# kanwei/algorithms

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 =begin rdoc A kd-tree is a binary tree that allows one to store points (of any space dimension: 2D, 3D, etc). The structure of the resulting tree makes it so that large portions of the tree are pruned during queries. One very good use of the tree is to allow nearest neighbor searching. Let's say you have a number of points in 2D space, and you want to find the nearest 2 points from a specific point: First, put the points into the tree: kdtree = Containers::KDTree.new( {0 => [4, 3], 1 => [3, 4], 2 => [-1, 2], 3 => [6, 4], 4 => [3, -5], 5 => [-2, -5] }) Then, query on the tree: puts kd.find_nearest([0, 0], 2) => [[5, 2], [9, 1]] The result is an array of [distance, id] pairs. There seems to be a bug in this version. Note that the point queried on does not have to exist in the tree. However, if it does exist, it will be returned. =end class Containers::KDTree Node = Struct.new(:id, :coords, :left, :right) # Points is a hash of id => [coord, coord] pairs. def initialize(points) raise "must pass in a hash" unless points.kind_of?(Hash) @dimensions = points[ points.keys.first ].size @root = build_tree(points.to_a) @nearest = [] end # Find k closest points to given coordinates def find_nearest(target, k_nearest) @nearest = [] nearest(@root, target, k_nearest, 0) end # points is an array def build_tree(points, depth=0) return if points.empty? axis = depth % @dimensions points.sort! { |a, b| a.last[axis] <=> b.last[axis] } median = points.size / 2 node = Node.new(points[median].first, points[median].last, nil, nil) node.left = build_tree(points[0...median], depth+1) node.right = build_tree(points[median+1..-1], depth+1) node end private :build_tree # Euclidian distanced, squared, between a node and target coords def distance2(node, target) return nil if node.nil? or target.nil? c = (node.coords[0] - target[0]) d = (node.coords[1] - target[1]) c * c + d * d end private :distance2 # Update array of nearest elements if necessary def check_nearest(nearest, node, target, k_nearest) d = distance2(node, target) if nearest.size < k_nearest || d < nearest.last[0] nearest.pop if nearest.size >= k_nearest nearest << [d, node.id] nearest.sort! { |a, b| a[0] <=> b[0] } end nearest end private :check_nearest # Recursively find nearest coordinates, going down the appropriate branch as needed def nearest(node, target, k_nearest, depth) axis = depth % @dimensions if node.left.nil? && node.right.nil? # Leaf node @nearest = check_nearest(@nearest, node, target, k_nearest) return end # Go down the nearest split if node.right.nil? || (node.left && target[axis] <= node.coords[axis]) nearer = node.left further = node.right else nearer = node.right further = node.left end nearest(nearer, target, k_nearest, depth+1) # See if we have to check other side if further if @nearest.size < k_nearest || (target[axis] - node.coords[axis])**2 < @nearest.last[0] nearest(further, target, k_nearest, depth+1) end end @nearest = check_nearest(@nearest, node, target, k_nearest) end private :nearest end