Algorithms Exercise 2

Imports



In [48]:

    
%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 [49]:

    
def find_peaks(a):
    """Find the indices of the local maxima in a sequence."""
    # YOUR CODE HERE
    #I always start with an empty list k.
    k=[]
    for i in range(0, len(a)):
        #Check to see if the number in index i is greater than the numbers in the adjacent indicies, whilst being in range of the list.
        if (i==len(a)-1 or a[i]>a[i+1]) and a[i]>a[i-1]:
            k.append(i)
    return np.array(k)



In [50]:

    
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 [51]:

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



In [62]:

    
# YOUR CODE HERE
h = pi_digits_str
j=[]
for i in h:
    j.append(int(i))
n = np.array(j)
v = find_peaks(n)
m = np.diff(v)

f = plt.figure(figsize=(10,6))
plt.hist(m, bins=20)
plt.ylabel('Distance between maxima')
plt.xlabel('Index of maxima')
m









    Out[62]:





array([3, 2, 5, ..., 5, 2, 4])



In [40]:

    
assert True # use this for grading the pi digits histogram