Level Order of an Indexed Binary Tree

Challenge

Return a list of tree levels, each containing values from left to right. The first level contains only the root. Empty input returns []. The tree is a flat list: nodes[i]=[value, left_index, right_index]. Child indices are zero-based or null (None in Python). The root is index 0. All nodes are reachable exactly once, no cycles or shared children exist, and indices do NOT imply positions in a complete binary tree.

Input and output contract

0 ≤ n ≤ 2,000; |node value| ≤ 1,000,000. A child can have a smaller index than its parent except that the root is 0. Output is nested lists of VALUES, not node indices. w denotes maximum level width.

All tests follow this contract. You do not need to validate malformed input. Return the requested result from binary_tree_level_order; printed output is not your answer. Standard-library tools are allowed. Implement your solution in Python 3.12.

Target complexity: O(n) time; O(w) auxiliary space plus O(n) output

Return values are checked by type. Use the exact function name. Print output is not your answer. Tests have time and memory limits.

Public examples

[[[10, 2, 1], [30, None, None], [20, None, 3], [40, None, None]]]

[[10], [20, 30], [40]]

[[]]

[]

[[[7, None, None]]]

[[7]]

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