101. Symmetric Tree

本文介绍了一种检查二叉树是否为中心对称的方法,提供了递归与非递归两种解决方案。递归方法通过比较左右子树节点值来判断,而非递归则使用队列实现层次遍历。

Given a binary tree, check whether it is a mirror of itself (ie, symmetric around its center).

For example, this binary tree is symmetric:

    1
   / \
  2   2
 / \ / \
3  4 4  3

But the following is not:

    1
   / \
  2   2
   \   \
   3    3

Note:
Bonus points if you could solve it both recursively and iteratively.

confused what "{1,#,2,3}" means? > read more on how binary tree is serialized on OJ.

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class Solution {
public:
    bool judge(TreeNode *p,TreeNode *q)
    {
        if(!p&&!q)return true;
        else  if(p&&q&&p->val==q->val) return judge(p->left,q->right)&&judge(p->right,q->left);
        else return false;
        
    }
    
    bool isSymmetric(TreeNode* root) {
        if(!root)return true;
        else return judge(root->left,root->right);
    }
};
非递归:<pre name="code" class="cpp">class Solution {
public:
    bool isSymmetric(TreeNode *root) {
       
        if (!root) return true;
        queue<TreeNode*> q1, q2;
        q1.push(root->left);
        q2.push(root->right);
        while (!q1.empty() && !q2.empty())
        {
            TreeNode *t1 = q1.front();
            TreeNode *t2 = q2.front();
            q1.pop();
            q2.pop();
            if (!t1 && !t2) continue;
            if (!t1|| !t2) return false;
            if(t1->val!=t2->val) return false;
            q1.push(t1->left);
            q1.push(t1->right);
            q2.push(t2->right);
            q2.push(t2->left);
        }
        return true;
    }
};


                
2025-09-01 17:23:58 INFO com.putian.datapush.presto.PrestoServiceImpl - cn.hutool.crypto.CryptoException: SecurityException: JCE cannot authenticate the provider BC at cn.hutool.crypto.SecureUtil.createCipher(SecureUtil.java:1034) at cn.hutool.crypto.CipherWrapper.<init>(CipherWrapper.java:39) at cn.hutool.crypto.symmetric.SymmetricCrypto.init(SymmetricCrypto.java:150) at cn.hutool.crypto.symmetric.SymmetricCrypto.<init>(SymmetricCrypto.java:127) at cn.hutool.crypto.symmetric.SymmetricCrypto.<init>(SymmetricCrypto.java:115) at cn.hutool.crypto.symmetric.SymmetricCrypto.<init>(SymmetricCrypto.java:104) at com.putian.common.secure.SecureUtil.sm4Encrypt(SecureUtil.java:1443) at com.putian.datapush.service.PushDataService.executeEncipher(PushDataService.java:452) at com.putian.datapush.service.PushDataService.encipher(PushDataService.java:407) at com.putian.datapush.service.PushDataService.makeUpData(PushDataService.java:360) at com.putian.datapush.service.PushDataService.processInBatches(PushDataService.java:307) at com.putian.PushDataJobStartor.main(PushDataJobStartor.java:35) Caused by: java.lang.SecurityException: JCE cannot authenticate the provider BC at javax.crypto.Cipher.getInstance(Cipher.java:662) at cn.hutool.crypto.SecureUtil.createCipher(SecureUtil.java:1032) ... 11 more Caused by: java.util.jar.JarException: file:/home/dataShared/job/putian-data-pushdata.jar has unsigned entries - cn/hutool/Hutool.class at javax.crypto.JarVerifier.verifySingleJar(JarVerifier.java:510) at javax.crypto.JarVerifier.verifyJars(JarVerifier.java:371) at javax.crypto.JarVerifier.verify(JarVerifier.java:297) at javax.crypto.JceSecurity.verifyProviderJar(JceSecurity.java:164) at javax.crypto.JceSecurity.getVerificationResult(JceSecurity.java:190) at javax.crypto.Cipher.getInstance(Cipher.java:658) ... 12 more 2025-09-01 17:24:02 ERROR com.putian.PushDataJobStartor - 数据推送任务运行失败! cn.hutool.crypto.CryptoException: SecurityException: JCE cannot authenticate the provider BC at cn.hutool.crypto.SecureUtil.createCipher(SecureUtil.java:1034) at cn.hutool.crypto.CipherWrapper.<init>(CipherWrapper.java:39) at cn.hutool.crypto.symmetric.SymmetricCrypto.init(SymmetricCrypto.java:150) at cn.hutool.crypto.symmetric.SymmetricCrypto.<init>(SymmetricCrypto.java:127) at cn.hutool.crypto.symmetric.SymmetricCrypto.<init>(SymmetricCrypto.java:115) at cn.hutool.crypto.symmetric.SymmetricCrypto.<init>(SymmetricCrypto.java:104) at com.putian.common.secure.SecureUtil.sm4Encrypt(SecureUtil.java:1443) at com.putian.datapush.service.PushDataService.executeEncipher(PushDataService.java:452) at com.putian.datapush.service.PushDataService.encipher(PushDataService.java:407) at com.putian.datapush.service.PushDataService.makeUpData(PushDataService.java:360) at com.putian.datapush.service.PushDataService.processInBatches(PushDataService.java:307) at com.putian.PushDataJobStartor.main(PushDataJobStartor.java:35) Caused by: java.lang.SecurityException: JCE cannot authenticate the provider BC at javax.crypto.Cipher.getInstance(Cipher.java:662) at cn.hutool.crypto.SecureUtil.createCipher(SecureUtil.java:1032) 这个问题的解决办法?
09-03
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