662. Maximum Width of Binary Tree

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DFS

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class Solution {
    private static class State {
        private int maxWidth;
    }

    public int widthOfBinaryTree(TreeNode root) {
        State state = new State();
        Map<Integer, Integer> depthToLeftIndexMap = new HashMap<>();
        dfs(root, depthToLeftIndexMap, 0, 1, state);
        return state.maxWidth;
    }

    private void dfs(TreeNode root, Map<Integer, Integer> depthToLeftIndexMap, int depth, int index, State state) {
        if (root == null) {
            return;
        }

        depthToLeftIndexMap.putIfAbsent(depth, index);
        state.maxWidth = Math.max(state.maxWidth, index - depthToLeftIndexMap.get(depth) + 1);

        dfs(root.left, depthToLeftIndexMap, depth + 1, index * 2, state);
        dfs(root.right, depthToLeftIndexMap, depth + 1, index * 2 + 1, state);
    }
}

BFS

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class Solution {
    public int widthOfBinaryTree(TreeNode root) {
        int maxWidth = 1;

        Queue<TreeNode> queue = new LinkedList<>(); // 队列中不包含空节点
        Deque<Integer> indexDeque = new LinkedList<>();

        queue.offer(root);
        indexDeque.offer(1);
        
        while (!queue.isEmpty()) {
            for (int i = queue.size(); i > 0; i--) {
                TreeNode node = queue.poll();
                int index = indexDeque.poll();

                if (node.left != null) {
                    queue.offer(node.left);
                    indexDeque.offer(index * 2);
                }
                if (node.right != null) {
                    queue.offer(node.right);
                    indexDeque.offer(index * 2 + 1);
                }
            }

            if (!indexDeque.isEmpty()) {
                maxWidth = Math.max(maxWidth, indexDeque.getLast() - indexDeque.getFirst() + 1);
            }
        }

        return maxWidth;
    }
}

队列中不存储空节点，以避免二叉树高度很高时需要存储大量的空节点导致内存溢出。

References

662. Maximum Width of Binary Tree