# Algorithms Exercise 2

## Imports


```python
%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.


```python
def find_peaks(a):
    """Find the indices of the local maxima in a sequence."""
    
```


```python
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.


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


```python
w=pi_digits_str
r=[]
for x in w:
    r.append(int(x))
a=np.array(r)
m=find_peaks(a)
s=np.diff(m)
plt.hist(s,bins=50)
s
```


```python
assert True # use this for grading the pi digits histogram
```

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Jupyter Notebook
assignments/assignment07/AlgorithmsEx02.ipynb
ajhenrikson/phys202-2015-work
05fcf7c0cab66b290ed081d344942f7fff308095
MIT
assignments/assignment07/AlgorithmsEx02.ipynb
ajhenrikson/phys202-2015-work
05fcf7c0cab66b290ed081d344942f7fff308095
MIT
assignments/assignment07/AlgorithmsEx02.ipynb
ajhenrikson/phys202-2015-work
05fcf7c0cab66b290ed081d344942f7fff308095
MIT
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1. YES
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