left nil implies ( < left ( < left yp right nil implies ( < right ( < right where ( rdiv left left right right for all node pand root xminroot xmax decisive advantage of the radix scheme is that maintenance operations (preserving the invariants under insertion and deletionare confined to single spine of the treebecause the dividing lines have fixed values of irrespective of the -values of the inserted nodes typical operations on priority search trees are insertiondeletionfinding an element with the least (largestvalue of (or ylarger (smallerthan given limitand enumerating the points lying within given rectangle given below are procedures for inserting and enumerating they are based on the following type declarationstype node pointer to record xyintegerleftrightnode end notice that the attributes xl and xr need not be recorded in the nodes themselves they are rather computed during each search thishoweverrequires two additional parameters of the recursive procedure insert their values for the first call (with rootare xmin and xmax respectively apart from thisa search proceeds similarly to that of regular search tree if an empty node is encounteredthe element is inserted if the node to be inserted has -value smaller than the one being inspectedthe new node is exchanged with the inspected node finallythe node is inserted in the left subtreeif its -value is less than the middle value of the intervalor the right subtree otherwise procedure insert (var pnodexyxlxrinteger)var xmtinteger(adens _prioritysearchtrees *begin if nil then (*not in treeinsert*new( ) :xp :yp left :nilp right :nil elsif then (*founddon' insert*else if then : xp :xx :tt : yp :yy : endxm :(xl xrdiv if xm then insert( leftxyxlxmelse insert( rightxyxmxrend end end insert the task of enumerating all points xy lying in given rectanglei satisfying < and < is accomplished by the following procedure enumerate it calls procedure report( ,yfor each point