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

  • Time: $O(n^2 \log_4 n)$
  • Space: $O(\log_4 n)$
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class Solution {
 public:
  Node* intersect(Node* quadTree1, Node* quadTree2) {
    if (quadTree1->isLeaf)
      return quadTree1->val ? quadTree1 : quadTree2;
    if (quadTree2->isLeaf)
      return quadTree2->val ? quadTree2 : quadTree1;

    Node* topLeft = intersect(quadTree1->topLeft, quadTree2->topLeft);
    Node* topRight = intersect(quadTree1->topRight, quadTree2->topRight);
    Node* bottomLeft = intersect(quadTree1->bottomLeft, quadTree2->bottomLeft);
    Node* bottomRight =
        intersect(quadTree1->bottomRight, quadTree2->bottomRight);

    if (topLeft->val == topRight->val &&        //
        topLeft->val == bottomLeft->val &&      //
        topLeft->val == bottomRight->val &&     //
        topLeft->isLeaf && topRight->isLeaf &&  //
        bottomLeft->isLeaf && bottomRight->isLeaf)
      return new Node(topLeft->val, true);
    return new Node(false, false, topLeft, topRight, bottomLeft, bottomRight);
  }
};

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class Solution {
  public Node intersect(Node quadTree1, Node quadTree2) {
    if (quadTree1.isLeaf)
      return quadTree1.val ? quadTree1 : quadTree2;
    if (quadTree2.isLeaf)
      return quadTree2.val ? quadTree2 : quadTree1;

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

    if (topLeft.val == topRight.val &&       //
        topLeft.val == bottomLeft.val &&     //
        topLeft.val == bottomRight.val &&    //
        topLeft.isLeaf && topRight.isLeaf && //
        bottomLeft.isLeaf && bottomRight.isLeaf)
      return new Node(topLeft.val, true);
    return new Node(false, false, topLeft, topRight, bottomLeft, bottomRight);
  }
}