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Given the following text description, write Python code to implement the functionality described below step by step
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Description:
 Algorithms Exercise 2
Imports
Step2:  Peak finding
Write a function find_peaks that finds and returns the indices of the local maxima in a sequence. Your function should
Step3:  Here is a string with the first 10000 digits of $\pi$ (after the decimal). Write code to perform the following
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Python Code:
%matplotlib inline
from matplotlib import pyplot as plt
import seaborn as sns
import numpy as np
Explanation: Algorithms Exercise 2
Imports
End of explanation
def find_peaks(a):
    Find the indices of the local maxima in a sequence.
    leest = []
    if a[0] > a[1]:
        leest.append(0)
    for x in range(1,len(a)-1):
        if (a[x-1]<a[x]) and (a[x]>a[x+1]):
            leest.append(x)
    if a[len(a)-1] > a[len(a)-2]:
        leest.append(len(a)-1)
    return leest
    
    
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]))
Explanation: 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.
End of explanation
from sympy import pi, N
pi_digits_str = str(N(pi, 10001))[2:]
x = np.zeros(10000, dtype=int )
for a in range(len(pi_digits_str)):
    x[a] = int(pi_digits_str[a])
    
ind = find_peaks(x)
dis = np.diff(ind)
plt.hist(dis, bins=20, range=(0,15))
plt.title('Distribution of local Maxima in Pi')
plt.xlabel('Distantce between local maxima')
plt.ylabel('Frequency')
plt.show()
assert True # use this for grading the pi digits histogram
Explanation: 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.
End of explanation
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