Place a Binary Tree in Its Prescribed String Grid

### Problem Construct a string grid for root. Let h be tree height in edges, so the grid has h+1 rows and 2^(h+1)-1 columns. Put root at row 0 and the middle column. A node at (r,c) places its children at row r+1 and columns c-2^(h-r-1) and c+2^(h-r-1), respectively. Fill every unused cell with "" and store node values as decimal strings. ```cpp class Solution { public: vector<vector<string>> printTree(TreeNode* root); }; ``` ### Examples **Example 1:** ```text root = [7,2,9] Output: [["","7",""],["2","","9"]] Explanation: Height one gives three columns. ``` **Example 2:** ```text root = [-4] Output: [["-4"]] Explanation: Height zero gives one row and one column. ``` ### Constraints - Tree size: 1..1024 nodes. Node values are in -99..99, and tree depth in nodes is in 1..10. ### Clarifying Questions Use the exact row and column formulas and retain empty strings rather than spaces or null values. ```hint Read the boundary condition How does each child's reserved column interval relate to its parent's interval? ``` ### Contract considerations Use the exact row and column formulas and retain empty strings rather than spaces or null values.