Algorithms Exercise 2

Imports



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%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 [2]:

    
def find_peaks(a):
    """Find the indices of the local maxima in a sequence."""
    # YOUR CODE HERE
    r = []
    for i in range(0, len(a)):
        if (i == len(a)-1 or a[i]>a[i+1]) and a[i]>a[i-1]:
            r.append(i)
    return np.array(r)



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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 [4]:

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



In [5]:

    
# YOUR CODE HERE
h =  pi_digits_str
p = []
for i in h:
    p.append(int(i))
e = np.array(p)
g = find_peaks(e)
y = np.diff(g)
plt.hist(y, bins = 90)
plt.ylabel('minanma spacing')
plt.xlabel('minima')









    Out[5]:





<matplotlib.text.Text at 0x7fde54c4c5c0>



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assert True # use this for grading the pi digits histogram



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