Functions

• Fibonacci numbers Definition:     

f₀ = 0

f₁ = 1

f_n = f_n-1 + f_n-2 ∀n > 2

• This can be written as recursive
  function ( a function which calls
  itself again)

def fib(x):
    if (x == 0): 
        return 0
    elif (x == 1): 
        return 1
    else:
        return fib(x-1) + fib(x-2)

 

for i in range(10):
    print(fib(i))

Example: Similarity of two DNA sequences

Biological intuition:

Sequence = string of characters

Informal:

Arrange sequences in such a way that
similarity becomes visible

GATCGTTCG

    | |     | | |

CATGGTTGA

Distance function:

$d\left(a,b\right)\:=\:\begin{cases} 0, & \text{if } a= b\\ 1, & \text{otherwise} \end{cases}$

Example:

A = GATCGTTCG, B = CATGGTTGA

G A T C G T T C G

     |  |      |  |  |

C A T G G T T G A

     |  |      |  |  |

           1  0 0  1  0 0  0  1  1 

distance = 4

# Simple calculation of distances

A = "GATCGTTCG"

B = "CATGGTTGA"

distance = 0 

# Calculate the distance for each position and sum it up  


for i in range(len(A)):
    if (A[i] == B[i]):
        d = 0
    else:
        d = 1

    distance = distance + d

print("Distance of sequences A and B: ", distance)

Distance of Sequences with Function

# Simple calculation of distances
A = "GATCGTTCG"
B = "CATGGTTGA"


def d(a, b):
    
    distance = 0

    for i in range(len(a)):

        if(a[i] != b[i]):

            distance += 1

    return distance


distance = d(A, B)

print("Distance of sequences A and B: ", distance)