節點定義
class Node(object):
def __init__(self, left_child, right_child, value):
self._left_child = left_child
self._right_child = right_child
self._value = value
@property
def left_child(self):
return self._left_child
@property
def right_child(self):
return self._right_child
@left_child.setter
def left_child(self, value):
self._left_child = value
@right_child.setter
def right_child(self, value):
self._right_child = value
@property
def value(self):
return self._value
@value.setter
def value(self, value):
self._value = value
二叉樹定義
class Tree(object):
def __init__(self, value):
self._root = Node(None, None, value=value)
@property
def root(self):
return self._root
先序遍歷
遞歸方式
'''
先序遍歷，遞歸方式
'''
def preoder(root):
if not isinstance(root, Node):
return None
preorder_res = []
if root:
preorder_res.append(root.value)
preorder_res += preoder(root.left_child)
preorder_res += preoder(root.right_child)
return preorder_res
非遞歸方式
'''
先序遍歷，非遞歸方式
'''
def pre_order_not_recursion(root):
if not isinstance(root, Node):
return None
stack = [root]
result = []
while stack:
node = stack.pop(-1)
if node:
result.append(node.value)
stack.append(node.right_child)
stack.append(node.left_child)
return result
中序遍歷
遞歸方式
'''
中序遍歷，遞歸方式
'''
def middle_order(root):
if not isinstance(root, Node):
return None
middle_res = []
if root:
middle_res += middle_order(root.left_child)
middle_res.append(root.value)
middle_res += middle_order(root.right_child)
return middle_res
非遞歸方式
'''
中序遍歷，非遞歸方式
'''
def middle_order_bot_recursion(root):
if not isinstance(root, Node):
return None
result = []
stack = [root.right_child, root.value, root.left_child]
while stack:
temp = stack.pop(-1)
if temp:
if isinstance(temp, Node):
stack.append(temp.right_child)
stack.append(temp.value)
stack.append(temp.left_child)
else:
result.append(temp)
return result
後序遍歷
遞歸方式
'''
後序遍歷，遞歸方式
'''
def post_order(root):
if not isinstance(root, Node):
return None
post_res = []
if root:
post_res += post_order(root.left_child)
post_res += post_order(root.right_child)
post_res.append(root.value)
return post_res
非遞歸方式
'''
後序遍歷，非遞歸方式
'''
def post_order_not_recursion(root):
if not isinstance(root, Node):
return None
stack = [root.value, root.right_child, root.left_child]
result = []
while stack:
temp_node = stack.pop(-1)
if temp_node:
if isinstance(temp_node, Node):
stack.append(temp_node.value)
stack.append(temp_node.right_child)
stack.append(temp_node.left_child)
else:
result.append(temp_node)
return result
分層遍歷
'''
分層遍歷，使用隊列實現
'''
def layer_order(root):
if not isinstance(root, Node):
return None
queue = [root.value, root.left_child, root.right_child]
result = []
while queue:
temp = queue.pop(0)
if temp:
if isinstance(temp, Node):
queue.append(temp.value)
queue.append(temp.left_child)
queue.append(temp.right_child)
else:
result.append(temp)
return result
計算二叉樹結點個數
'''
計算二叉樹結點個數，遞歸方式
NodeCount(root) = NodeCount(root.left_child) + NodeCount(root.right_child)
'''
def node_count(root):
if root and not isinstance(root, Node):
return None
if root:
return node_count(root.left_child) + node_count(root.right_child) + 1
else:
return 0
'''
計算二叉樹結點個數，非遞歸方式
借用分層遍歷計算
'''
def node_count_not_recursion(root):
if root and not isinstance(root, Node):
return None
return len(layer_order(root))
計算二叉樹深度
'''
計算二叉樹深度，遞歸方式
tree_deep(root) = 1 + max(tree_deep(root.left_child), tree_deep(root.right_child))
'''
def tree_deep(root):
if root and not isinstance(root, Node):
return None
if root:
return 1 + max(tree_deep(root.left_child), tree_deep(root.right_child))
else:
return 0
'''
計算二叉樹深度，非遞歸方法
同理參考分層遍歷的思想
'''
def tree_deep_not_recursion(root):
if root and not isinstance(root, Node):
return None
result = 0
queue = [(root, 1)]
while queue:
temp_node, temp_layer = queue.pop(0)
if temp_node:
queue.append((temp_node.left_child, temp_layer+1))
queue.append((temp_node.right_child, temp_layer+1))
result = temp_layer + 1
return result-1
計算二叉樹第k層節點個數
'''
計算二叉樹第k層節點個數，遞歸方式
kth_node_count(root, k) = kth_node_count(root.left_count, k-1) + kth_node_count(root.right_count, k-1)
'''
def kth_node_count(root, k):
if root and not isinstance(root, Node):
return None
if not root or k <= 0:
return 0
if k == 1:
return 1
return kth_node_count(root.left_child, k-1) + kth_node_count(root.right_child, k-1)
'''
計算二叉樹第K層節點個數，非遞歸方式
'''
def kth_node_count_not_recursion(root, k):
if root and not isinstance(root, Node):
return None
if not root or k <= 0:
return 0
if k == 1:
return 1
queue = [(root, 1)]
result = 0
while queue:
temp_node, temp_layer = queue.pop(0)
if temp_node:
if temp_layer == k:
result += 1
elif temp_layer > k:
return result
else:
queue.append((temp_node.left_child, temp_layer+1))
queue.append((temp_node.right_child, temp_layer+1))
return result
計算二叉樹葉子節點個數
'''
計算二叉樹葉子節點個數，遞歸方式
關鍵點是葉子節點的判斷標準，左右孩子皆爲None
'''
def leaf_count(root):
if root and not isinstance(root, Node):
return None
if not root:
return 0
if not root.left_child and not root.right_child:
return 1
return leaf_count(root.left_child) + leaf_count(root.right_child)
判斷兩個二叉樹是不是相同
'''
判斷兩個二叉樹是不是相同，遞歸方式
isSame(root1, root2) = (root1.value == root2.value)
and isSame(root1.left, root2.left)
and isSame(root1.right, root2.right)
'''
def is_same_tree(root1, root2):
if not root1 and not root2:
return True
if root1 and root2:
return (root1.value == root2.value) and \
is_same_tree(root1.left_child, root2.left_child) and \
is_same_tree(root1.right_child, root2.right_child)
else:
return False
判斷是否爲二分查找樹BST
'''
判斷是否爲二分查找樹BST，遞歸方式
二分查找樹的定義搞清楚，二分查找樹的中序遍歷結果爲遞增序列
'''
def is_bst_tree(root):
if root and not isinstance(root, Node):
return None
def is_asc(order):
for i in range(len(order)-1):
if order[i] > order[i+1]:
return False
return True
return is_asc(middle_order_bot_recursion(root))
測試方法
if __name__ == "__main__":
tree = Tree(1)
tree1 = Tree(1)
node6 = Node(None, None, 7)
node5 = Node(None, None, 6)
node4 = Node(None, None, 5)
node3 = Node(None, None, 4)
node2 = Node(node5, node6, 3)
node1 = Node(node3, node4, 2)
tree.root.left_child = node1
tree.root.right_child = node2
tree1.root.left_child = node2
tree1.root.right_child = node2
print(is_bst_tree(tree.root))
