Algorithm: RobotCoinCollection$($C$[1..$n$,1..$m$])$

F$[1,1]$ C$[1,1]$; for j $2$ to m do F$[1,$ j$]$ F$[1,$ j $1]+$ C$[1,$ j$]$;

for i $2$ to n do

F$[$i$,1]$ F$[$i $1,1]+$ C$[$i$,1]$;

for j $2$ to m do

F$[$i$,$ j$]$ max$($F$[$i $1,$ j$],$ F$[$i$,$ j $1])+$ C$[$i$,$ j$]$;

return F$[$n$,$ m$]$

$($i$)$ What are the time and space complexities of this algorithm? $(4$ Marks$)$

$($ii$)$ Consider the following coin setup, with robot in the cell C$[1,1]$