Algorithms Exercise 2


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 [15]:
def find_peaks(a):
    """Find the indices of the local maxima in a sequence."""
    peaks = []
    data = np.array(a)
    deriv = np.diff(data)
    if deriv[0] < 0:
    for i in range(1,len(deriv)):
        if deriv[i]<0 and deriv[i-1]>0:
    if deriv[-1] >0:
    return np.array(peaks)

In [16]:
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 [24]:
from sympy import pi, N
pi_digits_str = str(N(pi, 10001))[2:]

[1 4 1 ..., 6 7 8]

In [59]:
plt.hist(peakdiff, bins=100, width=1, color='k',edgecolor='b', align='right');
plt.xlabel("Distance between adjacent local maxima in pi")
plt.title("Distance between adjacent local maxima in pi");

In [60]:
assert True # use this for grading the pi digits histogram

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