Tree——No.987 Vertical Order Traversal of a Binary Tree

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本文介绍了一种二叉树的纵向遍历算法，通过记录每个节点的位置信息并进行排序，实现了从左到右按列返回节点值的功能。具体方法包括构建位置信息类并实现比较方法，以及遍历树来收集所有节点的位置。

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Problem：

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.

Explanation：

以一棵树的根节点为(0,0)，左孩子为(-1,-1)，右孩子为(1,-1)，依次类推，纵向遍历树，即横坐标相同的为一组。

My Thinking：

My Solution：

Optimum Thinking:

使用一个location类保存结点位置信息

Optimum Solution：

class Solution {
    List<Location> locations=new ArrayList();
    public List<List<Integer>> verticalTraversal(TreeNode root) {
        traversal(root,0,0);//构建位置信息列表
        Collections.sort(locations);//对列表按照自定义排序方式进行排序
        
        List<List<Integer>> result=new ArrayList<>();
        result.add(new ArrayList<Integer>());
        int prev = locations.get(0).x;
        for (Location loc: locations) {
            if (loc.x != prev) {
                prev = loc.x;
                result.add(new ArrayList<Integer>());
            }
            result.get(result.size() - 1).add(loc.val);
        }
        return result;
    }
    
    public void traversal(TreeNode root,int x,int y){//为每个结点构建一个位置信息
        if(root==null)
            return;
        locations.add(new Location(x,y,root.val));
        traversal(root.left,x-1,y+1);
        traversal(root.right,x+1,y+1);
    }


}
class Location implements Comparable<Location>{//位置信息类，重写compareto方法用于比较
    int x, y, val;
    Location(int x, int y, int val) {
        this.x = x;
        this.y = y;
        this.val = val;
    }

    @Override
    public int compareTo(Location that) {
        if (this.x != that.x)
            return Integer.compare(this.x, that.x);
        else if (this.y != that.y)
            return Integer.compare(this.y, that.y);
        else
            return Integer.compare(this.val, that.val);
    }
}