Tuesday, October 20, 2020

LeetCode [987] Vertical Order Traversal of a Binary Tree

 987. Vertical Order Traversal of a Binary Tree

Medium

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.

 

Example 1:

Input: [3,9,20,null,null,15,7]
Output: [[9],[3,15],[20],[7]]
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).

Example 2:

Input: [1,2,3,4,5,6,7]
Output: [[4],[2],[1,5,6],[3],[7]]
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.

 

Note:

  1. The tree will have between 1 and 1000 nodes.
  2. Each node's value will be between 0 and 1000.
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/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode() {}
 *     TreeNode(int val) { this.val = val; }
 *     TreeNode(int val, TreeNode left, TreeNode right) {
 *         this.val = val;
 *         this.left = left;
 *         this.right = right;
 *     }
 * }
 */
class Solution {
    Map<Integer, Map<Integer, List<Integer>>> map = new TreeMap<>();
    public List<List<Integer>> verticalTraversal(TreeNode root) {
        helper(0, 0, root);
        List<List<Integer>> lists = new ArrayList<>();
        for(Map.Entry<Integer, Map<Integer, List<Integer>>> m : map.entrySet()){
            List<Integer> col = new ArrayList<>();
            for(Map.Entry<Integer, List<Integer>> e : m.getValue().entrySet()){
                List<Integer> list = e.getValue();
                Collections.sort(list);
                col.addAll(list);
            }
            lists.add(col);
        }
        return lists;
    }

    void helper(int x, int y, TreeNode node){
        if(node==null) return;
        if(!map.containsKey(x)){
            map.put(x, new TreeMap<>());
        }
        
        if(!map.get(x).containsKey(y)){
            map.get(x).put(y, new ArrayList<>());
        }
        map.get(x).get(y).add(node.val);
        
        helper(x-1, y+1, node.left);
        helper(x+1, y+1, node.right);
    }
}
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