Stern-Brocot Tree(SB树)代码
时间: 2024-10-14 13:14:44 浏览: 1
Stern-Brocot Tree,也称为黄金分割树或赫伦树,是一种用于生成所有分数序列的二叉搜索树。这个树的构建规则是从两个最简单的分数1/0和0/1开始,每次添加一个新的分数,它是前两个分数的平均数,然后将结果替换这两个分数。
以下是基于Python的一个简单示例,展示了如何创建并遍历SB树:
```python
class FractionNode:
def __init__(self, numerator, denominator):
self.numerator = numerator
self.denominator = denominator
self.left = None
self.right = None
def add_node(root, node):
if root is None or node.numerator == 0:
return node
elif node.numerator > root.numerator:
root.right = add_node(root.right, node)
else:
root.left = add_node(root.left, node)
return root
# 创建初始节点
root = FractionNode(1, 0)
root.left = FractionNode(0, 1)
# 添加新节点生成Stern-Brocot序列
next_fraction = FractionNode(1, 1)
while next_fraction.numerator != 0 and next_fraction.denominator != 0:
root = add_node(root, next_fraction)
next_fraction = FractionNode(next_fraction.numerator + next_fraction.denominator, next_fraction.numerator)
# 遍历树并打印分数
def print_sequence(node):
if node is not None:
print(f"{node.numerator}/{node.denominator}")
print_sequence(node.left)
print_sequence(node.right)
print_sequence(root)
```