Find the number of robots needed to walk through the rectangular grid

[Joe]

On Saturday, 9 April 2016 18:44:20 UTC+2, Ian  wrote:
> On Sat, Apr 9, 2016 at 8:18 AM, Joe  wrote:
> > How to find the number of robots needed to walk through the rectangular grid
> > The movement of a robot in the field is divided into successive steps
> >
> > In one step a robot can move either horizontally or vertically (in one row or in one column of cells) by some number of cells
> >
> > A robot can move in one step from cell X to cell Y if and only if the distance between the centers of the cells X and Y is equal to the sum of integers contained in X and Y
> >
> > Cell X is reachable for robot A if either A is currently standing in the cell X or A can reach X after some number of steps. During the transfer the robot can choose the direction (horizontal or vertical) of each step arbitrarily
> > [![enter image description here][1]][1]
> >
> > I started implementing it by first checking the row and print the index of the Cell X and Y where the distance is equal to the sum of integers contained in X and Y
> >
> > but after coding I found it difficult to remember the index when moving vertically
> >
> >  So I thought to Build a graph where nodes are grid cells and edges are legal direct movements, then run any connected components algorithm to find which cells are reachable from each other
> >
> >
> > Can anyone implement it with graphs or queue?
> 
> I'd use a disjoint-set data structure. The number of robots needed is
> equal to the number of disjoint subsets.
> 
> https://en.wikipedia.org/wiki/Disjoint-set_data_structure

Could you post a formal solution of disjoint-set using my algorithm