Algorithms Exercise 2

Imports



In [1]:

    
%matplotlib inline
from matplotlib import pyplot as plt
import seaborn as sns
import numpy as np

Peak finding

Write a function find_peaks that finds and returns the indices of the local maxima in a sequence. Your function should:

Properly handle local maxima at the endpoints of the input array.
Return a Numpy array of integer indices.
Handle any Python iterable as input.



In [28]:

    
def find_peaks(a):
    """Find the indices of the local maxima in a sequence."""
    P=[]
    for i in range(0,len(a)):
        if i==0 and a[1]<a[0]:
            P.append(0)
        elif i==len(a)-1 and a[i-1]<a[i]:
            P.append(i)
        else:
            if a[i-1]<a[i] and a[i+1]<a[i]:
                P.append(i)
    return np.array(P)



In [32]:

    
p1 = find_peaks([2,0,1,0,2,0,1])
assert np.allclose(p1, np.array([0,2,4,6]))
p2 = find_peaks(np.array([0,1,2,3]))
assert np.allclose(p2, np.array([3]))
p3 = find_peaks([3,2,1,0])
assert np.allclose(p3, np.array([0]))

Here is a string with the first 10000 digits of $\pi$ (after the decimal). Write code to perform the following:

Convert that string to a Numpy array of integers.
Find the indices of the local maxima in the digits of $\pi$.
Use np.diff to find the distances between consequtive local maxima.
Visualize that distribution using an appropriately customized histogram.



In [33]:

    
from sympy import pi, N
pi_digits_str = str(N(pi, 10001))[2:]



In [46]:

    
from IPython.display import display



In [51]:

    
pi=find_peaks(pi_digits_str)
df=np.diff(pi)
plt.hist(df,range=(0,max(df)),bins=max(df))
plt.title('$\Pi$ Maximums')
plt.xlabel('Digits between Maxes')









    Out[51]:





<matplotlib.text.Text at 0x7ffdde200eb8>



In [ ]:

    
assert True # use this for grading the pi digits histogram