I use Python with `numpy`

.

I have a numpy array of indexes `a`

:

```
>>> a
array([[5, 7],
[12, 18],
[20, 29]])
>>> type(a)
<type 'numpy.ndarray'>
```

I have a numpy array of indexes `b`

:

```
>>> b
array([[2, 4],
[8, 11],
[33, 35]])
>>> type(b)
<type 'numpy.ndarray'>
```

I need to join an array `a`

with an array `b`

:

`a`

+ `b`

=> `[2, 4] [5, 7] [8, 11] [12, 18] [20, 29] [33, 35]`

=> `a`

and `b`

there are arrays of indexes => `[2, 18] [20, 29] [33, 35]`

( indexes `([2, 4][5, 7][8, 11][12, 18])`

go sequentially

=> `2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18`

=> `[2, 18]`

)

For this example:

```
>>> out_c
array([[2, 18],
[20, 29],
[33, 35]])
```

Can someone please suggest, **how do I get** `**out_c**`

**?**

**Update**: @Geoff suggested solution python union of multiple ranges. Whether this solution the fastest and best in large data arrays?

Best answer

## (New Answer) Using Numpy

```
ranges = np.vstack((a,b))
ranges.sort(0)
# List of non-overlapping ranges
nonoverlapping = (ranges[1:,0] - ranges[:-1,1] > 1).nonzero()[0]
# Starts are 0, and all the starts not overlapped by their predecessor
starts = np.hstack(([0], nonoverlapping + 1))
# Ends are -1 and all the ends who aren't overlapped by their successor
ends = np.hstack(( nonoverlapping, [-1]))
# Result
result = np.vstack((ranges[starts, 0], ranges[ends, 1])).T
```

**(Old answer) Using lists and sets**

```
import numpy as np
import itertools
def ranges(s):
""" Converts a list of integers into start, end pairs """
for a, b in itertools.groupby(enumerate(s), lambda(x, y): y - x):
b = list(b)
yield b[0][1], b[-1][1]
def intersect(*args):
""" Converts any number of numpy arrays containing start, end pairs
into a set of indexes """
s = set()
for start, end in np.vstack(args):
s = s | set(range(start,end+1))
return s
a = np.array([[5,7],[12, 18],[20,29]])
b = np.array([[2,4],[8,11],[33,35]])
result = np.array(list(ranges(intersect(a,b))))
```

## References

- How to find range overlap in python?
- http://docs.python.org/2/library/sets.html
- converting a list of integers into range in python
- http://docs.python.org/2/library/itertools.html#itertools.groupby