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Designing Algorithms

Designing Algorithms. Csci 107 Lecture 4. Outline. Last time Computing 1+2+…+n Adding 2 n-digit numbers Today: More algorithms Sequential search Variations of sequential search Pattern matching. A Search Algorithm.

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Designing Algorithms

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  1. Designing Algorithms Csci 107 Lecture 4

  2. Outline Last time • Computing 1+2+…+n • Adding 2 n-digit numbers Today: More algorithms • Sequential search • Variations of sequential search • Pattern matching

  3. A Search Algorithm Problem statement: Write a pseudocode algorithm to find the location of a target value in a list of values. Input: a list of values and the target value Output: the location of the target value, or else a message that the value does not appear in the list. Variables:

  4. The (sequential) search algorithm (Fig 2.9) Variables: target, n, list list of n values Get the value of target, n, and the listof n values Set index to 1 Set found to false Repeat until found = true orindex > 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

  5. Variations of sequential search.. • 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

  6. 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

  7. More algorithms • 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 range of a list of numbers • Range= largest - smallest • the average of a list of numbers • the sum of a list of numbers

  8. 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

  9. 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

  10. 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.

  11. Pattern Matching • Input • 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?

  12. 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?

  13. Pattern Matching • Algorithm idea • 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

  14. 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

  15. 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.

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