1. Designing Algorithms
Csci 107
Lecture 4

2. Outline Last time Today: More algorithms Sequential search
Variations of sequential search
Pattern matching
Reading: Finish Chapter 2 textbook

3. The (sequential) search algorithm (Fig 2.9)
Variables: target, n, list list of n values
Get the value of target, n, and the list of n values
Set index to 1
Set found to false
Repeat until found = true or index > n
If the value of listindex = target
then
Output the index
Set found to true
else
Increment the index by 1
If found is false then
Output a message that target was not found
Stop

4. Iterating through a list
Assume the input list is stored in a1, a2, …, an
In general, an algorithm that will have to explore every single element in the list in order will look something like this
Set i = 1
Repeat until (i>n)
<do something with element ai>
Set i = i+1

5. More algorithms Modify the sequential search algorithm in order
To find all occurrences of target in the list and print the positions where they occur
To count the number of occurrences of target in the list
To count how many elements in the list are larger than target
Given a list of numbers from the user, write algorithms to find
the largest number in a list of numbers (and the position where it occurs)
the smallest number in a list of numbers (and the position where it occurs)
the (arithmetic) average of a list of numbers
the sum of a list of numbers

6. A Search Application in Bioinformatics
Human genome: sequence of billions of nucleotides
Gene
Determines human behavior
Sequence of tens of thousands of nucleotides{A,C, G, T}
The sequence is not fully known, only a portion of it..
Problem: How to determine a gene in the human genome?
Genome: …….TCAGGCTAATCGTAGG…….
Gene probe: TAATC
Idea: Find all matches of the probe within the genome and then examine the nucleotides in that neighborhood

7. A Search Application in Bioinformatics
Problem:
Suppose we have a text T = TCAGGCTAATCGTAGG and a pattern P = TA. Design an algorithm that searches T to find the position of every instance of P that appears in T.
E.g., for this text, the algorithm should return the answer:
There is a match at position 7
There is a match at position 13
This problem is similar to the search algorithm
except that for every possible starting position every character of P must be compared with a character of T.

8. Pattern Matching Input Output: Algorithm:
Text of n characters T1, T2, …, Tn
Pattern of m (m < n) characters P1, P2, …Pm
Output:
Location (index) of every occurrence of pattern within text
Algorithm:
What is the idea?

9. Pattern Matching Algorithm idea:
Check if pattern matches starting at position 1
Then check if it matches starting at position 2
…and so on
How to check if pattern matches text starting at position k?
Check that every character of pattern matches corresponding character of text
How many loops will you need?

10. Pattern Matching Algorithm idea Question: is this an algorithm?
Get input (text and pattern)
Set starting location k to 1
Repeat until reach end of text
Attempt to match every character in the pattern beginning at pos k in text
If there was a match, print k
Add 1 to k
Stop
Question: is this an algorithm?
Yes, at a high level of abstraction
Now we need to write in pseudocode

11. Pattern Matching Algorithm (Fig. 2.12)
Variables: n, m, T1T2…Tn , P1P2…Pm , k, mismatch
Get values for n, m, the text T1T2…Tn and the pattern P1P2…Pm
Set k =1
Repeat until k>n-m+1
Set i to 1
Set mismatch=“NO”
Repeat until either (i>m) or (mismatch = “YES”)
if Pi ≠ Tk+(i-1) then
Set mismatch=“YES”
else Increment i by 1
if mismatch = “NO” then
Print the message “There is a match at position” k
increment k by 1
Stop

12. Variations on the pattern matching algorithm
How would you modify the algorithm in order to
Find only the first match for P in T.
Find only the last match for P in T.