代码随想录算法训练Day14 | 二叉树理论基础 & 递归遍历 & 迭代遍历 | 统一迭代

二叉树理论基础

二叉树主要有两种形式：满二叉树和完全二叉树

满二叉树

如果一颗二叉树只有度为0的结点和度为2的结点，且度为0的结点在同一层。

完全二叉树

在完全二叉树中，除了最底层节点可能没填满外，其余每层节点数都达到最大值，并且最下面一层的节点都集中在该层最左边的若干位置。

递归遍历

144.二叉树的前序遍历

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode() : val(0), left(nullptr), right(nullptr) {}
 *     TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
 *     TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
 * };
 */
class Solution {
public:
    void traversal(TreeNode* root, vector& vec) {
        if (root == nullptr) return;
        vec.push_back(root->val);
        traversal(root->left, vec);
        traversal(root->right, vec);
    }
    
    vector preorderTraversal(TreeNode* root) {
        vector result;
        traversal(root, result);
        return result;
    }
};

 145.二叉树的后序遍历

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode() : val(0), left(nullptr), right(nullptr) {}
 *     TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
 *     TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
 * };
 */
class Solution {
public:
    void traversal(TreeNode *root, vector& vec) {
        if (root == nullptr) return;
        traversal(root->left, vec);
        traversal(root->right, vec);
        vec.push_back(root->val);
    }

    vector postorderTraversal(TreeNode* root) {
        vector result;
        traversal(root, result);
        return result;
    }
};

94.二叉树的中序遍历

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode() : val(0), left(nullptr), right(nullptr) {}
 *     TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
 *     TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
 * };
 */
class Solution {
public:
    void traversal(TreeNode* root, vector& vec) {
        if (root == nullptr) return;
        traversal(root->left, vec);
        vec.push_back(root->val);
        traversal(root->right, vec);
    }

    vector inorderTraversal(TreeNode* root) {
        vector result;
        traversal(root, result);
        return result; 
    }
};

迭代遍历

前序遍历

class Solution {
public:
    vector preorderTraversal(TreeNode* root) {
        vector result;
        stack st;
        if (root == nullptr) return result;
        st.push(root);
        while (!st.empty()) {
            TreeNode* node = st.top();
            st.pop();
            result.push_back(node->val);
            if (node->right) st.push(node->right);
            if (node->left) st.push(node->left);
        }
        return result;
    }
};

后序遍历

class Solution {
public:
    vector postorderTraversal(TreeNode* root) {
        vector result;
        stack st;
        if (root == nullptr) return result;
        st.push(root);
        while (!st.empty()) {
            TreeNode* node = st.top();
            st.pop();
            result.push_back(node->val);
            if (node->left) st.push(node->left);
            if (node->right) st.push(node->right);
        }
        reverse(result.begin(), result.end());
        return result;
    }
};

中序遍历

class Solution {
public:
    vector inorderTraversal(TreeNode* root) {
        vector result;
        stack st;
        TreeNode* cur = root;
        while (cur != nullptr || !st.empty()) {
            if (cur != nullptr) {
                st.push(cur);
                cur = cur->left;
            } else {
                cur = st.top();
                st.pop();
                result.push_back(cur->val);
                cur = cur->right;
            }
        }
        return result;
    }
};