Suppose we store a relation Points $(x,y)$ in a grid file. Both attributes have range of values from $0$ to $1000.$ The partitions of this grid file happen to be uniformly spaced; for $x$ there are partitions every $20$ units, at $20,40,60,$ and so on$,$ while for $y$ the partitions are every $50$ units, at $50,100,150,$ and so on

a$.$ How many buckets $($cells in the grid file$)$ need to be searched in order to answer the following range query? $(5\mathrm{.}5pts)$

select $*$

from Points where and $y<mn>7</mn><mn>3</mn><mn>0</mn>$;

$b.Ifwe$ wish $to$ perform a nearest$-$neighbor query for a given point $(xi,yi),$ and find that there $isat$ least one other point $in$ the same grid cell where $(xi,yi)is,dowe$ need $to$ search any other cell $in$ the grid? Briefly explain why

$YE\frac{S}{N}O.(2\mathrm{.}5pts)310$ and $x<mn>4</mn><mn>0</mn><mn>0</mn>$ and $520$ and $y<mn>7</mn><mn>3</mn><mn>0</mn>$;

$b.Ifwe$ wish $to$ perform a nearest$-$neighbor query for a given point $(xi,yi),$ and find that there $isat$ least one other point $in$ the same grid cell where $(xi,yi)is,dowe$ need $to$ search any other cell $in$ the grid? Briefly explain why

$YE\frac{S}{N}O.(2\mathrm{.}5pts)$