[LeetCode] 314. Binary Tree Vertical Order Traversal 二叉树的竖直遍历

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]
]

这道题让我们竖直遍历二叉树，并把每一列存入一个二维数组，看题目中给的第一个例子，3和 15 属于同一列，3在前，第二个例子中，3,5,2 在同一列，3在前，5和2紧随其后，那么隐约的可以感觉到好像是一种层序遍历的前后顺序，如何来确定列的顺序呢，这里可以把根节点给个序号0，然后开始层序遍历，凡是左子节点则序号减1，右子节点序号加1，这样可以通过序号来把相同列的节点值放到一起，用一个 TreeMap 来建立序号和其对应的节点值的映射，用 TreeMap 的另一个好处是其自动排序功能可以让列从左到右，由于层序遍历需要用到 queue，此时 queue 里不能只存节点，而是要存序号和节点组成的 pair 对儿，这样每次取出就可以操作序号，而且排入队中的节点也赋上其正确的序号，代码如下：

class Solution {
public:
    vector<vector<int>> verticalOrder(TreeNode* root) {
        vector<vector<int>> res;
        if (!root) return res;
        map<int, vector<int>> m;
        queue<pair<int, TreeNode*>> q;
        q.push({, root});
        while (!q.empty()) {
            auto a = q.front(); q.pop();
            m[a.first].push_back(a.second->val);
            if (a.second->left) q.push({a.first - , a.second->left});
            if (a.second->right) q.push({a.first + , a.second->right});
        }
        for (auto a : m) {
            res.push_back(a.second);
        }
        return res;
    }
};

Github 同步地址：

https://github.com/grandyang/leetcode/issues/314

类似题目：

Binary Tree Level Order Traversal

参考资料：

https://leetcode.com/problems/binary-tree-vertical-order-traversal/

https://leetcode.com/problems/binary-tree-vertical-order-traversal/discuss/76401/5ms-Java-Clean-Solution

https://leetcode.com/problems/binary-tree-vertical-order-traversal/discuss/76508/3ms-java-solution-beats-100

https://leetcode.com/problems/binary-tree-vertical-order-traversal/discuss/76463/Using-HashMapBFS-Java-Solution

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