Binary Tree Level Order Traversal

Question

• leetcode: Binary Tree Level Order Traversal | LeetCode OJ
• lintcode: (69) Binary Tree Level Order Traversal

Problem Statement

Given a binary tree, return the level order traversal of its nodes' values. (ie, from left to right, level by level).

Example

Given binary tree {3,9,20,#,#,15,7},

    3
   / \
  9  20
    /  \
   15   7

return its level order traversal as:

[
  [3],
  [9,20],
  [15,7]
]

Challenge

Challenge 1: Using only 1 queue to implement it.

Challenge 2: Use DFS algorithm to do it.

題解 - 使用隊列

此題爲廣度優先搜索(BFS)的基礎題，使用一個隊列保存每層的節點即可。出隊列和將子節點入隊列的實現使用 for 循環，將每一輪的節點輸出。

C++

/**
 * Definition of TreeNode:
 * class TreeNode {
 * public:
 *     int val;
 *     TreeNode *left, *right;
 *     TreeNode(int val) {
 *         this->val = val;
 *         this->left = this->right = NULL;
 *     }
 * }
 */

class Solution {
    /**
     * @param root: The root of binary tree.
     * @return: Level order a list of lists of integer
     */
public:
    vector<vector<int> > levelOrder(TreeNode *root) {
        vector<vector<int> > result;

        if (NULL == root) {
            return result;
        }

        queue<TreeNode *> q;
        q.push(root);
        while (!q.empty()) {
            vector<int> list;
            int size = q.size(); // keep the queue size first
            for (int i = 0; i != size; ++i) {
                TreeNode * node = q.front();
                q.pop();
                list.push_back(node->val);
                if (node->left) {
                    q.push(node->left);
                }
                if (node->right) {
                    q.push(node->right);
                }
            }
            result.push_back(list);
        }

        return result;
    }
};

Java

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
public class Solution {
    public List<List<Integer>> levelOrder(TreeNode root) {
        List<List<Integer>> result = new ArrayList<List<Integer>>();
        if (root == null) return result;

        Queue<TreeNode> q = new LinkedList<TreeNode>();
        q.offer(root);
        while (!q.isEmpty()) {
            List<Integer> list = new ArrayList<Integer>();
            int qSize = q.size();
            for (int i = 0; i < qSize; i++) {
                TreeNode node = q.poll();
                list.add(node.val);
                // push child node into queue
                if (node.left != null) q.offer(node.left);
                if (node.right != null) q.offer(node.right);
            }
            result.add(new ArrayList<Integer>(list));
        }

        return result;
    }
}

源碼分析

1. 異常，還是異常
2. 使用STL的queue數據結構，將root添加進隊列
3. 遍歷當前層所有節點，注意需要先保存隊列大小，因爲在入隊出隊時隊列大小會變化
4. list保存每層節點的值，每次使用均要初始化

複雜度分析

使用輔助隊列，空間複雜度 $O(n)$, 時間複雜度 $O(n)$.