advanced data structures and implementation figure three cases when is left child and has two black children treaps our last type of binary search treeknown as the treapis probably the simplest of all like the skip listit uses random numbers and gives (log nexpected time behavior for any input searching time is identical to an unbalanced binary search tree (and thus slower than balanced search trees)while insertion time is only slightly slower than recursive unbalanced binary search tree implementation although deletion is much slowerit is still (log nexpected time the treap is so simple that we can describe it without picture each node in the tree stores an itema left and right pointerand priority that is randomly assigned when the node is created treap is binary search tree with the property that the node priorities satisfy heap orderany node' priority must be at least as large as its parent' collection of distinct items each of which has distinct priority can only be represented by one treap this is easily deduced by inductionsince the node with the lowest priority must be the root consequentlythe tree is formed on the basis of the npossible arrangements of priority instead of the nitem orderings the node declarations are straightforwardrequiring only the addition of the priority data member the sentinel nullnode will have priority of as shown in figure