给定一个包含大于 0 的正整数值的二叉搜索树。任务是检查 BST 是否包含死胡同。这里的死胡同意味着，我们无法在该节点之后插入任何元素。
例子：
Input : 8
/ \
5 9
/ \
2 7
/
1
Output : Yes
Explanation : Node "1" is the dead End because
after that we cant insert any element.
Input : 8
/ \
7 10
/ / \
2 9 13
Output : Yes
Explanation : We can't insert any element at
node 9.
如果我们仔细观察这个问题，我们可以注意到，我们基本上需要检查是否存在值为 x 的叶节点，使得 x+1 和 x-1 存在于 BST 中，x = 1 除外。对于 x = 1，我们不能插入 0，因为问题陈述说 BST 只包含正整数。
为了实现上述想法，我们首先遍历整个 BST 并将所有节点存储在 hash_map 中。我们还将所有叶子存储在单独的哈希中，以避免重新遍历 BST。最后，我们检查每个叶节点 x，是否在 hash_map 中存在 x-1 和 x+1。
下面是上述想法的 C++ 实现。
C++
// C++ program check weather BST contains
// dead end or not
#include
using namespace std;
// A BST node
struct Node
{
int data;
struct Node *left, *right;
};
// A utility function to create a new node
Node *newNode(int data)
{
Node *temp = new Node;
temp->data = data;
temp->left = temp->right = NULL;
return temp;
}
/* A utility function to insert a new Node
with given key in BST */
struct Node* insert(struct Node* node, int key)
{
/* If the tree is empty, return a new Node */
if (node == NULL) return newNode(key);
/* Otherwise, recur down the tree */
if (key < node->data)
node->left = insert(node->left, key);
else if (key > node->data)
node->right = insert(node->right, key);
/* return the (unchanged) Node pointer */
return node;
}
// Function to store all node of given binary search tree
void storeNodes(Node * root, unordered_set &all_nodes,
unordered_set &leaf_nodes)
{
if (root == NULL)
return ;
// store all node of binary search tree
all_nodes.insert(root->data);
// store leaf node in leaf_hash
if (root->left==NULL && root->right==NULL)
{
leaf_nodes.insert(root->data);
return ;
}
// recur call rest tree
storeNodes(root-> left, all_nodes, leaf_nodes);
storeNodes(root->right, all_nodes, leaf_nodes);
}
// Returns true if there is a dead end in tree,
// else false.
bool isDeadEnd(Node *root)
{
// Base case
if (root == NULL)
return false ;
// create two empty hash sets that store all
// BST elements and leaf nodes respectively.
unordered_set all_nodes, leaf_nodes;
// insert 0 in 'all_nodes' for handle case
// if bst contain value 1
all_nodes.insert(0);
// Call storeNodes function to store all BST Node
storeNodes(root, all_nodes, leaf_nodes);
// Traversal leaf node and check Tree contain
// continuous sequence of
// size tree or Not
for (auto i = leaf_nodes.begin() ; i != leaf_nodes.end(); i++)
{
int x = (*i);
// Here we check first and last element of
// continuous sequence that are x-1 & x+1
if (all_nodes.find(x+1) != all_nodes.end() &&
all_nodes.find(x-1) != all_nodes.end())
return true;
}
return false ;
}
// Driver program
int main()
{
/* 8
/ \
5 11
/ \
2 7
\
3
\
4 */
Node *root = NULL;
root = insert(root, 8);
root = insert(root, 5);
root = insert(root, 2);
root = insert(root, 3);
root = insert(root, 7);
root = insert(root, 11);
root = insert(root, 4);
if (isDeadEnd(root) == true)
cout << "Yes " << endl;
else
cout << "No " << endl;
return 0;
} Python3
# Python 3 program check
# weather BST contains
# dead end or not
all_nodes = set()
leaf_nodes = set()
# A BST node
class newNode:
def __init__(self, data):
self.data = data
self.left = None
self.right = None
''' A utility function to
insert a new Node with
given key in BST '''
def insert(node, key):
'''/* If the tree is empty,
return a new Node */ '''
if (node == None):
return newNode(key)
# Otherwise, recur down
# the tree
if (key < node.data):
node.left = insert(node.left,
key)
elif (key > node.data):
node.right = insert(node.right,
key)
# return the (unchanged)
# Node pointer
return node
# Function to store all node
# of given binary search tree
def storeNodes(root):
global all_nodes
global leaf_nodes
if (root == None):
return
# store all node of binary
# search tree
all_nodes.add(root.data)
# store leaf node in leaf_hash
if (root.left == None and
root.right == None):
leaf_nodes.add(root.data)
return
# recur call rest tree
storeNodes(root. left)
storeNodes(root.right)
# Returns true if there is
# a dead end in tree,
# else false.
def isDeadEnd(root):
global all_nodes
global leaf_nodes
# Base case
if (root == None):
return False
# create two empty hash
# sets that store all BST
# elements and leaf nodes
# respectively.
# insert 0 in 'all_nodes'
# for handle case if bst
# contain value 1
all_nodes.add(0)
# Call storeNodes function
# to store all BST Node
storeNodes(root)
# Traversal leaf node and
# check Tree contain
# continuous sequence of
# size tree or Not
for x in leaf_nodes:
# Here we check first and
# last element of continuous
# sequence that are x-1 & x+1
if ((x + 1) in all_nodes and
(x - 1) in all_nodes):
return True
return False
# Driver code
if __name__ == '__main__':
'''/* 8
/ \
5 11
/ \
2 7
\
3
\
4 */
'''
root = None
root = insert(root, 8)
root = insert(root, 5)
root = insert(root, 2)
root = insert(root, 3)
root = insert(root, 7)
root = insert(root, 11)
root = insert(root, 4)
if(isDeadEnd(root) == True):
print("Yes")
else:
print("No")
# This code is contributed by bgangwar59输出：
Yes
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