Construct Quad Tree

class Solution {
public:
    Node* constructSubtree(vector<vector<int>>& matrix, int x, int y, int len) {
        if (len == 1) {
            return new Node(matrix[x][y], true);
        }

        Node* topLeftNode = constructSubtree(matrix, x, y, len / 2);
        Node* topRightNode = constructSubtree(matrix, x, y + len / 2, len / 2);
        Node* bottomLeftNode = constructSubtree(matrix, x + len / 2, y, len / 2);
        Node* bottomRightNode = constructSubtree(matrix, x + len / 2, y + len / 2, len / 2);

        if (topLeftNode -> isLeaf && topRightNode -> isLeaf && 
            bottomLeftNode -> isLeaf && bottomRightNode -> isLeaf &&
            topLeftNode -> val == topRightNode -> val && 
            topRightNode -> val == bottomLeftNode -> val && 
            bottomLeftNode -> val == bottomRightNode -> val) {
            return new Node(topLeftNode -> val, true);
        }

        return new Node(false, false, topLeftNode, topRightNode, bottomLeftNode, bottomRightNode);
    }

    Node* build(vector<vector<int>>& matrix) {
        return constructSubtree(matrix, 0, 0, matrix.size());
    }
};

The provided C++ code outlines a solution for constructing a quad tree from a given 2D matrix. This code effectively decomposes the matrix into submatrices until each element is individually represented in the quad tree, maintaining the groupings where possible. Here’s a breakdown of the program's functionality:

• Node Structure: A custom node class Node is likely used, which should include properties like the node's value (val), whether it is a leaf (isLeaf), and references to its child nodes (topLeft, topRight, bottomLeft, bottomRight).

• Function constructSubtree():

  • This recursively generates the tree.
  • Base case: If the current submatrix length (len) is 1, creates a new node that directly represents the value of the matrix at that point.
  • Recursive division: If len is greater than 1, the matrix is split into four equal parts:
    • Top left
    • Top right
    • Bottom left
    • Bottom right
  • Each quadrant is processed through recursive calls with halved length.
  • After processing, if all four nodes are leaves and contain same value, they are merged into a single node. Otherwise, the node representing current quadrant is set as an internal node linking all four child areas.

• Function build():

  • Acts as an initial trigger for constructSubtree() function, covering the entire matrix size.

This approach is efficient in reducing the complexity of the data when uniform regions are present in the matrix, thereby significantly compressing the data size when possible. Ensure your implementations of Node and other system specifics adhere closely to what is described to ensure seamless functionality and accurate tree creation.

class Solution {
    private Node processGrid(int[][] matrix, int topLeftX, int topLeftY, int size) {
        if (size == 1) {
            return new Node(matrix[topLeftX][topLeftY] == 1, true);
        }

        Node tl = processGrid(matrix, topLeftX, topLeftY, size / 2);
        Node tr = processGrid(matrix, topLeftX, topLeftY + size / 2, size / 2);
        Node bl = processGrid(matrix, topLeftX + size / 2, topLeftY, size / 2);
        Node br = processGrid(matrix, topLeftX + size / 2, topLeftY + size / 2, size / 2);

        if (tl.isLeaf && tr.isLeaf && bl.isLeaf && br.isLeaf
            && tl.val == tr.val && tr.val == bl.val && bl.val == br.val) {
            return new Node(tl.val, true);
        }

        return new Node(false, false, tl, tr, bl, br);
    }

    public Node construct(int[][] matrix) {
        return processGrid(matrix, 0, 0, matrix.length);
    }
}

The Java solution provided is an implementation of constructing a Quad Tree from a 2D matrix. The Quad Tree is a type of data structure suitable for managing hierarchical spatial data. Each node in this tree can either store a single value if it's a leaf node, or it can link to four children representing the subdivisions of the area that the node covers.

To implement this, the solution defines a recursive method processGrid which checks if the current part of the matrix it's examining is uniform in value. Here's how it operates:

• Base Case: If the subdivided region is a single element (size == 1), it returns a leaf node with the value set to the element's value (either true if 1 or false if 0).
• Recursive Case: The method splits the region into four equal parts and processes each part:
  • Top-left (tl)
  • Top-right (tr)
  • Bottom-left (bl)
  • Bottom-right (br)
• After recursive division, if all four parts are leaf nodes and have the same boolean value, those parts are consolidated into a single leaf node representing that larger area. If the values differ, it creates a parent node with those four parts as children but sets the node as non-leaf.

The main construct method serves as an entry point that initiates the recursion from the top level of the matrix spanning its entire dimension.

This efficient Quad Tree building process divides the data until all minimum units (matrix elements) are processed, either creating leaf nodes for homogeneous areas or parent nodes for mixed data, providing effective spatial decomposition that can be essential for applications like image processing or spatial analysis.