# 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."""
    maxima = np.array([])
    
    if a[0] > a[1]:
        maxima = np.append(maxima, 0)
        
    for n in range (1, len(a) - 1):
        if a[n] > a[n-1] and a[n] > a[n+1]:
            maxima = np.append(maxima, n)
            
    if a[len(a) - 1] > a[len(a) - 2]:
        maxima = np.append(maxima, len(a) - 1)
        
    return maxima
```


```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
pi_digits_array = np.array([])
for n in range(0, 10000):
    pi_digits_array = np.append(pi_digits_array, pi_digits_str[n])
    
    #there may be a more efficient way to do this with arrays, but I couldn't
    #find it, and I only need to do it once anyway and it only takes ~2 seconds
    
pi_maxima = find_peaks(pi_digits_array)
pi_diff = np.diff(pi_maxima)

plt.hist(pi_diff, bins=15, range=(0,15), color="g")
plt.xlabel("Seperation")
```


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

d6e81fdb241a92225fe97a7e5b5f410136b05add
ipynb
Jupyter Notebook
assignments/assignment07/AlgorithmsEx02.ipynb
SJSlavin/phys202-2015-work
60311479d6a27ca4c530b057036a326e87805b61
MIT
assignments/assignment07/AlgorithmsEx02.ipynb
SJSlavin/phys202-2015-work
60311479d6a27ca4c530b057036a326e87805b61
MIT
assignments/assignment07/AlgorithmsEx02.ipynb
SJSlavin/phys202-2015-work
60311479d6a27ca4c530b057036a326e87805b61
MIT
Qwen/Qwen-72B
1. YES
2. YES