code javascript: Given a forest containing N trees, find the width of the widest vertical path that can be built without cutting any tree.

Task description

There are N trees $($numbered from $0$ to N$1)$ in a forest. The K$-$th tree is located at coordinates $($X$[$K$],$ Y$[$K$]).$

We want to build the widest possible vertical path, such that there is no tree on it$.$ The path must be built somewhere between a leftmost and a rightmost tree, which means that the width of the path cannot be infinite.

What is the width of the widest possible path that can be built?

Write a function:

function solution$($X$,$ Y$)$;

that, given two arrays X and Y consisting of N integers each, denoting the positions of trees, returns the width of the widest possible path that can be built.

Examples:

$1.$ Given X $=[1,8,7,3,4,1,8],$ Y$=[6,4,1,8,5,1,7],$ the function should return $3.$

$2.$ Given X $=[5,5,5,7,7,7],$ Y$=[3,4,5,1,3,7],$ the function should return $2.$

$3.$ Given X $=[6,10,1,4,3],$ Y$=[2,5,3,1,6],$ the function should return $4.$

$4.$ Given X $=[4,1,5,4],$ Y$=[4,5,1,3],$ the function should return $3.$

Write an efficient algorithm for the following assumptions:

$$ N is an integer within the range $[2.\mathrm{.}100,000]$;

$$ each element of arrays X and Y is an integer within the range $[0.\mathrm{.}1,000,000,000]$;

$$ there are no two trees with the same coordinates;

$$ a path of width at least $1$ can always be built.