Python Array Rotation

Question

So I am implementing a block swap algorithm in python.

The algorithm I am following is this:

Initialize A = arr[0..d-1] and B = arr[d..n-1] 1) Do following until size of A is equal to size of B

a) If A is shorter, divide B into Bl and Br such that Br is of same length as A. Swap A and Br to change ABlBr into BrBlA. Now A is at its final place, so recur on pieces of B.

b) If A is longer, divide A into Al and Ar such that Al is of same length as B Swap Al and B to change AlArB into BArAl. Now B is at its final place, so recur on pieces of A.

2) Finally when A and B are of equal size, block swap them.

The same algorithm has been implemented in C on this website - Array Rotation

My python code for the same is

a = [1,2,3,4,5,6,7,8]

x = 2

n = len(a)


def rotate(a,x):
    n = len(a)

    if x == 0 or x == n:
        return a

    if x == n -x:
        print(a)
        for i in range(x):
            a[i], a[(i-x+n) % n] = a[(i-x+n) % n], a[i]
        print(a)
        return a

    if x < n-x:
        print(a)
        for i in range(x):
            a[i], a[(i-x+n) % n] = a[(i-x+n) % n], a[i]
        print(a)
        rotate(a[:n-x],x)
    else:
        print(a)
        for i in range(n-x):
            a[i], a[(i-(n-x) + n) % n] = a[(i-(n-x) + n) % n] , a[i]
        print(a)
        rotate(a[n-x:], n-x)

rotate(a,x)
print(a)

I am getting the right values at each stage but the recursive function call is not returning the expected result and I cannot seem to understand the cause. Can someone explain whats wrong with my recursion ? and what can be the possible alternative.

Answer 1

You can rotate a list in place in Python by using a deque:

>>> from collections import deque
>>> d=deque([1,2,3,4,5])
>>> d
deque([1, 2, 3, 4, 5])
>>> d.rotate(2)
>>> d
deque([4, 5, 1, 2, 3])
>>> d.rotate(-2)
>>> d
deque([1, 2, 3, 4, 5])

Or with list slices:

>>> li=[1,2,3,4,5]
>>> li[2:]+li[:2]
[3, 4, 5, 1, 2]
>>> li[-2:]+li[:-2]
[4, 5, 1, 2, 3]

Note that the sign convention is opposite with deque.rotate vs slices.

If you want a function that has the same sign convention:

def rotate(l, y=1):
   if len(l) == 0:
      return l
   y = -y % len(l)     # flip rotation direction
   return l[y:] + l[:y]

>>> rotate([1,2,3,4,5],2)
[4, 5, 1, 2, 3]
>>> rotate([1,2,3,4,5],-22)
[3, 4, 5, 1, 2]
>>> rotate('abcdefg',3)
'efgabcd'

---

For numpy, just use np.roll

>>> a
array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
>>> np.roll(a, 1)
array([9, 0, 1, 2, 3, 4, 5, 6, 7, 8])
>>> np.roll(a, -1)
array([1, 2, 3, 4, 5, 6, 7, 8, 9, 0])

Or you can use a numpy version of the same rotate above (again noting the difference in sign vs np.roll):

def rotate(a,n=1):
    if len(a) == 0:
        return a
    n = -n % len(a)     # flip rotation direction
    return np.concatenate((a[n:],a[:n]))  

Answer 2

A simple and shorthand syntax for array rotation in Python is

arr = arr[numOfRotations:]+arr[:numOfRotations]

Example:

arr = [1,2,3,4,5]
rotations = 4
then 

arr = arr[4:]+arr[:4]

gives us

[5,1,2,3,4]