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.
判断树本身是否自己的镜像树,即是否为中轴对称树。递归的思想很简单,保存树的左右节点,对于当前的两个节点,判断值是否相同,同时判断当前两个节点对称的 左右 和 右左 孩子是否相同,分辨以左右 右左孩子为当前节点进行递归。
class Solution { public: bool isSymmetricRec(TreeNode *lRoot,TreeNode *rRoot){ if(lRoot==NULL&&rRoot==NULL)return true; if(lRoot==NULL||rRoot==NULL)return false; return lRoot->val==rRoot->val&&isSymmetricRec(lRoot->left,rRoot->right)&&isSymmetricRec(lRoot->right,rRoot->left); } bool isSymmetric(TreeNode *root) { if(root==NULL)return true; return isSymmetricRec(root->left,root->right); } };对于迭代,一层一层的遍历比较,设前一层为ver[pre],存储的前一层的成对的相同的节点,设当前层为ver[cur],则由pre层生成cur层。这里存储的形式为对称的一对一对的节点,故数组的遍历步长为2.
class Solution { public: bool isSymmetric(TreeNode *root) { if(root==NULL)return true; vector<TreeNode*> ver[2]; int pre=1,cur=0; if(root->left==NULL&&root->right==NULL)return true; else if(root->left==NULL||root->right==NULL)return false; else if(root->left->val!=root->right->val)return false; ver[cur].push_back(root->left);ver[cur].push_back(root->right); while(ver[cur].size()>0){ cur=!cur; pre=!pre; ver[cur].clear(); for(int i=0;i<ver[pre].size();i+=2){ if(ver[pre][i]->left==NULL&&ver[pre][i+1]->right==NULL); else if(ver[pre][i]->left==NULL||ver[pre][i+1]->right==NULL)return false; else if(ver[pre][i]->left->val!=ver[pre][i+1]->right->val)return false; else{ ver[cur].push_back(ver[pre][i]->left);ver[cur].push_back(ver[pre][i+1]->right); } if(ver[pre][i]->right==NULL&&ver[pre][i+1]->left==NULL); else if(ver[pre][i]->right==NULL||ver[pre][i+1]->left==NULL)return false; else if(ver[pre][i]->right->val!=ver[pre][i+1]->left->val)return false; else{ ver[cur].push_back(ver[pre][i]->right);ver[cur].push_back(ver[pre][i+1]->left); } } } return true; } };