> For the complete documentation index, see [llms.txt](https://jimmylin1991.gitbook.io/practice-of-algorithm-problems/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://jimmylin1991.gitbook.io/practice-of-algorithm-problems/tree/314.-binary-tree-vertical-order-traversal.md).

# 314. Binary Tree Vertical Order Traversal

Given a binary tree, return the vertical order traversal of its nodes' values. (ie, from top to bottom, column by column).

If two nodes are in the same row and column, the order should be from **left to right**.

**Examples 1:**

```
Input: [3,9,20,null,null,15,7]

   3
  /\
 /  \
 9  20
    /\
   /  \
  15   7 

Output:

[
  [9],
  [3,15],
  [20],
  [7]
]
```

**Examples 2:**

```
Input: [3,9,8,4,0,1,7]

     3
    /\
   /  \
   9   8
  /\  /\
 /  \/  \
 4  01   7 

Output:

[
  [4],
  [9],
  [3,0,1],
  [8],
  [7]
]
```

**Examples 3:**

```
Input: [3,9,8,4,0,1,7,null,null,null,2,5] (0's right child is 2 and 1's left child is 5)

     3
    /\
   /  \
   9   8
  /\  /\
 /  \/  \
 4  01   7
    /\
   /  \
   5   2

Output:

[
  [4],
  [9,5],
  [3,0,1],
  [8,2],
  [7]
]
```

{% hint style="info" %}
題目要求從上到下，然後col by col，想到用level order traversal為主體來掃描，搭配使用treemap來記錄同個col上的所有節點值。一開始root的col值定為0，往左就是減1，往右就是加1，掃描時每個節點會有各自的col值，把該節點本身的val存入map中相應的col值中。最後再把map掃過一遍把所有垂直掃描順序加入要返回的2D vector中。
{% endhint %}

```cpp
vector<vector<int>> verticalOrder(TreeNode* root) { // time: O(n); space: O(n)
    vector<vector<int> > res;
    if (!root) return res;
    map<int, vector<int> > m;
    queue<pair<int, TreeNode*> > q;
    q.push({0, root});
    while (!q.empty()) {
        auto t = q.front(); q.pop();
        m[t.first].push_back(t.second->val);
        if (t.second->left) 
            q.push({t.first - 1, t.second->left});
        if (t.second->right) 
            q.push({t.first + 1, t.second->right});
    }
    for (auto& a : m) {
        res.push_back(a.second);
    }
    return res;
}
```


---

# Agent Instructions
This documentation is published with GitBook. GitBook is the documentation platform designed so that both humans and AI agents can read, navigate, and reason over technical content effectively. Learn more at gitbook.com.

## Querying This Documentation
If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter:

```
GET https://jimmylin1991.gitbook.io/practice-of-algorithm-problems/tree/314.-binary-tree-vertical-order-traversal.md?ask=<question>
```

The question should be specific, self-contained, and written in natural language.
The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.