In-place interleaving of the two halves of a string

Question

Given a string of even size, say:

abcdef123456

How would I interleave the two halves, such that the same string would become

Answer 1

Ok lets start over. Here is what we are going to do:

def interleave(string):
    i = (len(string)/2) - 1
    j = i+1

    while(i > 0):
        k = i
        while(k < j):
            tmp = string[k]
            string[k] = string[k+1]
            string[k+1] = tmp
            k+=2 #increment by 2 since were swapping every OTHER character
        i-=1 #move lower bound by one
        j+=1 #move upper bound by one

Here is an example of what the program is going to do. We are going to use variables i,j,k. i and j will be the lower and upper bounds respectively, where k is going to be the index at which we swap.

Example

`abcd1234`

i = 3 //got this from (length(string)/2) -1

j = 4 //this is really i+1 to begin with

k = 3 //k always starts off reset to whatever i is 

swap d and 1
increment k by 2 (k = 3 + 2 = 5), since k > j we stop swapping

result `abc1d234` after the first swap

i = 3 - 1 //decrement i
j = 4 + 1 //increment j
k= 2 //reset k to i

swap c and 1, increment k (k = 2 + 2 = 4), we can swap again since k < j
swap d and 2, increment k (k = 4 + 2 = 6), k > j so we stop
//notice at EACH SWAP, the swap is occurring at index `k` and `k+1`

result `ab1c2d34`

i = 2 - 1
j = 5 + 1
k = 1

swap b and 1, increment k (k = 1 + 2 = 3), k < j so continue
swap c and 2, increment k (k = 3 + 2 = 5), k < j so continue
swap d and 3, increment k (k = 5 + 2 = 7), k > j so were done

result `a1b2c3d4`

As for proving program correctness, see this link. It explains how to prove this is correct by means of a loop invariant.

A rough proof would be the following:

1. Initialization: Prior to the first iteration of the loop we can see that i is set to (length(string)/2) - 1. We can see that i <= length(string) before we enter the loop.
2. Maintenance. After each iteration, i is decremented (i = i-1, i=i-2,...) and there must be a point at which i.
3. Termination: Since i is a decreasing sequence of positive integers, the loop invariant i > 0 will eventually equate to false and the loop will exit.