Problem editorial

Construct Quad Tree

MediumTree Traversal Patterns (DFS & BFS)ArrayMatrixTree

Construct Quad Tree: the approach in brief

The problem

Implement Solution.construct(grid) to build a quad tree representing the binary matrix grid. The matrix has n rows and n columns. A node represents a square region of the matrix and has an isLeaf flag, a val, and up to four children in this order: topLeft, topRight, bottomLeft, and bottomRight.

Pattern

Construct Quad Tree is a Tree Traversal Patterns (DFS & BFS) problem, in the Recursive Preorder Traversal subpattern. The pattern covers preorder, inorder, level order traversal, LCA, and serialization

Approach outline

Represent each recursive call by the boundaries of one square region.
Before splitting a region, determine whether all of its cells have one value.
A mixed region is divided at its midpoint into four quadrants; preserve the required child order.

Complexity

The reference solution runs in O(n^2) time and O(n^2) space.

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Practise Construct Quad Tree and the problems around it

Construct Quad Tree is a Tree Traversal Patterns (DFS & BFS) problem, in the Recursive Preorder Traversal subpattern. Once the approach above makes sense, write it yourself and then work through the neighbouring problems that reuse it.

Construct Quad Tree