random cover of a range

[Andrei Alexandrescu]

Andrei Alexandrescu wrote:
> Given an array of length m, return a range that iterates the array in 
> random order such that the entire array is visited without going through 
> the same element more than once. Consume minimal amounts of memory and 
> time. Baseline solution: allocate an array of indices, shuffle it, then 
> follow indices stored in the array.

Ok, here's something that should work.

Start with array a of length a.length, allocate a bitmap with one bit 
per element in the map. Also the number of unselected elements left in 
the array is kept, call it k.

To implement next():

1. Walk from the beginning of the array to the first unselected element.

2. Roll a fair dice with k faces. If the dice chooses a specific face, 
choose that first unselected element. Otherwise continue.

3. Continue walking until the next unselected element.

4. Roll a fair dice with k-1 faces. If the dice chooses a specific face, 
choose that unselected element. Otherwise continue from step 3 using 
dices with k-1, k-2, ..., 1 faces.

This has O(n log n) complexity. There is one obvious optimization: 
eliminate the first selected elements so we don't need to walk over them 
at each iteration. It's unclear to me how this affects complexity.


Andrei