Please show me a Haskell Bipartite Graph Partitioning DFS based on this psuedocode and using only Data.list and making it a module Bipartite $($bipartite$)$ where, and using the function bipartite :: $[($Char$,$ Char$)]->([$Char$],[$Char$])$Depth$-$First Search for Bipartite Graph Partitioning

BIPARTITE$($G$)$

$//$ Construct a stack for depth$-$first search.

$1S=$STACK$()$

$//$ Initialize partition for all variables $($unassigned at first$).$

for each vinV

partition $[v]=$Nil

$//$ Select any variable. Add to either partition and the stack.

$4$ S$.$push $(V[0])$

$5$ partition $[V[0]]=$ left

$//$ Depth$-$First Search for partition of any remaining vertices.

$6$ while not S$.$empty$()$

$7,$ current $=S*$ pop $()$

$8$ for each vin NEIGHBORS$[$current$]$

$9,$ if partition $[v]==$Nil

$10,$ partition $[v]=$ opposite$($partition $[$current$])$

$11$ S$.$push$($v$)$

$//$ Partitioning conflict $($graph is not bipartite$).$ Exit without an assignment.

elseif partition $[v]==$ partition$[$current$]$

return Nil

return partition

Algorithm details:

The choice of starting vertex in line $4$ is arbitrary.

The above notation implies an ordered representation for $V($not required$).$

V $($vertices$),$ NEIGHBors$($v$)$ are facet of the graph G$.$

Implementation$/$underlying representation left up to the reader.

Resulting vector identifies partition of each vertex.

Presumes partitions are "left" and "right".

Underlying representation$($s$)$ left up to the reader.