mark-william-schumacher / datastructuresandalgorithms

Practice for technical interviews, done in preparation for onsite interviews during winter of 2015

DataStructuresAndAlgorithms

Practice for technical interviews, done in preparation for onsite interviews during winter of 2015

These are technical interview prep questions taken from Elements of a Programming interview http://elementsofprogramminginterviews.com/pdf/epi-light-1.4.10.pdf and leetcode.com

Local and Global Alignment and Fitting Algorithms

GlobalAndLocalAlignment.java have some tester code written to solve some small scale dynamic programming local/global alignment problems. Algorithms are O(nm) space / time.

Example: Solving Global alignment for s1= "TAGATA" , s2= "GTAGGCTTAAGGTTA"

Global Alignment Matrix:

-    -    T    A    G    A    T    A

-    0   -1   -2   -3   -4   -5   -6 

G   -1   -1   -2   -1   -2   -3   -4 

T   -2    0   -1   -2   -2   -1   -2 

A   -3   -1    1    0   -1   -2    0 

G   -4   -2    0    2    1    0   -1 

G   -5   -3   -1    1    1    0   -1 

C   -6   -4   -2    0    0    0   -1 

T   -7   -5   -3   -1   -1    1    0 

T   -8   -6   -4   -2   -2    0    0 

A   -9   -7   -5   -3   -1   -1    1 

A  -10   -8   -6   -4   -2   -2    0 

G  -11   -9   -7   -5   -3   -3   -1 

G  -12  -10   -8   -6   -4   -4   -2 

T  -13  -11   -9   -7   -5   -3   -3 

T  -14  -12  -10   -8   -6   -4   -4 

A  -15  -13  -11   -9   -7   -5   -3 

Can be done in O(n) space at not cost to time with a clever solution

Local Alignment Theroy

In local alignment we are looking for any path which generates the large score in the entire matrix. To Achieve this, we can run the exact same algorythm (seen in GlobalAndLocalAlignment.java function LocalAlignment) the table is set up initalized to all 0's as is default in java. Now to achieve the Global alignment in our 0th column and 0th row we initialize with increasing numbers, this step is skipped in local alignment to achieve the alignment shown in the picture to the left. Note in local alignment that we can NEVER have a spot in our matrix filled with a negative number , it the result of max (up-1, left-1, diagonal+match) is negative, we set it to 0.