## [Leetcode]987. Vertical Order Traversal of a Binary Tree

### 题目描述

Given a binary tree, return the vertical order traversal of its nodes values.

For each node at position (X, Y), its left and right children respectively will be at positions (X-1, Y-1) and (X+1, Y-1).

Running a vertical line from X = -infinity to X = +infinity, whenever the vertical line touches some nodes, we report the values of the nodes in order from top to bottom (decreasing Y coordinates).

If two nodes have the same position, then the value of the node that is reported first is the value that is smaller.

Return an list of non-empty reports in order of X coordinate. Every report will have a list of values of nodes.

### 例子

#### 例子 1

Input: [3,9,20,null,null,15,7] Output: [,[3,15],,] **Explanation:**Without loss of generality, we can assume the root node is at position (0, 0): Then, the node with value 9 occurs at position (-1, -1); The nodes with values 3 and 15 occur at positions (0, 0) and (0, -2); The node with value 20 occurs at position (1, -1); The node with value 7 occurs at position (2, -2).

#### 例子 2

Input: [1,2,3,4,5,6,7] Output: [,,[1,5,6],,] **Explanation:**The node with value 5 and the node with value 6 have the same position according to the given scheme. However, in the report “[1,5,6]”, the node value of 5 comes first since 5 is smaller than 6.

### 解题思路

``````/**
* 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:
vector<vector<int>> verticalTraversal(TreeNode* root) {
std::vector<std::vector<int>> results;

std::map<int, std::map<int, std::vector<int>>> node_map;
dfs(root, 0, 0, node_map);
for (auto iter_col = node_map.begin(); iter_col != node_map.end(); iter_col++) {
std::vector<int> col;
std::map<int, std::vector<int>> col_map = iter_col->second;
for (auto iter_row = col_map.begin(); iter_row != col_map.end(); iter_row++) {
std::sort(iter_row->second.begin(), iter_row->second.end());
col.insert(col.end(), iter_row->second.begin(), iter_row->second.end());
}
results.push_back(col);
}

return results;
}

private:
void dfs(TreeNode* node, int row, int col, std::map<int, std::map<int, std::vector<int>>>& node_map) {
if (!node) return;
node_map[col][row].push_back(node->val);
dfs(node->left, row + 1, col - 1, node_map);
dfs(node->right, row + 1, col + 1, node_map);
}
};
``````
• 时间复杂度: O(nlogn) （最坏情况是在分支只有一条的情况，不太确定）
• 空间复杂度: O(n)