Day-07-Vertical Order Traversal of a Binary Tree.cpp

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() : val(0), left(nullptr), right(nullptr) {}
 *     TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
 *     TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
 * };
 */

struct nodes {
    int x, y, val;
};

class Solution {
public:

    vector<nodes> coords;

    static bool comp(nodes a, nodes b){
        if(a.x < b.x) return true;
        else if(a.x > b.x) return false;
        else if(a.y > b.y) return true;
        else if(a.y < b.y)return false;
        else return a.val < b.val;
    }

    void traversal(TreeNode* root, int x, int y){
        if(!root) return;
        coords.push_back({x, y, root->val});
        traversal(root->left, x-1, y-1);
        traversal(root->right, x+1, y-1);

    }

    vector<vector<int>> verticalTraversal(TreeNode* root) {
        vector<vector<int>> res;

        traversal(root, 0, 0);  // <root, x coordinate, y coordinate>

        sort(coords.begin(), coords.end(), comp);

        int n=coords.size(), i=0;
        while(i<n){
            vector<int> tmp;
            do {
                tmp.push_back(coords[i].val);
                i++;
            }while(i<n && coords[i].x==coords[i-1].x);
            res.push_back(tmp);
        }


        return res;

    }
};