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Longest Common
Subsequence (LCS)
Dr. Nancy Warter-Perez
Functions

Function definition


def adder(a, b, c): return a+b+c
Function calls

adder(1, 2, 3) -> 6
Introduction to Python – Part III
2
Functions – Polymorphism
>>>def fn2(c):
…
a=c*3
…
return a
>>> print fn2(5)
15
>>> print fn2(1.5)
4.5
>>> print fn2([1,2,3])
[1,2,3,1,2,3,1,2,3]
>>> print fn2("Hi")
HiHiHi
Introduction to Python – Part III
3
Functions - Recursion
def fn_Rec(x):
if x == []:
return
fn_Rec(x[1:])
print x[0],
y = [1,2,3,4]
fn_Rec(y)
>>> 4 3 2 1
Introduction to Python – Part III
4
Scopes




Scopes divine the
“visibility” of a variable
Variables defined outside
of a function are visible
to all of the functions
within a module (file)
Variables defined within
a function are local to
that function
To make a variable that
is defined within a
function global, use the
global keyword
Ex 1:
Ex 2:
x=5
x=5
def fnc():
def fnc():
x=2
global x
print x,
x=2
fnc()
print x,
print x
fnc()
>>> 2 5
print x
Developing Pairwise Sequence
Alignment Algorithms
>>> 2 2
5
Modules

Why use?




Code reuse
System namespace partitioning (avoid name
clashes)
Implementing shared services or data
How to structure a Program

One top-level file


Main control flow of program
Zero or more supplemental files known as
modules

Libraries of tools
Developing Pairwise Sequence
Alignment Algorithms
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Modules - Import

Import – used to gain access to tools in
modules
Ex:
contents of file b.py
def spam(text):
print text, 'spam'
contents of file a.py
import b
b.spam('gumby')
Developing Pairwise Sequence
Alignment Algorithms
7
Dynamic Programming
Applied to optimization problems
 Useful when

Problem can be recursively divided into
sub-problems
 Sub-problems are not independent


Examples


Needleman-Wunch Global Alignment Algorithm
Smith-Waterman Local Alignment Algorithm
Developing Pairwise Sequence
Alignment Algorithms
8
Longest Common
Subsequence (LCS) Problem


Can have insertion and deletions but no
substitutions (no mismatches)
Ex: V: ATCTGAT
W: TGCATA
LCS: TCTA
Developing Pairwise Sequence
Alignment Algorithms
9
LCS Problem (cont.)

Similarity score
si-1,j
si,j = max {
si,j-1
si-1,j-1 + 1, if vi = wj

On board example


V: ATCTGAT
W:TGCATA
Developing Pairwise Sequence
Alignment Algorithms
10
Indels – insertions and
deletions (e.g., gaps)

alignment of V and W



V = rows of similarity matrix (vertical axis)
W = columns of similarity matrix (horizontal axis)
Space (gap) in W
 (UP)


Space (gap) in V


insertion
 (LEFT)
deletion
Match (no mismatch in LCS)
Developing Pairwise Sequence
Alignment Algorithms
(DIAG)
11
LCS(V,W) Algorithm
for i = 0 to n
si,0 = 0
for j = 1 to m
s0,j = 0
for i = 1 to n
for j = 1 to m
if vi = wj
si,j = si-1,j-1 + 1; bi,j = DIAG
else if si-1,j >= si,j-1
si,j = si-1,j; bi,j = UP
else
si,j = si,j-1; bi,j = LEFT
Developing Pairwise Sequence
Alignment Algorithms
12
Print-LCS(b,V,i,j)
if i == 0 or j == 0
return
if bi,j = DIAG
PRINT-LCS(b, V, i-1, j-1)
print vi
else if bi,j = UP
PRINT-LCS(b, V, i-1, j)
else
PRINT-LCS(b, V, i, j-1)
Developing Pairwise Sequence
Alignment Algorithms
Note: b and V
could be global
variables
13
Programming Workshop and
Homework – Implement LCS


Workshop/Homework – Write a Python script to
implement LCS (V, W). Prompt the user for 2
sequences (V and W) and display b and s
Homework (due Thursday, November 15th with
Automatic Extension to Tuesday, November 27th)
– Add the Print-LCS(V, i, j) function to your
Python script. The script should prompt the user
for 2 sequences and print the longest common
sequence.
Developing Pairwise Sequence
Alignment Algorithms
14
Classic Papers


Needleman, S.B. and Wunsch, C.D. A General
Method Applicable to the Search for Similarities in
Amino Acid Sequence of Two Proteins. J. Mol. Biol.,
48, pp. 443-453, 1970.
(http://www.cs.umd.edu/class/spring2003/cmsc838t/
papers/needlemanandwunsch1970.pdf)
Smith, T.F. and Waterman, M.S. Identification of
Common Molecular Subsequences. J. Mol. Biol.,
147, pp. 195-197,
1981.(http://www.cmb.usc.edu/papers/msw_papers/
msw-042.pdf)
Developing Pairwise Sequence
Alignment Algorithms
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