginning
Finding a substring within a larger string
Counting occurances in a string (e.g. how many vowels)
Tokenizing: splitting a string into substrings by delimiters
Sorting an array of strings

3. String Matching Find occurrences of T (length m) inside S (length n)
Basic matching can use library functions
Requires reasonably small strings
Longer matching: naïve approach
Loop over S (1 to n)
Check whether T occurs starting at that point (1 to m)
So, O(nm) total
Better: Knuth-Morris-Pratt (KMP) Algorithm

4. Knuth-Morris-Pratt (KMP) Algorithm
Idea: preprocess T (the one to find) – use matches there to know where to start the next match
Preprocess: For character i in T,
If the string matched to character i, but not to character i+1,
Then, how many digits of the string match up until that point
This tells you where to start matching again
Match like naïve. But, when you stop getting a match:
Go back a given number of spaces (based on preprocess)
Start match there

5. KMP Algorithm - running
Example: T is abracadabra
Could represent differently – where the # stored is the number matching the prefix, but then need to offset everything else by 1
Example: S is abrabracabracadabracadabra a b r c d 1 2 3

6. a b r c d 1 2 3
i: S: abrabracabracadabracadabra T: abracadabra j: Mismatch at slot 4 (i=4, j=4). Back table has value 1 there. So, next we’ll continue with i=4, but j will go back to 1.

7. a b r c d 1 2 3
i: S: abrabracabracadabracadabra T: abracadabra j: Mismatch at slot j=6 (and i=9). Back table has value 1 there. So, next we’ll continue with i=9, but j will go back to slot 1:

8. a b r c d 1 2 3
i: S: abrabracabracadabracadabra T: abracadabra j: Full match here. Mark as found (at slot 8). Next one starts 4 back (i=18, j=4).

9. a b r c d 1 2 3
i: S: abrabracabracadabracadabra T: abracadabra j: Full match here again. Mark as found (at slot 15). Next one would start 4 back (i=21).

10. Dynamic Programming on Strings
Edit Distance: Given two strings, how many edits (insert space, delete digit, or have mismatch) are needed between them?
Use DP: String A[1..n], B[1..m]:
For A[1..i], B[1..j], we have V(i,j) = edit distance for substrings. We want V(n,m)
V(0,0) = 0
V(i,0) = penalty to delete all i elements from A
V(0,j) = penalty to delete all j elements from B
V(i,j) = max:
V(i-1,j-1) + score(A[i],B[i])
V(i-1,j)+score(A[i],-)
V(i,j-1)+score(-,B[j])
Where
score(A[i],B[j]) = 2 if matching, -1 if nonmatching, and
score(x,-)=score(-,x) = -1 (penalty to delete = penalty to add a space)

11. More DP on Strings For Longest Common Subsequence
Same as String Alignment
Penalty for mismatch = infinity
Penalty for add/delete = 0
Points for match = 1