检查对称二叉树（迭代方法）
给定一棵二叉树，检查它是否是自身的镜像，无需递归。
例子：
Input :
1
/ \
2 2
/ \ / \
3 4 4 3
Output : Symmetric
Input :
1
/ \
2 2
\ \
3 3
Output : Not Symmetric我们在下面的帖子中讨论了解决此问题的递归方法：
对称树（自身的镜像）
在这篇文章中，讨论了迭代方法。我们在这里使用队列。请注意，对于对称元素，每个级别的元素都是回文的。在示例 2 中，在叶级别 - 元素不是回文。
换一种说法，
1.左子树的左孩子=右子树的右孩子。
2. 左子树的右孩子=右子树的左孩子。
如果我们在队列中先插入左子树的左子树，再插入右子树的右子树，我们只需要确保它们相等即可。
同样，如果我们在队列中插入左子树的右子树，然后是右子树的左子树，我们再次需要确保它们相等。
下面是基于上述思想的实现。
C++
// C++ program to check if a given Binary
// Tree is symmetric or not
#include
using namespace std;
// A Binary Tree Node
struct Node
{
int key;
struct Node* left, *right;
};
// Utility function to create new Node
Node *newNode(int key)
{
Node *temp = new Node;
temp->key = key;
temp->left = temp->right = NULL;
return (temp);
}
// Returns true if a tree is symmetric
// i.e. mirror image of itself
bool isSymmetric(struct Node* root)
{
if(root == NULL)
return true;
// If it is a single tree node, then
// it is a symmetric tree.
if(!root->left && !root->right)
return true;
queue q;
// Add root to queue two times so that
// it can be checked if either one child
// alone is NULL or not.
q.push(root);
q.push(root);
// To store two nodes for checking their
// symmetry.
Node* leftNode, *rightNode;
while(!q.empty()){
// Remove first two nodes to check
// their symmetry.
leftNode = q.front();
q.pop();
rightNode = q.front();
q.pop();
// if both left and right nodes
// exist, but have different
// values--> inequality, return false
if(leftNode->key != rightNode->key){
return false;
}
// Push left child of left subtree node
// and right child of right subtree
// node in queue.
if(leftNode->left && rightNode->right){
q.push(leftNode->left);
q.push(rightNode->right);
}
// If only one child is present alone
// and other is NULL, then tree
// is not symmetric.
else if (leftNode->left || rightNode->right)
return false;
// Push right child of left subtree node
// and left child of right subtree node
// in queue.
if(leftNode->right && rightNode->left){
q.push(leftNode->right);
q.push(rightNode->left);
}
// If only one child is present alone
// and other is NULL, then tree
// is not symmetric.
else if(leftNode->right || rightNode->left)
return false;
}
return true;
}
// Driver program
int main()
{
// Let us construct the Tree shown in
// the above figure
Node *root = newNode(1);
root->left = newNode(2);
root->right = newNode(2);
root->left->left = newNode(3);
root->left->right = newNode(4);
root->right->left = newNode(4);
root->right->right = newNode(3);
if(isSymmetric(root))
cout << "The given tree is Symmetric";
else
cout << "The given tree is not Symmetric";
return 0;
}
// This code is contributed by Nikhil jindal. Java
// Iterative Java program to check if
// given binary tree symmetric
import java.util.* ;
public class BinaryTree
{
Node root;
static class Node
{
int val;
Node left, right;
Node(int v)
{
val = v;
left = null;
right = null;
}
}
/* constructor to initialise the root */
BinaryTree(Node r) { root = r; }
/* empty constructor */
BinaryTree() { }
/* function to check if the tree is Symmetric */
public boolean isSymmetric(Node root)
{
/* This allows adding null elements to the queue */
Queue q = new LinkedList();
/* Initially, add left and right nodes of root */
q.add(root.left);
q.add(root.right);
while (!q.isEmpty())
{
/* remove the front 2 nodes to
check for equality */
Node tempLeft = q.remove();
Node tempRight = q.remove();
/* if both are null, continue and check
for further elements */
if (tempLeft==null && tempRight==null)
continue;
/* if only one is null---inequality, return false */
if ((tempLeft==null && tempRight!=null) ||
(tempLeft!=null && tempRight==null))
return false;
/* if both left and right nodes exist, but
have different values-- inequality,
return false*/
if (tempLeft.val != tempRight.val)
return false;
/* Note the order of insertion of elements
to the queue :
1) left child of left subtree
2) right child of right subtree
3) right child of left subtree
4) left child of right subtree */
q.add(tempLeft.left);
q.add(tempRight.right);
q.add(tempLeft.right);
q.add(tempRight.left);
}
/* if the flow reaches here, return true*/
return true;
}
/* driver function to test other functions */
public static void main(String[] args)
{
Node n = new Node(1);
BinaryTree bt = new BinaryTree(n);
bt.root.left = new Node(2);
bt.root.right = new Node(2);
bt.root.left.left = new Node(3);
bt.root.left.right = new Node(4);
bt.root.right.left = new Node(4);
bt.root.right.right = new Node(3);
if (bt.isSymmetric(bt.root))
System.out.println("The given tree is Symmetric");
else
System.out.println("The given tree is not Symmetric");
}
} Python3
# Python3 program to program to check if a
# given Binary Tree is symmetric or not
# Helper function that allocates a new
# node with the given data and None
# left and right pairs.
class newNode:
# Constructor to create a new node
def __init__(self, key):
self.key = key
self.left = None
self.right = None
# function to check if a given
# Binary Tree is symmetric or not
def isSymmetric( root) :
# if tree is empty
if (root == None) :
return True
# If it is a single tree node,
# then it is a symmetric tree.
if(not root.left and not root.right):
return True
q = []
# Add root to queue two times so that
# it can be checked if either one
# child alone is NULL or not.
q.append(root)
q.append(root)
# To store two nodes for checking
# their symmetry.
leftNode = 0
rightNode = 0
while(not len(q)):
# Remove first two nodes to
# check their symmetry.
leftNode = q[0]
q.pop(0)
rightNode = q[0]
q.pop(0)
# if both left and right nodes
# exist, but have different
# values-. inequality, return False
if(leftNode.key != rightNode.key):
return False
# append left child of left subtree
# node and right child of right
# subtree node in queue.
if(leftNode.left and rightNode.right) :
q.append(leftNode.left)
q.append(rightNode.right)
# If only one child is present
# alone and other is NULL, then
# tree is not symmetric.
else if (leftNode.left or rightNode.right) :
return False
# append right child of left subtree
# node and left child of right subtree
# node in queue.
if(leftNode.right and rightNode.left):
q.append(leftNode.right)
q.append(rightNode.left)
# If only one child is present
# alone and other is NULL, then
# tree is not symmetric.
else if(leftNode.right or rightNode.left):
return False
return True
# Driver Code
if __name__ == '__main__':
# Let us construct the Tree
# shown in the above figure
root = newNode(1)
root.left = newNode(2)
root.right = newNode(2)
root.left.left = newNode(3)
root.left.right = newNode(4)
root.right.left = newNode(4)
root.right.right = newNode(3)
if (isSymmetric(root)) :
print("The given tree is Symmetric")
else:
print("The given tree is not Symmetric")
# This code is contributed by
# Shubham Singh(SHUBHAMSINGH10)C#
// Iterative C# program to check if
// given binary tree symmetric
using System;
using System.Collections.Generic;
public class BinaryTree
{
public Node root;
public class Node
{
public int val;
public Node left, right;
public Node(int v)
{
val = v;
left = null;
right = null;
}
}
/* constructor to initialise the root */
BinaryTree(Node r) { root = r; }
/* empty constructor */
BinaryTree() { }
/* function to check if the tree is Symmetric */
public bool isSymmetric(Node root)
{
/* This allows adding null elements to the queue */
Queue q = new Queue();
/* Initially, add left and right nodes of root */
q.Enqueue(root.left);
q.Enqueue(root.right);
while (q.Count!=0)
{
/* remove the front 2 nodes to
check for equality */
Node tempLeft = q.Dequeue();
Node tempRight = q.Dequeue();
/* if both are null, continue and check
for further elements */
if (tempLeft==null && tempRight==null)
continue;
/* if only one is null---inequality, return false */
if ((tempLeft==null && tempRight!=null) ||
(tempLeft!=null && tempRight==null))
return false;
/* if both left and right nodes exist, but
have different values-- inequality,
return false*/
if (tempLeft.val != tempRight.val)
return false;
/* Note the order of insertion of elements
to the queue :
1) left child of left subtree
2) right child of right subtree
3) right child of left subtree
4) left child of right subtree */
q.Enqueue(tempLeft.left);
q.Enqueue(tempRight.right);
q.Enqueue(tempLeft.right);
q.Enqueue(tempRight.left);
}
/* if the flow reaches here, return true*/
return true;
}
/* driver code */
public static void Main(String[] args)
{
Node n = new Node(1);
BinaryTree bt = new BinaryTree(n);
bt.root.left = new Node(2);
bt.root.right = new Node(2);
bt.root.left.left = new Node(3);
bt.root.left.right = new Node(4);
bt.root.right.left = new Node(4);
bt.root.right.right = new Node(3);
if (bt.isSymmetric(bt.root))
Console.WriteLine("The given tree is Symmetric");
else
Console.WriteLine("The given tree is not Symmetric");
}
}
// This code is contributed by PrinciRaj1992 Javascript
输出：
The given tree is Symmetric