# 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."""
    # YOUR CODE HERE
    r = []
    for i in range(0, len(a)):
        if (i == len(a)-1 or a[i]>a[i+1]) and a[i]>a[i-1]:
            r.append(i)
    return np.array(r)
```


```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
# YOUR CODE HERE
h =  pi_digits_str
p = []
for i in h:
    p.append(int(i))
e = np.array(p)
g = find_peaks(e)
y = np.diff(g)
plt.hist(y, bins = 90)
plt.ylabel('minanma spacing')
plt.xlabel('minima')
```


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


```python

```


```python

```

c8ad9fa4cda735b3cd239dc67d758b2bd4dc3a2c
ipynb
Jupyter Notebook
assignments/assignment07/AlgorithmsEx02.ipynb
sraejones/phys202-2015-work
988db3174fed541a85564b7aebeb618c3ad46075
MIT
assignments/assignment07/AlgorithmsEx02.ipynb
sraejones/phys202-2015-work
988db3174fed541a85564b7aebeb618c3ad46075
MIT
assignments/assignment07/AlgorithmsEx02.ipynb
sraejones/phys202-2015-work
988db3174fed541a85564b7aebeb618c3ad46075
MIT
Qwen/Qwen-72B
1. YES
2. YES