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Treap (tree + heap) in Python
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import random | |
class TreapNode(object): | |
def __init__(self, key, data): | |
self.key = key | |
self.ran = random.random() | |
self.size = 1 | |
self.cnt = 1 | |
self.data = data | |
self.left = None | |
self.right = None | |
def left_rotate(self): | |
a = self | |
b = a.right | |
a.right = b.left | |
b.left = a | |
a = b | |
b = a.left | |
b.size = b.left_size() + b.right_size() + b.cnt | |
a.size = a.left_size() + a.right_size() + a.cnt | |
return a | |
def right_rotate(self): | |
a = self | |
b = a.left | |
a.left = b.right | |
b.right = a | |
a = b | |
b = a.right | |
b.size = b.left_size() + b.right_size() + b.cnt | |
a.size = a.left_size() + a.right_size() + a.cnt | |
return a | |
def left_size(self): | |
return 0 if self.left is None else self.left.size | |
def right_size(self): | |
return 0 if self.right is None else self.right.size | |
def __repr__(self): | |
return '<node key:%s ran:%f size:%d left:%s right:%s>' % (str(self.key), self.ran, self.size, str(self.left), str(self.right)) | |
class Treap(object): | |
def __init__(self): | |
self.root = None | |
def _insert(self, node, key, data=None): | |
if node is None: | |
node = TreapNode(key, data) | |
return node | |
node.size += 1 | |
if key < node.key: | |
node.left = self._insert(node.left, key, data) | |
if node.left.ran < node.ran: | |
node = node.right_rotate() | |
elif key >= node.key: | |
node.right = self._insert(node.right, key, data) | |
if node.right.ran < node.ran: | |
node = node.left_rotate() | |
#else: | |
# node.cnt += 1 | |
return node | |
def insert(self, key, data=None): | |
self.root = self._insert(self.root, key, data) | |
def _find(self, node, key): | |
if node == None: | |
return None | |
if node.key == key: | |
return node | |
if key < node.key: | |
return self._find(node.left, key) | |
else: | |
return self._find(node.right, key) | |
def find(self, key): | |
return self._find(self.root, key) | |
def _delete(self, node, key): | |
if node is None: | |
return False | |
if node.key == key: | |
if node.left is None and node.right is None: | |
return None | |
elif node.left is None: | |
return node.right | |
elif node.right is None: | |
return node.left | |
else: | |
if node.left.ran < node.right.ran: | |
node = node.right_rotate() | |
node.right = self._delete(node.right, key) | |
else: | |
node = node.left_rotate() | |
node.left = self._delete(node.left, key) | |
elif key < node.key: | |
node.left = self._delete(node.left, key) | |
else: | |
node.right = self._delete(node.right, key) | |
node.size = node.left_size() + node.right_size() + node.cnt | |
return node | |
def delete(self, key): | |
if self.find(key) is None: return False | |
self.root = self._delete(self.root, key) | |
return True | |
def _find_kth(self, node, k): | |
if node is None: return None | |
if k <= node.left_size(): | |
return self._find_kth(node.left, k) | |
if k > node.left_size() + node.cnt: | |
return self._find_kth(node.right, k - node.left_size() - node.cnt) | |
return node | |
def find_kth(self, k): | |
if k <=0 or k > self.size(): | |
return None | |
return self._find_kth(self.root, k) | |
def size(self): | |
return 0 if self.root is None else self.root.size | |
def median(self): | |
s = self.size() | |
if s == 0: return 0 | |
result = 0 | |
if s % 2 == 1: | |
result = self.find_kth(s / 2 + 1).key | |
else: | |
result = (self.find_kth(s / 2).key + self.find_kth(s / 2 + 1).key) / 2.0 | |
if result == int(result): result = int(result) | |
return result | |
def _traverse(self, node): | |
if node == None: return | |
self._traverse(node.left) | |
print node.key, | |
self._traverse(node.right) | |
def traverse(self): | |
self._traverse(self.root) | |
def __repr__(self): | |
return str(self.root) |
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