# Fill the steps (randomly)!

This is Hole-9 from The Autumn Tournament of APL CodeGolf. I am the original author of the problem there, and thus allowed to re-post it here.

Given a simple (rectangular, non-jagged) Boolean array (of one or more dimensions) return a list of thusly shaped arrays where the first array is identical to the input and the last is all-true. All intermediary steps must have one more truth than its neighbor to the left (but otherwise be identical). For each step, the bit that is changed must be pseudo-randomly chosen (and you may take a seed if necessary).

### Examples

[0] gives [[0],[1]]

[[0]] gives [[[0]],[[1]]]

[[[1,1,1],[1,1,1],[1,1,1]],[[1,1,1],[1,1,1],[1,1,1]],[[1,1,1],[1,1,1],[1,1,1]]] gives [[[[1,1,1],[1,1,1],[1,1,1]],[[1,1,1],[1,1,1],[1,1,1]],[[1,1,1],[1,1,1],[1,1,1]]]]

The following examples' results may of course vary due to randomness; these are just examples of valid output:

[0,1,0,0] gives [[0,1,0,0],[1,1,0,0],[1,1,0,1],[1,1,1,1]]

[[0,1,0],[0,0,1]] gives [[[0,1,0],[0,0,1]],[[1,1,0],[0,0,1]],[[1,1,0],[0,1,1]],[[1,1,1],[0,1,1]],[[1,1,1],[1,1,1]]]

[[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0]] gives [[[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0]],[[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0]],[[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0],[1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0]],[[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0],[1,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0]],[[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0],[1,1,1,0,0,0,0,0],[0,0,0,1,0,0,0,0]],[[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0],[1,1,1,0,0,0,0,0],[0,0,0,1,0,0,0,0]],[[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0],[1,1,1,0,0,0,0,0],[0,0,0,1,0,0,0,0]],[[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0],[0,1,0,0,0,0,1,0],[1,1,1,0,0,0,0,0],[0,0,0,1,0,0,0,0]],[[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,1,0,1,0],[0,1,0,0,0,0,1,0],[1,1,1,0,0,0,0,0],[0,0,0,1,0,0,0,0]],[[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,0,1,1,0],[0,0,0,0,1,0,0,0],[0,0,0,0,1,0,1,0],[0,1,0,0,0,0,1,0],[1,1,1,0,0,0,0,0],[0,0,0,1,0,0,0,0]],[[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,0,1,1,0],[0,0,0,0,1,0,0,0],[0,0,0,0,1,0,1,0],[0,1,0,0,0,0,1,0],[1,1,1,0,0,0,0,0],[0,0,0,1,0,0,0,0]],[[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,0,1,1,0],[0,0,0,0,1,0,0,0],[0,0,0,0,1,0,1,0],[0,1,0,0,1,0,1,0],[1,1,1,0,0,0,0,0],[0,0,0,1,0,0,0,0]],[[1,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,0,1,1,0],[0,0,0,0,1,0,0,0],[0,0,0,0,1,0,1,0],[0,1,0,0,1,0,1,0],[1,1,1,0,0,0,0,0],[0,0,0,1,0,0,0,0]],[[1,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,0,1,1,0],[0,0,0,0,1,0,0,0],[1,0,0,0,1,0,1,0],[0,1,0,0,1,0,1,0],[1,1,1,0,0,0,0,0],[0,0,0,1,0,0,0,0]],[[1,0,1,0,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,1,0],[0,0,0,0,1,0,0,0],[1,0,0,0,1,0,1,0],[0,1,0,0,1,0,1,0],[1,1,1,0,0,0,0,0],[0,0,0,1,0,0,0,0]],[[1,0,1,0,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,1,0],[0,0,0,0,1,0,0,0],[1,0,0,0,1,0,1,0],[0,1,0,0,1,0,1,0],[1,1,1,0,0,0,0,1],[0,0,0,1,0,0,0,0]],[[1,0,1,0,0,0,0,0],[0,0,0,0,1,0,1,0],[0,0,0,0,0,1,1,0],[0,0,0,0,1,0,0,0],[1,0,0,0,1,0,1,0],[0,1,0,0,1,0,1,0],[1,1,1,0,0,0,0,1],[0,0,0,1,0,0,0,0]],[[1,0,1,0,0,0,0,0],[0,0,0,0,1,0,1,0],[0,0,0,0,0,1,1,0],[0,0,0,0,1,0,0,0],[1,0,0,0,1,0,1,0],[0,1,0,0,1,0,1,1],[1,1,1,0,0,0,0,1],[0,0,0,1,0,0,0,0]],[[1,0,1,0,0,0,0,0],[0,0,0,1,1,0,1,0],[0,0,0,0,0,1,1,0],[0,0,0,0,1,0,0,0],[1,0,0,0,1,0,1,0],[0,1,0,0,1,0,1,1],[1,1,1,0,0,0,0,1],[0,0,0,1,0,0,0,0]],[[1,0,1,0,0,0,0,0],[0,0,1,1,1,0,1,0],[0,0,0,0,0,1,1,0],[0,0,0,0,1,0,0,0],[1,0,0,0,1,0,1,0],[0,1,0,0,1,0,1,1],[1,1,1,0,0,0,0,1],[0,0,0,1,0,0,0,0]],[[1,0,1,0,0,0,0,0],[0,0,1,1,1,0,1,0],[0,0,0,0,0,1,1,0],[0,0,0,0,1,0,0,0],[1,0,0,0,1,0,1,0],[0,1,0,0,1,0,1,1],[1,1,1,0,0,0,0,1],[0,1,0,1,0,0,0,0]],[[1,0,1,0,0,0,0,0],[0,0,1,1,1,0,1,0],[0,0,0,0,0,1,1,0],[0,0,0,0,1,0,0,1],[1,0,0,0,1,0,1,0],[0,1,0,0,1,0,1,1],[1,1,1,0,0,0,0,1],[0,1,0,1,0,0,0,0]],[[1,0,1,0,0,0,0,0],[0,0,1,1,1,0,1,0],[0,0,0,0,0,1,1,0],[0,0,0,0,1,0,0,1],[1,0,0,0,1,0,1,0],[0,1,0,0,1,0,1,1],[1,1,1,0,1,0,0,1],[0,1,0,1,0,0,0,0]],[[1,0,1,0,0,0,0,0],[0,0,1,1,1,0,1,0],[0,0,0,0,1,1,1,0],[0,0,0,0,1,0,0,1],[1,0,0,0,1,0,1,0],[0,1,0,0,1,0,1,1],[1,1,1,0,1,0,0,1],[0,1,0,1,0,0,0,0]],[[1,0,1,0,0,0,0,0],[0,0,1,1,1,0,1,0],[0,0,0,0,1,1,1,1],[0,0,0,0,1,0,0,1],[1,0,0,0,1,0,1,0],[0,1,0,0,1,0,1,1],[1,1,1,0,1,0,0,1],[0,1,0,1,0,0,0,0]],[[1,0,1,0,0,0,0,0],[0,0,1,1,1,0,1,0],[0,0,0,0,1,1,1,1],[0,0,0,0,1,0,0,1],[1,0,0,0,1,0,1,0],[0,1,0,0,1,0,1,1],[1,1,1,0,1,0,1,1],[0,1,0,1,0,0,0,0]],[[1,0,1,1,0,0,0,0],[0,0,1,1,1,0,1,0],[0,0,0,0,1,1,1,1],[0,0,0,0,1,0,0,1],[1,0,0,0,1,0,1,0],[0,1,0,0,1,0,1,1],[1,1,1,0,1,0,1,1],[0,1,0,1,0,0,0,0]],[[1,0,1,1,0,0,0,0],[0,0,1,1,1,0,1,0],[0,0,0,0,1,1,1,1],[0,0,1,0,1,0,0,1],[1,0,0,0,1,0,1,0],[0,1,0,0,1,0,1,1],[1,1,1,0,1,0,1,1],[0,1,0,1,0,0,0,0]],[[1,0,1,1,0,0,0,0],[0,0,1,1,1,0,1,0],[0,0,0,0,1,1,1,1],[0,0,1,0,1,0,0,1],[1,0,0,0,1,0,1,0],[0,1,0,0,1,0,1,1],[1,1,1,0,1,1,1,1],[0,1,0,1,0,0,0,0]],[[1,0,1,1,0,0,0,0],[0,0,1,1,1,0,1,0],[0,0,0,0,1,1,1,1],[0,0,1,0,1,0,0,1],[1,1,0,0,1,0,1,0],[0,1,0,0,1,0,1,1],[1,1,1,0,1,1,1,1],[0,1,0,1,0,0,0,0]],[[1,0,1,1,0,1,0,0],[0,0,1,1,1,0,1,0],[0,0,0,0,1,1,1,1],[0,0,1,0,1,0,0,1],[1,1,0,0,1,0,1,0],[0,1,0,0,1,0,1,1],[1,1,1,0,1,1,1,1],[0,1,0,1,0,0,0,0]],[[1,0,1,1,0,1,0,0],[0,1,1,1,1,0,1,0],[0,0,0,0,1,1,1,1],[0,0,1,0,1,0,0,1],[1,1,0,0,1,0,1,0],[0,1,0,0,1,0,1,1],[1,1,1,0,1,1,1,1],[0,1,0,1,0,0,0,0]],[[1,0,1,1,0,1,0,0],[0,1,1,1,1,0,1,0],[0,0,0,0,1,1,1,1],[0,0,1,0,1,0,0,1],[1,1,0,0,1,0,1,0],[0,1,0,0,1,0,1,1],[1,1,1,0,1,1,1,1],[0,1,0,1,0,0,0,1]],[[1,0,1,1,0,1,0,0],[0,1,1,1,1,0,1,1],[0,0,0,0,1,1,1,1],[0,0,1,0,1,0,0,1],[1,1,0,0,1,0,1,0],[0,1,0,0,1,0,1,1],[1,1,1,0,1,1,1,1],[0,1,0,1,0,0,0,1]],[[1,0,1,1,0,1,0,0],[0,1,1,1,1,0,1,1],[0,0,0,0,1,1,1,1],[0,0,1,0,1,0,0,1],[1,1,0,0,1,0,1,0],[0,1,1,0,1,0,1,1],[1,1,1,0,1,1,1,1],[0,1,0,1,0,0,0,1]],[[1,0,1,1,0,1,0,0],[0,1,1,1,1,0,1,1],[0,0,0,0,1,1,1,1],[0,0,1,0,1,0,0,1],[1,1,0,0,1,0,1,0],[0,1,1,0,1,0,1,1],[1,1,1,0,1,1,1,1],[0,1,0,1,1,0,0,1]],[[1,0,1,1,0,1,0,0],[0,1,1,1,1,0,1,1],[0,0,0,0,1,1,1,1],[0,0,1,0,1,0,0,1],[1,1,0,0,1,0,1,0],[1,1,1,0,1,0,1,1],[1,1,1,0,1,1,1,1],[0,1,0,1,1,0,0,1]],[[1,1,1,1,0,1,0,0],[0,1,1,1,1,0,1,1],[0,0,0,0,1,1,1,1],[0,0,1,0,1,0,0,1],[1,1,0,0,1,0,1,0],[1,1,1,0,1,0,1,1],[1,1,1,0,1,1,1,1],[0,1,0,1,1,0,0,1]],[[1,1,1,1,0,1,1,0],[0,1,1,1,1,0,1,1],[0,0,0,0,1,1,1,1],[0,0,1,0,1,0,0,1],[1,1,0,0,1,0,1,0],[1,1,1,0,1,0,1,1],[1,1,1,0,1,1,1,1],[0,1,0,1,1,0,0,1]],[[1,1,1,1,0,1,1,0],[0,1,1,1,1,0,1,1],[0,0,0,0,1,1,1,1],[0,0,1,0,1,0,0,1],[1,1,0,0,1,0,1,0],[1,1,1,0,1,0,1,1],[1,1,1,0,1,1,1,1],[0,1,1,1,1,0,0,1]],[[1,1,1,1,0,1,1,0],[0,1,1,1,1,0,1,1],[0,1,0,0,1,1,1,1],[0,0,1,0,1,0,0,1],[1,1,0,0,1,0,1,0],[1,1,1,0,1,0,1,1],[1,1,1,0,1,1,1,1],[0,1,1,1,1,0,0,1]],[[1,1,1,1,0,1,1,0],[0,1,1,1,1,0,1,1],[1,1,0,0,1,1,1,1],[0,0,1,0,1,0,0,1],[1,1,0,0,1,0,1,0],[1,1,1,0,1,0,1,1],[1,1,1,0,1,1,1,1],[0,1,1,1,1,0,0,1]],[[1,1,1,1,0,1,1,0],[0,1,1,1,1,0,1,1],[1,1,0,0,1,1,1,1],[0,0,1,0,1,0,0,1],[1,1,0,0,1,0,1,1],[1,1,1,0,1,0,1,1],[1,1,1,0,1,1,1,1],[0,1,1,1,1,0,0,1]],[[1,1,1,1,0,1,1,0],[0,1,1,1,1,0,1,1],[1,1,0,0,1,1,1,1],[0,1,1,0,1,0,0,1],[1,1,0,0,1,0,1,1],[1,1,1,0,1,0,1,1],[1,1,1,0,1,1,1,1],[0,1,1,1,1,0,0,1]],[[1,1,1,1,0,1,1,0],[0,1,1,1,1,0,1,1],[1,1,0,0,1,1,1,1],[0,1,1,0,1,0,0,1],[1,1,0,0,1,1,1,1],[1,1,1,0,1,0,1,1],[1,1,1,0,1,1,1,1],[0,1,1,1,1,0,0,1]],[[1,1,1,1,1,1,1,0],[0,1,1,1,1,0,1,1],[1,1,0,0,1,1,1,1],[0,1,1,0,1,0,0,1],[1,1,0,0,1,1,1,1],[1,1,1,0,1,0,1,1],[1,1,1,0,1,1,1,1],[0,1,1,1,1,0,0,1]],[[1,1,1,1,1,1,1,0],[0,1,1,1,1,0,1,1],[1,1,1,0,1,1,1,1],[0,1,1,0,1,0,0,1],[1,1,0,0,1,1,1,1],[1,1,1,0,1,0,1,1],[1,1,1,0,1,1,1,1],[0,1,1,1,1,0,0,1]],[[1,1,1,1,1,1,1,0],[0,1,1,1,1,0,1,1],[1,1,1,0,1,1,1,1],[0,1,1,0,1,0,0,1],[1,1,0,0,1,1,1,1],[1,1,1,0,1,0,1,1],[1,1,1,0,1,1,1,1],[0,1,1,1,1,0,1,1]],[[1,1,1,1,1,1,1,0],[0,1,1,1,1,0,1,1],[1,1,1,0,1,1,1,1],[0,1,1,1,1,0,0,1],[1,1,0,0,1,1,1,1],[1,1,1,0,1,0,1,1],[1,1,1,0,1,1,1,1],[0,1,1,1,1,0,1,1]],[[1,1,1,1,1,1,1,0],[0,1,1,1,1,1,1,1],[1,1,1,0,1,1,1,1],[0,1,1,1,1,0,0,1],[1,1,0,0,1,1,1,1],[1,1,1,0,1,0,1,1],[1,1,1,0,1,1,1,1],[0,1,1,1,1,0,1,1]],[[1,1,1,1,1,1,1,1],[0,1,1,1,1,1,1,1],[1,1,1,0,1,1,1,1],[0,1,1,1,1,0,0,1],[1,1,0,0,1,1,1,1],[1,1,1,0,1,0,1,1],[1,1,1,0,1,1,1,1],[0,1,1,1,1,0,1,1]],[[1,1,1,1,1,1,1,1],[0,1,1,1,1,1,1,1],[1,1,1,0,1,1,1,1],[0,1,1,1,1,0,0,1],[1,1,0,0,1,1,1,1],[1,1,1,0,1,1,1,1],[1,1,1,0,1,1,1,1],[0,1,1,1,1,0,1,1]],[[1,1,1,1,1,1,1,1],[0,1,1,1,1,1,1,1],[1,1,1,0,1,1,1,1],[0,1,1,1,1,0,0,1],[1,1,0,1,1,1,1,1],[1,1,1,0,1,1,1,1],[1,1,1,0,1,1,1,1],[0,1,1,1,1,0,1,1]],[[1,1,1,1,1,1,1,1],[0,1,1,1,1,1,1,1],[1,1,1,0,1,1,1,1],[0,1,1,1,1,0,1,1],[1,1,0,1,1,1,1,1],[1,1,1,0,1,1,1,1],[1,1,1,0,1,1,1,1],[0,1,1,1,1,0,1,1]],[[1,1,1,1,1,1,1,1],[0,1,1,1,1,1,1,1],[1,1,1,0,1,1,1,1],[0,1,1,1,1,0,1,1],[1,1,0,1,1,1,1,1],[1,1,1,0,1,1,1,1],[1,1,1,0,1,1,1,1],[0,1,1,1,1,1,1,1]],[[1,1,1,1,1,1,1,1],[0,1,1,1,1,1,1,1],[1,1,1,0,1,1,1,1],[1,1,1,1,1,0,1,1],[1,1,0,1,1,1,1,1],[1,1,1,0,1,1,1,1],[1,1,1,0,1,1,1,1],[0,1,1,1,1,1,1,1]],[[1,1,1,1,1,1,1,1],[0,1,1,1,1,1,1,1],[1,1,1,0,1,1,1,1],[1,1,1,1,1,0,1,1],[1,1,0,1,1,1,1,1],[1,1,1,0,1,1,1,1],[1,1,1,1,1,1,1,1],[0,1,1,1,1,1,1,1]],[[1,1,1,1,1,1,1,1],[0,1,1,1,1,1,1,1],[1,1,1,0,1,1,1,1],[1,1,1,1,1,0,1,1],[1,1,1,1,1,1,1,1],[1,1,1,0,1,1,1,1],[1,1,1,1,1,1,1,1],[0,1,1,1,1,1,1,1]],[[1,1,1,1,1,1,1,1],[0,1,1,1,1,1,1,1],[1,1,1,0,1,1,1,1],[1,1,1,1,1,0,1,1],[1,1,1,1,1,1,1,1],[1,1,1,0,1,1,1,1],[1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1]],[[1,1,1,1,1,1,1,1],[0,1,1,1,1,1,1,1],[1,1,1,0,1,1,1,1],[1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1],[1,1,1,0,1,1,1,1],[1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1]],[[1,1,1,1,1,1,1,1],[0,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1],[1,1,1,0,1,1,1,1],[1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1]],[[1,1,1,1,1,1,1,1],[0,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1]],[[1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1]]]

• These challenges have really made me start to question the decisions the R/S developers made... Oct 19 '17 at 13:56
• @Giuseppe R/S developers?
Oct 20 '17 at 7:17
• R (and S-plus) is an implementation of S, so a lot of the base R functions operate the way that S specifies them, or are maintained to allow compatibility with S (or worse, S-plus). I'm not sure who to blame for some of the unexpected behaviors I've encountered while attempting to solve some of these challenges! Oct 21 '17 at 22:17

# Jelly, 12 bytes

F¬0TX$¦ÐĿ¬ṁ€  Try it online! ### How it works F¬0TX$¦ÐĿ¬ṁ€  Main link. Argument: A (array)

F             Flatten A.
¬            Negate all Booleans in the result.
DĿ     Repeatedly call the link to the left until the results are no longer
unique. Yield the array of all unique results.
¦         Sparse application:
TX$Pseudo-randomly select an index of a 1. 0 Replace the element at that index with 0. ¬ Once again negate all Booleans. ṁ€ Shape each flat array in the result like A.  # Python 2, 197 bytes import random,copy A=[input()] while"0"inA[-1]: A+=copy.deepcopy(A[-1]), while~0: j="A[-1]" while[]<eval(j):j+="[%s]"%random.randint(0,~-len(eval(j))) if eval(j)<1:exec"%s=1"%j;break print A  Try it online! ## Wolfram Language (Mathematica), 61 bytes FoldList[ReplacePart[#,#2->1]&,#,RandomSample@Position[#,0]]&  Try it online! ### Explanation Position[#,0]  Find all positions of 0s in the nested array. RandomSample@...  Shuffle the list of positions. FoldList[...&,#,...]  Fold the function on the left over the shuffled list of positions, using the input as the starting value, and collect all steps of the fold operation in the result. ReplacePart[#,#2->1]  Set the value at the given position to 1. # R, 9382 74 bytes function(a)Reduce(function(x,y){x[y]=T;x},sample(as.list(which(!a))),a,,T)  Try it online! Takes an R logical array and returns a list of logical arrays. The nasty sample(as.list(which(!a))) is to prevent an edge case in sample. When a contains exactly one FALSE value at index i, sample returns a random permutation of 1:i rather than a random sample of size 1 containing only the value i, so I used as.list to prevent which(!a) from being numeric. The R documentation for sample is mildly apologetic about this behavior: If x has length 1, is numeric (in the sense of is.numeric) and x >= 1, sampling via sample takes place from 1:x. Note that this convenience feature may lead to undesired behaviour when x is of varying length in calls such as sample(x). # Perl 5, 78 + 1 (-p) = 79 bytes while(@a=/0/g){$o.="$_,";for$i(0..rand@a){/0/g}substr$_,-1+pos,1,1}$_="[$o$_]"


Try it online!

Array? What array? It's just a long string.

F¬TṬ€$$o€ṁ€µXÐĿṖṖ  Try it online! Probably could be shorter # Explanation F¬TṬ€$$o€$ṁ€µX$ÐĿṖṖ  Main Link
ÐĿ    While results are unique:
F                    Flatten the array
              3 links will form a monad
¬                   Logical NOT on each element
T                  Find indices of 1s (0s in the original)
€                For each 0 in the original
Ṭ                 Make an array of all 0s containing one 1 there
$2 links will form a monad € For each of the mask arrays o Vectorizing logical OR it with the original (flat) array € For each of these subarrays ṁ Reshape it to the original array's shape µ Start a new monadic chain, using the list of possible next steps as the argument$      2 links will form a monad
X       Pick a random element
ṖṖ  Remove the last two elements (0 and '' which are selected by X when the list is empty)


# Python 2, 134132 129 bytes

from random import*
a=input()
print a;l=list(a)
while'0'in l:l[choice([i for i,c in enumerate(l)if'0'==c])]='1';print''.join(l)


Try it online!