987.vertical-order-traversal-of-a-binary-tree.cpp

/*
 * @lc app=leetcode id=987 lang=cpp
 *
 * [987] Vertical Order Traversal of a Binary Tree
 *
 * https://leetcode.com/problems/vertical-order-traversal-of-a-binary-tree/description/
 *
 * algorithms
 * Medium (33.38%)
 * Likes:    98
 * Dislikes: 236
 * Total Accepted:    8.2K
 * Total Submissions: 25.2K
 * Testcase Example:  '[3,9,20,null,null,15,7]'
 *
 * 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:
 * 
 * 
 * The tree will have between 1 and 1000 nodes.
 * Each node's value will be between 0 and 1000.
 * 
 * 
 * 
 * 
 * 
 * 
 * 
 */
/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
 * };
 */
#include<bits/stdc++.h>
using namespace std;

class Solution {
public:
    map<int, map<int, vector<int>>> mm;
    void traverse(TreeNode* root, int x, int y){
        if(root == NULL)    return;
        mm[x][y].push_back(root->val);
        traverse(root->left, x-1, y+1);
        traverse(root->right, x+1, y+1);
    }
    vector<vector<int>> verticalTraversal(TreeNode* root) {
        mm.clear();
        traverse(root, 0, 0);
        vector<vector<int>> ans;
        for(auto x: mm){
            vector<int> tmp;
            for(auto y: mm[x.first]){
                sort(y.second.begin(), y.second.end());
                for(auto e: y.second)
                    tmp.push_back(e);
            }
            ans.push_back(tmp);
        }
        return ans;
    }
};