From ca89605db547f55dc598041eac0c75ecef4623eb Mon Sep 17 00:00:00 2001 From: Bruno BELANYI Date: Sat, 20 Jul 2024 19:23:13 +0100 Subject: [PATCH] posts: treap: add insertion --- content/posts/2024-07-20-treap/index.md | 60 +++++++++++++++++++++++++ 1 file changed, 60 insertions(+) diff --git a/content/posts/2024-07-20-treap/index.md b/content/posts/2024-07-20-treap/index.md index e9578a7..cbca5fe 100644 --- a/content/posts/2024-07-20-treap/index.md +++ b/content/posts/2024-07-20-treap/index.md @@ -97,3 +97,63 @@ def get(self, key: K) -> T | None: node = node.left return None ``` + +### Insertion + +To insert a new `key` into the tree, we identify which leaf position it should +be inserted at. We then generate the node's priority, insert it at this +position, and rotate the node upwards until the heap property is respected. + +```python +type ChildField = Literal["left, right"] + +def insert(self, key: K, value: V) -> bool: + # Empty treap base-case + if self._root is None: + self._root = Node(key, value) + # Signal that we're not overwriting the value + return False + # Keep track of the parent chain for rotation after insertion + parents = [] + node = self._root + while node is not None: + # Insert a pre-existing key + if node.key == key: + node.value = value + return True + # Go down the tree, keep track of the path through the tree + field = "left" if key < node.key else "right" + parents.append((node, field)) + node = getattr(node, field) + # Key wasn't found, we're inserting a new node + child = Node(key, value) + parent, field = parents[-1] + setattr(parent, field, child) + # Rotate the new node up until we respect the decreasing priority property + self._rotate_up(child, parents) + # Key wasn't found, signal that we inserted a new node + return False + +def _rotate_up( + self, + node: Node[K, V], + parents: list[tuple[Node[K, V], ChildField]], +) -> None: + while parents: + parent, field = parents.pop() + # If the parent has higher priority, we're done rotating + if parent.priority >= node.priority: + break + # Check for grand-parent/root of tree edge-case + if parents: + # Update grand-parent to point to the new rotated node + grand_parent, field = parents[-1] + setattr(grand_parent, field, node) + else: + # Point the root to the new rotated node + self._root = node + other_field = "left" if field == "right" else "right" + # Rotate the node up + setattr(parent, field, getattr(node, other_field)) + setattr(node, other_field, parent) +```