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 [157]:

    
def find_peaks(a):
    """Find the indices of the local maxima in a sequence."""
    
    #empty list and make the parameter into an array
    empty = []
    f = np.array(a)
    
    #Loop through the parameter and tell if it is a max
    for i in range(len(f)):
        if i == 0 and f[i] > f[i+1]:
            empty.append(i)

        if i == len(f)-1 and f[i]> f[i-1]:
            empty.append(i)
        if i > 0 and i < len(f)-1:
            if f[i]>f[i-1] and f[i] > f[i+1]:
                empty.append(i)

        
    return empty



In [158]:

    
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 [159]:

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



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#iterate through pi_digits_str
f = [c for c in pi_digits_str]

#find peaks in f
x = find_peaks(f)

#graph
plt.hist(np.diff(x),10, align = 'left')
plt.xticks(range(0,11))
plt.title("Differences of Local Maxima for pi");
plt.xlabel("Difference");
plt.ylabel("Frequency");



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assert True # use this for grading the pi digits histogram