Algorithm to apply permutation in constant memory space

Question

I saw this question is a programming interview book, here I\'m simplifying the question.

Assume you have an array A of length n, and you ha

Answer 1

The simplest case is when there is only a single swap for an element to the destination index. for ex: array=abcd perm =1032. you just need two direct swaps: ab swap, cd swap

for other cases, we need to keep swapping until an element reaches its final destination. for ex: abcd, 3021 starting with first element, we swap a and d. we check if a's destination is 0 at perm[perm[0]]. its not, so we swap a with elem at array[perm[perm[0]]] which is b. again we check if a's has reached its destination at perm[perm[perm[0]]] and yes it is. so we stop.

we repeat this for each array index. Every item is moved in-place only once, so it's O(N) with O(1) storage.

def permute(array, perm):

for i in range(len(array)):
    elem, p = array[i], perm[i]

    while( p != i ): 
        elem, array[p] = array[p], elem  
        elem = array[p]
        p = perm[p]

return array