def insert(self, e: Any):
"""插入"""
x = self.search(e)
if x:
return x
x = BinNode(e, parent=self._hot, lc=None,
rc=None) # 创立红节点x:以self._hot为父节点,黑高度为-1
x.height = -1
if not self._hot:
self._root = x
else:
if e < self._hot.data:
self._hot.lc = x
else:
self._hot.rc = x
self._size += 1
self._solveDoubleRed(x)
if x:
return x
else:
return self._hot.parent
def _solveDoubleBlack(self, r: BinNode):
"""
双黑修正: 解决节点x与被其替代的节点均为黑色的问题
"""
p = r.parent if r else self._hot # r的父亲
if not p:
return
s = p.rc if r == p.lc else p.lc # r的兄弟
if RedBlack.IsBlack(s):
t = None
if BinNode.HasLChild(s) and RedBlack.IsRed(s.lc):
t = s.lc
elif BinNode.HasRChild(s) and RedBlack.IsRed(s.rc):
t = s.rc
if t is not None:
oldColor = p.color
p = super()._rotateAt(t)
if p.parent is None:
self.root = p
else:
if p.parent.data <= p.data:
p.parent.rc = p
else:
p.parent.lc = p
b = p
if BinNode.HasLChild(b):
b.lc.color = RBColor.RB_BLACK
self._updateHeight(b.lc)
if BinNode.HasRChild(b):
b.rc.color = RBColor.RB_BLACK
self._updateHeight(b.rc)
b.color = oldColor
self._updateHeight(b)
else:
s.color = RBColor.RB_RED
s.height -= 1
if RedBlack.IsRed(p):
p.color = RBColor.RB_BLACK
else:
p.height -= 1
self._solveDoubleBlack(p)
else:
s.color = RBColor.RB_BLACK
p.color = RBColor.RB_RED
t = s.lc if BinNode.IsLChild(s) else s.rc
self._hot = p
p = super()._rotateAt(t)
if p.parent is None:
self.root = p
else:
if p.parent.data <= p.data:
p.parent.rc = p
else:
p.parent.lc = p
self._solveDoubleBlack(r)
def removeAt(self, x: BinNode):
w = x # 实际被摘除的节点,初值同x
succ = None # 实际被删除节点的接替者
if not BinNode.HasLChild(x): # 若x的左子树为空,则可直接将x替换为其右子树
succ = x = x.rc
elif not BinNode.HasRChild(x): # 若x的右子树为空,对称处理 此时succ != None
succ = x = x.lc
else:
w = w.succ()
x.data, w.data = w.data, x.data
u = w.parent
succ = w.rc
if u == x:
u.rc = succ
else:
u.lc = succ
self._hot = w.parent
if succ:
succ.parent = self._hot
if self._hot.data <= succ.data:
self._hot.rc = succ
else:
self._hot.lc = succ
w.data = None
del w
return succ
def insert(self, e: Any):
"""将关键码e插入伸展树中"""
if not self.root: # 处理原树为空的退化情况
self._size += 1
self.root = BinNode(e, parent=None)
return self.root
x = self.search(e)
if x:
if e == x.data:
return self.root
self._size += 1
t = self.root
if self.root.data < e:
self.root = BinNode(e, parent=None, lc=t, rc=t.rc)
t.parent = self.root
if BinNode.HasRChild(t):
t.rc.parent = self.root
t.rc = None
else:
self.root = BinNode(e, parent=None, lc=t.lc, rc=t)
t.parent = self.root
if BinNode.HasLChild(t):
t.lc.parent = self.root
t.lc = None
super()._updateHeightAbove(t)
return self.root
def _merge(self, a: BinNode, b: BinNode):
"""合并算法: 不失一般性 npl(a)>= npl(b)"""
if not a:
return b
if not b:
return a
if npl(a) < npl(b):
a, b = b, a
a.npl = npl(a.rc) + 1 if a.rc else 1
if a.data < b.data:
a.data, b.data = b.data, a.data # 一般情况: 首先确保b不大
a.rc = self._merge(a.rc, b) # 将a的右子堆,与b合并
a.rc.parent = a # 并更新父子关系
return a # 返回合并后的堆顶
def _rotateAt(self, v: BinNode):
"""v为非空孙辈节点"""
p = v.parent
g = p.parent # 视v, p, g相对位置分四种情况
if BinNode.IsLChild(p):
if BinNode.IsLChild(v):
p.parent = g.parent # 向上联接
return self._connect34(v, p, g, v.lc, v.rc, p.rc, g.rc)
else:
v.parent = g.parent
return self._connect34(p, v, g, p.lc, v.lc, v.rc, g.rc)
else:
if BinNode.IsRchild(v):
p.parent = g.parent
return self._connect34(g, p, v, g.lc, p.lc, v.lc, v.rc)
else:
v.parent = g.parent
return self._connect34(g, v, p, g.lc, v.lc, v.rc, p.rc)
def tallerChild(x):
"""在左,右孩子中取更高者"""
if stature(x.lc) > stature(x.rc):
return x.lc
elif stature(x.lc) < stature(x.rc):
return x.rc
else:
if BinNode.IsLChild(x):
return x.lc
else:
return x.rc
def remove(self, e: Any):
"""从伸展树中删除关键码e"""
if not self.root:
return False
x = self.search(e)
if not x:
return False
if e != x.data:
return False
w = self.root
if not BinNode.HasLChild(self.root):
self.root = self.root.rc
if self.root:
self.root.parent = None
elif not BinNode.HasRChild(self.root):
self.root = self.root.lc
if self.root:
self.root.parent = None
else:
lTree = self.root.lc
lTree.parent = None
self.root.lc = None
self.root = self.root.rc
self.root.parent = None
self.search(w.data)
self.root.lc = lTree
lTree.parent = self.root
w.data = None
del w
self._size -= 1
if self.root:
super()._updateHeight(self.root)
return True
def _solveDoubleRed(self, x: BinNode):
"""双红修正"""
if BinNode.IsRoot(x):
self._root.color = RBColor.RB_BLACK
self._root.height += 1
return
p = x.parent
if RedBlack.IsBlack(p):
return
g = p.parent
u = BinNode.uncle(x)
if RedBlack.IsBlack(u):
if BinNode.IsLChild(x) == BinNode.IsLChild(p):
p.color = RBColor.RB_BLACK
else:
x.color = RBColor.RB_BLACK
g.color = RBColor.RB_RED
gg = g.parent
g = super()._rotateAt(x) # 旋转后 需要定位 顶部节点 与父节点的关系
if gg is None:
self.root = g
else:
if gg.data <= g.data:
gg.rc = g
else:
gg.lc = g
g.parent = gg
else:
p.color = RBColor.RB_BLACK
p.height += 1
u.color = RBColor.RB_BLACK
u.height += 1
if not BinNode.IsRoot(g):
g.color = RBColor.RB_RED
self._solveDoubleRed(g)
@staticmethod
def BlackHeightUpdated(x):
"""RedBlack高度更新条件"""
t1 = stature(x.lc) == stature(x.rc)
if RedBlack.IsRed(x):
t = stature(x.lc)
else:
t = stature(x.lc) + 1
t2 = (x.height == t)
return t1 and t2
if __name__ == '__main__':
# 1. 伸展树 例子
root = BinNode(36, parent=None)
# T = Splay(root=None)
# T.insert(27)
# T.insert(6)
# T.insert(58)
# T.insert(53)
# T.insert(64)
# T.insert(40)
# T.insert(46)
# print(T)
# T.insert(39)
# print(T)
# T.remove(39)
# T.remove(46)
# print(T)
def insert(self, e: Entry):
"""基于合并操作的词条插入算法"""
v = BinNode(e)
self._root = self._merge(self._root, v)
self._root.parent = None
self._size += 1
a.rc = self._merge(a.rc, b) # 将a的右子堆,与b合并
a.rc.parent = a # 并更新父子关系
return a # 返回合并后的堆顶
if __name__ == '__main__':
pq = PQ_ComplHeap(data=[17, 13, 12, 15, 10, 8, 6, 45, 28, 74])
print(pq.delMax(), pq.getMax())
print(pq.delMax(), pq.getMax())
print(pq.delMax(), pq.getMax())
print(pq.delMax(), pq.getMax())
print(pq.delMax(), pq.getMax())
print(pq.delMax(), pq.getMax())
print(pq.delMax(), pq.getMax())
print(pq.delMax(), pq.getMax())
print(pq.delMax(), pq.getMax())
print(pq.delMax())
print(pq)
lpq = PQ_LeftHeap(root=BinNode(19), data=[17, 13, 12, 15, 10, 8, 6, 45, 28, 74])
print(lpq.delMax(), lpq.getMax())
print(lpq.delMax(), lpq.getMax())
print(lpq.delMax(), lpq.getMax())
print(lpq.delMax(), lpq.getMax())
print(lpq.delMax(), lpq.getMax())
print(lpq.delMax(), lpq.getMax())
print(lpq.delMax(), lpq.getMax())
print(lpq.delMax(), lpq.getMax())
print(lpq)
def _connect34(self, a: BinNode, b: BinNode, c: BinNode, T0: BinNode,
T1: BinNode, T2: BinNode, T3: BinNode):
"""按照3+4连接3个节点和4个子树,返回重组之后局部子树根节点位置"""
a.lc = T0
if T0:
T0.parent = a
a.rc = T1
if T1:
T1.parent = a
super(BST, self)._updateHeight(a)
c.lc = T2
if T2:
T2.parent = c
c.rc = T3
if T3:
T3.parent = c
super(BST, self)._updateHeight(c)
b.lc = a
a.parent = b
b.rc = c
c.parent = b
super(BST, self)._updateHeight(b)
return b
def attachAsLChild(p: BinNode, lc: BinNode):
p.lc = lc
if lc:
lc.parent = p
@staticmethod
def tallerChild(x):
"""在左,右孩子中取更高者"""
if stature(x.lc) > stature(x.rc):
return x.lc
elif stature(x.lc) < stature(x.rc):
return x.rc
else:
if BinNode.IsLChild(x):
return x.lc
else:
return x.rc
if __name__ == '__main__':
x = BinNode(data=36, parent=None)
# T = BST(x)
# T.insert(27)
# T.insert(6)
# T.insert(58)
# T.insert(53)
# T.insert(64)
# T.insert(40)
# T.insert(46)
# T.insert(39)
# print(T)
# print(AVL.AvlBalanced(x))
# T = AVL(x)
# T.insert(27)
# print(AVL.AvlBalanced(T.root), T.root)
def attachAsRChild(p: BinNode, rc: BinNode):
p.rc = rc
if rc:
rc.parent = p
def _updateHeight(self, x: BinNode):
"""更新节点高度"""
x.height = max(stature(x.lc), stature(x.rc))
if RedBlack.IsBlack(x):
x.height += 1
return x.height
def _splay(self, v: BinNode):
"""Splay树伸展算法, 从节点v出发逐层伸展"""
if not v:
return
while v.parent and v.parent.parent:
p = v.parent
g = p.parent
gg = g.parent # 每轮之后v都以原曾祖父为父
if BinNode.IsLChild(v):
if BinNode.IsLChild(p):
Splay.attachAsLChild(g, p.rc)
Splay.attachAsLChild(p, v.rc)
Splay.attachAsRChild(p, g)
Splay.attachAsRChild(v, p)
else:
Splay.attachAsLChild(p, v.rc)
Splay.attachAsRChild(g, v.lc)
Splay.attachAsLChild(v, g)
Splay.attachAsRChild(v, p)
elif BinNode.IsRchild(p):
Splay.attachAsRChild(g, p.lc)
Splay.attachAsRChild(p, v.rc)
Splay.attachAsLChild(p, g)
Splay.attachAsLChild(v, p)
else:
Splay.attachAsRChild(p, v.lc)
Splay.attachAsLChild(g, v.rc)
Splay.attachAsRChild(v, g)
Splay.attachAsLChild(v, p)
if not gg:
v.parent = None
else:
if g == gg.lc:
Splay.attachAsLChild(gg, v)
else:
Splay.attachAsRChild(gg, v)
super()._updateHeight(g)
super()._updateHeight(p)
super()._updateHeight(v)
p = v.parent
if p: # 如果p果真非空,则额外再做一次单旋
if BinNode.IsLChild(v):
Splay.attachAsLChild(p, v.rc)
Splay.attachAsRChild(v, p)
else:
Splay.attachAsRChild(p, v.lc)
Splay.attachAsLChild(v, p)
super()._updateHeight(p)
super()._updateHeight(v)
v.parent = None
return v