Python实现二叉树的算法实例

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节点定义

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

二叉树定义

class Tree(object):
    def __init__(self, value):
        self._root = Node(None, None, value=value)
    @property
    def root(self):
        return self._root

先序遍历

递归方式

'''
先序遍历，递归方式
'''
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

非递归方式

'''
先序遍历，非递归方式
'''
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

中序遍历

递归方式

'''
中序遍历，递归方式
'''
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

非递归方式

'''
中序遍历，非递归方式
'''
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

后序遍历

递归方式

'''
后序遍历，递归方式
'''
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

非递归方式

'''
后序遍历，非递归方式
'''
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

分层遍历

'''
分层遍历，使用队列实现
'''
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

计算二叉树结点个数

'''
计算二叉树结点个数，递归方式
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
'''
计算二叉树结点个数，非递归方式
借用分层遍历计算
'''
def node_count_not_recursion(root):
    if root and not isinstance(root, Node):
        return None
    return len(layer_order(root))

计算二叉树深度

'''
计算二叉树深度，递归方式
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
'''
计算二叉树深度，非递归方法
同理参考分层遍历的思想
'''
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

计算二叉树第k层节点个数

'''
计算二叉树第k层节点个数，递归方式
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)
'''
计算二叉树第K层节点个数，非递归方式
'''
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

计算二叉树叶子节点个数

'''
计算二叉树叶子节点个数，递归方式
关键点是叶子节点的判断标准，左右孩子皆为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)

判断两个二叉树是不是相同

'''
判断两个二叉树是不是相同，递归方式
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

判断是否为二分查找树BST

'''
判断是否为二分查找树BST，递归方式
二分查找树的定义搞清楚，二分查找树的中序遍历

结果为递增序列 ''' 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))

测试方法

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))

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