private void rshelp(kdnode rtint[pointint radiusint levif (rt =nullreturnint[rtkey rt key()if (incircle(pointradiusrtkey)system out println(rt element())if (rtkey[lev(point[levradius)rshelp(rt left()pointradius(lev+ )% )if (rtkey[lev(point[levradius)rshelp(rt right()pointradius(lev+ )% )figure the - tree region search method tains more than single data pointthen the region is split into four equal quadrants the corresponding pr quadtree then contains an internal node and four subtreeseach subtree representing single quadrant of the regionwhich might in turn be split into subquadrants each internal node of pr quadtree represents single split of the two-dimensional region the four quadrants of the region (or equivalentlythe corresponding subtreesare designated (in ordernwneswand se each quadrant containing more than single point would in turn be recursively divided into subquadrants until each leaf of the corresponding pr quadtree contains at most one point for exampleconsider the region of figure (aand the corresponding pr quadtree in figure (bthe decomposition process demands fixed key range in this examplethe region is assumed to be of size note that the internal nodes of the pr quadtree are used solely to indicate decomposition of the regioninternal nodes do not store data records because the decomposition lines are predetermined ( ekey-space decomposition is used)the pr quadtree is trie search for record matching point in the pr quadtree is straightforward beginning at the rootwe continuously branch to the quadrant that contains until our search reaches leaf node if the root is leafthen just check to see if the node' data record matches point if the root is an internal nodeproceed to the child that contains the search coordinate for examplethe nw quadrant of figure contains points whose and values each fall in the range to the ne quadrant contains points whose value falls in the range to and whose value falls in the range to if the root' child is leaf nodethen that child is checked to see if has been found if the child is another internal nodethe search process continues through the tree until leaf node is found if this leaf node stores record whose position matches then the query is successfulotherwise is not in the tree