【算法总结】二叉树

模板：

1.先序遍历三种方法

1）迭代：

class Solution {
public:
    /**
     * @param root: The root of binary tree.
     * @return: Preorder in vector which contains node values.
     */    
    vector<int> preorderTraversal(TreeNode *root) {
        vector<int> res;
        stack<TreeNode*> stack;
        
        if (root == NULL) {
            return res;
        }
        
        stack.push(root);
        while (!stack.empty()) {
            TreeNode *node = stack.top();
            stack.pop();
            res.push_back(node->val);
            if (node->right != NULL) {
                stack.push(node->right);
            }
            if (node->left != NULL) {
                stack.push(node->left);
            }
        }
        
        return res;
    }
};

2）递归：

class Solution {
public:
    void traversal(TreeNode *root, vector<int>& res) {
        if (root == NULL) {
            return;
        }
        
        res.push_back(root->val);
        traversal(root->left, res);
        traversal(root->right, res);
    }
    vector<int> preorderTraversal(TreeNode *root) {
        vector<int> res;
        traversal(root, res);
        
        return res;
    }
};

3）分治：

class Solution {
public:    
    vector<int> preorderTraversal(TreeNode *root) {
        vector<int> res;
        if (root == NULL) {
            return res;
        }
        
        vector<int> left = preorderTraversal(root->left);
        vector<int> right = preorderTraversal(root->right);
        
        res.push_back(root->val);
        res.insert(res.end(), left.begin(), left.end());
        res.insert(res.end(), right.begin(), right.end());
        
        return res;
    }
};

 模板2：DFS:

1) Traverse

class Solution {
public:
    void traverse(TreeNode *root) {
        if (root == NULL) {
            return;
        }
        
        // do something with root
        traverse(root->left);
        // do something with root
        traverse(root->right);
        // do something with root
    }
};

2) Divide and Conquer

class Solution {
public:
    ResultType traversal(TreeNode * root) {
        if (root == NULL) {
            // do something and return
        }
        
        // Divide
        ResultType left = traversal(root->left);
        ResultType right = traversal(root->right);
        
        // Conquer
        ResultType result = Merge from left and right
        
        return result;
    }
};

 栈实现非递归DFS

//preOrderTraversal
void preOrderTraversal1(TreeNode* root) {
    if (root == NULL) {
        return;
    }
    
    stack<TreeNode*> s;
    TreeNode* p = root;
    
    while (!s.empty() || p) {
        while (p) {
            func(p);
            s.push(p);
            p = p->left;
        }
        if (!s.empty()) {
            p = s.top();
            s.pop();
            p = p->right;
        }
    }
}

void preOrderTraversal2(TreeNode* root) {
    if (root == NULL) {
        return;
    }
    
    stack<TreeNode*> s;
    s.push(root);
    
    while (!s.empty()) {
        TreeNode* tmp = s.top();
        s.pop();
        func(tmp);
        if (tmp->right) {
            s.push(tmp->right);
        }
        if (tmp->left) {
            s.push(tmp->left);
        }
    }
}

void preOrderTraversal3(TreeNode* root) {
    if (root == NULL) {
        return;
    }
    
    stack<TreeNode*> s;
    s.push(root);
    TreeNode* tmp = root;
    
    while (!s.empty()) {
        func(tmp);
        if (tmp->right) {
            s.push(tmp->right);
        }
        if (tmp->left) {
            s.push(tmp->left);
        } else {
            p = s.top();
            s.pop();
        }
    }
}

//inOrderTraversal
void inOrderTraversal1(TreeNode* root) {
    if (root == NULL) {
        return;
    }
    
    stack<TreeNode*> s;
    TreeNode* p = root;
    
    while (!s.empty() || p) {
        while (p) {
            s.push(p);
            p = p->left;
        }
        if (!s.empty()) {
            p = s.top();
            s.pop();
            func(p);
            p = p->right;
        }
    }
}
//postOrderTraversal