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#558 - Logical OR of Two Binary Grids Represented as Quad-Trees

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Problem Description

A Binary Matrix is a matrix in which all the elements are either 0 or 1.

Given quadTree1 and quadTree2. quadTree1 represents a n * n binary matrix and quadTree2 represents another n * n binary matrix.

Return a Quad-Tree representing the n * n binary matrix which is the result of logical bitwise OR of the two binary matrixes represented by quadTree1 and quadTree2.

Notice that you can assign the value of a node to True or False when isLeaf is False, and both are accepted in the answer.

A Quad-Tree is a tree data structure in which each internal node has exactly four children.

Besides, each node has two attributes:

  • val: True if the node represents a grid of 1's or False if the node represents a grid of 0's.
  • isLeaf: True if the node is leaf node on the tree or False if the node has the four children.

class Node { public boolean val; public boolean isLeaf; public Node topLeft; public Node topRight; public Node bottomLeft; public Node bottomRight; }.

We can construct a Quad-Tree from a two-dimensional area using the following steps:

  1. If the current grid has the same value (i.e all 1's or all 0's) set isLeaf True and set val to the value of the grid and set the four children to Null and stop.
  2. If the current grid has different values, set isLeaf to False and set val to any value and divide the current grid into four sub-grids as shown in the photo.
  3. Recurse for each of the children with the proper sub-grid.

Solution

/**
 * // Definition for a QuadTree node.
 * function _Node(val,isLeaf,topLeft,topRight,bottomLeft,bottomRight) {
 *    this.val = val;
 *    this.isLeaf = isLeaf;
 *    this.topLeft = topLeft;
 *    this.topRight = topRight;
 *    this.bottomLeft = bottomLeft;
 *    this.bottomRight = bottomRight;
 * };
 */

/**
 * @param {_Node} quadTree1
 * @param {_Node} quadTree2
 * @return {_Node}
 */
var intersect = function(quadTree1, quadTree2) {
  if (quadTree1.isLeaf) return quadTree1.val ? quadTree1 : quadTree2;
  if (quadTree2.isLeaf) return quadTree2.val ? quadTree2 : quadTree1;

  const topLeft = intersect(quadTree1.topLeft, quadTree2.topLeft);
  const topRight = intersect(quadTree1.topRight, quadTree2.topRight);
  const bottomLeft = intersect(quadTree1.bottomLeft, quadTree2.bottomLeft);
  const bottomRight = intersect(quadTree1.bottomRight, quadTree2.bottomRight);

  if (topLeft.isLeaf && topRight.isLeaf && bottomLeft.isLeaf && bottomRight.isLeaf
      && topLeft.val === topRight.val && topRight.val === bottomLeft.val
      && bottomLeft.val === bottomRight.val) {
    return new _Node(topLeft.val, true, null, null, null, null);
  }

  return new _Node(false, false, topLeft, topRight, bottomLeft, bottomRight);
};