k-d tree
Given a list of n points, the following algorithm will construct a balanced kd-tree containing those points.
function kdtree (list of points pointList, int depth) { if pointList is empty return nil; else { // Select axis based on depth so that axis cycles through all valid values var int axis := depth mod k; // Sort point list and choose median as pivot element select median from pointList; // Create node and construct subtrees var tree_node node; node.location := median; node.leftChild := kdtree(points in pointList before median, depth+1); node.rightChild := kdtree(points in pointList after median, depth+1); return node; } }
This algorithm implemented in the Python programming language is as follows:
class Node:pass def kdtree(pointList, depth=0): if not pointList: return # Select axis based on depth so that axis cycles through all valid values k = len(pointList[0]) # assumes all points have the same dimension axis = depth % k # Sort point list and choose median as pivot element pointList.sort(cmp=lambda x,y:cmp(x[axis],y[axis])) median = len(pointList)/2 # choose median # Create node and construct subtrees node = Node() node.location = pointList[median] node.leftChild = kdtree(pointList[0:median], depth+1) node.rightChild = kdtree(pointList[median+1:], depth+1) return node example:pointList = [(2,3), (5,4), (9,6), (4,7), (8,1), (7,2)] tree = kdtree(pointList) Balancing a kd-tree: http://en.wikipedia.org/wiki/Kd-tree