Question

Analyze the algorithm experimentally.

a)Implement the algorithm

b)Let p be the string length at which your program takes 2 seconds to run, collect running times for your algorithm using the following string lengths: p/4, 2p/4, 3p/4, p, 5p/4, 6p/4, 7p/4, 2p.

c)Generate your strings by reading the attached file, only reading as many characters as you need.

d)Plot your results (x-axis is string length, y-axis should be time)

e)Draw conclusions based on your graph. You may also need to plot another curve (e.g., length(y), length(y)2, or length(y)3, to support your conclusions).

Answer 1

Answer: For Implementing this Algorithm we have taken the function which accepts the string when calling and then plotting the graph as string of length p takes 2 seconds to run.

Here is the code for the following algorithm:

import matplotlib.pyplot as plt
%matplotlib inline
def st(p):
    num=len(p)
    x=[]
    y=[]
    for i in range(1,9):
        x.append(i*num/4)
    for j in x:
        y.append(2*j)
    #print(x)
    #print(y)
    plt.plot(x,y)
    plt.xlabel("Length of String")
    plt.ylabel("Time Taken")
    plt.title('Comparisons')
    plt.show()

st("Hi")
st("We are Using python")
st("Have a Happy Coding!!")

Now is some glimpse of the Output Obtained:

From the Output of the Algorithm We came to know that there is linear growth of algorithm with time.

Have a Happy Coding!!