Skip to content
Snippets Groups Projects
Commit fb122d64 authored by Martin Mareš's avatar Martin Mareš
Browse files

Geometric: Typos

parent 17300317
No related branches found
No related tags found
No related merge requests found
...@@ -153,7 +153,7 @@ with median $x$~coordinate in the root. We split the points to the two half-plan ...@@ -153,7 +153,7 @@ with median $x$~coordinate in the root. We split the points to the two half-plan
and recurse on each half-plane, which constructs the left and right subtree. and recurse on each half-plane, which constructs the left and right subtree.
During the recursion, we alternate coordinates. As the number of points in the During the recursion, we alternate coordinates. As the number of points in the
current subproblem decreases by a~factor of two in every recursive call, we obtain current subproblem decreases by a~factor of two in every recursive call, we obtain
a~tree a~tree of height $\lceil\log n\rceil$. a~tree of height $\lceil\log n\rceil$.
Time complexity of building can be analyzed using the recursion tree: since we can find a~median Time complexity of building can be analyzed using the recursion tree: since we can find a~median
of~$m$ items in time $\O(m)$, we spend $\O(n)$ time per tree level. We have $\O(\log n)$ of~$m$ items in time $\O(m)$, we spend $\O(n)$ time per tree level. We have $\O(\log n)$
...@@ -220,7 +220,7 @@ a~\em{band} in~$\R^2$ (an~open rectangle which is vertically unbounded). ...@@ -220,7 +220,7 @@ a~\em{band} in~$\R^2$ (an~open rectangle which is vertically unbounded).
For every band, we construct a~$y$-tree containing all points in the band For every band, we construct a~$y$-tree containing all points in the band
ordered by the $y$~coordinate. ordered by the $y$~coordinate.
If the $x$-tree is balanced, every node lies in $\O(log n)$ subtrees. If the $x$-tree is balanced, every node lies in $\O(\log n)$ subtrees.
So every point lies in $\O(\log n)$ bands and the whole structure takes So every point lies in $\O(\log n)$ bands and the whole structure takes
$\O(n\log n)$ space: $\O(n)$ for the $x$-tree, $\O(n\log n)$ for all $\O(n\log n)$ space: $\O(n)$ for the $x$-tree, $\O(n\log n)$ for all
$y$-trees. $y$-trees.
......
0% Loading or .
You are about to add 0 people to the discussion. Proceed with caution.
Please register or to comment