chap advanced tree structures figure searching in the - treeof figure (athe - tree decomposition for -unit region containing seven data points (bthe - tree for the region of (athe circle thussearch proceeds to the node containing record againd is outside the search circle because no record in ' right subtree could be within the search circle thusonly ' left subtree need be searched this leads to comparing record ' coordinates against the search circle record falls outside the search circleand processing is complete so we see that we only search subtrees whose rectangles fall within the search circle figure shows an implementation for the region search method when node is visitedfunction incircle is used to check the euclidean distance between the node' record and the query point it is not enough to simply check that the differences between the xand -coordinates are each less than the query distances because the the record could still be outside the search circleas illustrated by figure the pr quadtree in the point-region quadtree (hereafter referred to as the pr quadtreeeach node either has exactly four children or is leaf that isthe pr quadtree is full fourway branching ( -arytree in shape the pr quadtree represents collection of data points in two dimensions by decomposing the region containing the data points into four equal quadrantssubquadrantsand so onuntil no leaf node contains more than single point in other wordsif region contains zero or one data pointsthen it is represented by pr quadtree consisting of single leaf node if the region con