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LeetCode - Binary Tree Level Order Traversal

Problem statement

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

Problem statement taken from: https://leetcode.com/problems/binary-tree-level-order-traversal

Example 1:

Container

Input: root = [3, 9, 20, null, null, 15, 7]
Output: [[3], [9, 20], [15, 7]]

Example 2:

Input: root = [1]
Output: [[1]]

Example 3:

Input: root = []
Output: []

Constraints:

- The number of nodes in the tree is in the range [0, 2000]
- -1000 <= Node.val <= 1000

Explanation

Recursive function

With trees, recursion is the most widely used approach as the code is easy to read. But for a few problems, recursion increases the time complexity. For large trees, recursion can result in stack overflow or because of O(N^2) time complexity will take a lot of time.

For this problem, we can use recursion, but we need to calculate the height of the tree.

A small C++ snippet of the above approach will look as below:

void printLevelOrder(node* root){
    int h = height(root);
    for (int i = 0; i < h; i++)
        printCurrentLevel(root, i);
}

void printLevel(node* root, int level){
    if (root == NULL)
        return;

    if (level == 0)
        cout << root->data << " ";
    else if (level > 0) {
        printLevel(root->left, level - 1);
        printLevel(root->right, level - 1);
    }
}

The time complexity of the above approach is O(N^2) for skewed trees. The worst-case space complexity is O(N).

Iterative approach

We can improve the time complexity by using a queue as a data structure. Let's check the algorithm.

- initialize 2D array as vector vector<vector<int>> result
- initialize size and i

- return result if root == null

- initialize queue<TreeNode*> q
  - push root to queue : q.push(root)

- initialize TreeNode* node for iterating on the tree

- loop while( !q.empty() ) // queue is not empty
  - initialize vector<int> tmp
  - set size = q.size()

  - loop for i = 0; i < size; i++
    - set node = q.front()

    - if node->left
      - push in queue: q.push(node->left)

    - if node->right
      - push in queue: q.push(node->right)

    - remove the front node: q.pop()

  - push the tmp to result: result.push_back(tmp)

- return result

C++ solution

class Solution {
public:
    vector<vector<int>> levelOrder(TreeNode* root) {
        vector<vector<int>> result;
        int size, i;

        if(root == NULL)
            return result;

        queue<TreeNode*> q;
        q.push(root);

        TreeNode* node;

        while(!q.empty()){
            vector<int> tmp;
            size = q.size();

            for(i = 0; i < size; i++){
                node = q.front();
                if(node->left)
                    q.push(node->left);

                if(node->right)
                    q.push(node->right);

                q.pop();
                tmp.push_back(node->val);
            }

            result.push_back(tmp);
        }

        return result;
    }
};

Golang solution

func levelOrder(root *TreeNode) [][]int {
    result := [][]int{}

    queue := []*TreeNode{root}

    for len(queue) != 0 {
        tmp := []int{}
        size := len(queue)

        for i := 0; i < size; i++ {
            if queue[0] != nil {
                tmp = append(tmp, queue[0].Val)
                queue = append(queue, queue[0].Left)
                queue = append(queue, queue[0].Right)
            }

            queue = queue[1:]
        }

        result = append(result, tmp)
    }

    return result[:len(result)-1]
}

Javascript solution

var levelOrder = function(root) {
    let result = [];
    let queue = [];

    if(root)
        queue.push(root);

    while(queue.length > 0) {
        tmp = [];
        let len = queue.length;

        for (let i = 0; i< len; i++) {
            let node = queue.shift();
            tmp.push(node.val);

            if(node.left) {
                queue.push(node.left);
            }

            if(node.right) {
                queue.push(node.right);
            }
        }

        result.push(tmp);
    }

    return result;
};

Let's dry-run our algorithm to see how the solution works.

Input: root = [3, 9, 20, null, null, 15, 7]

Step 1: vector<vector<int>> result;
        int size, i;

Step 2: root == null
        [3, 9..] == null
        false

Step 3: queue<TreeNode*> q;
        q.push(root);

        q = [3]

Step 4: loop !q.empty()
        q = [3]
        q.empty() = false
        !false = true

        vector<int> tmp
        size = q.size()
             = 1

        for(i = 0; i < 1; i++)
          - 0 < 1
          - true

          node = q.front()
          node = 3

          if node->left
            - node->left = 9
            - q.push(node->left)
            - q = [3, 9]

          if node->right
            - node->right = 20
            - q.push(node->right)
            - q = [3, 9, 20]


          q.pop()
          q = [9, 20]

          tmp.push_back(node->val)
          tmp.push_back(3)

          i++
          i = 1

        for(i < 1)
        1 < 1
        false

        result.push_back(tmp)
        result = [[3]]

Step 5: loop !q.empty()
        q = [9, 20]
        q.empty() = false
        !false = true

        vector<int> tmp
        size = q.size()
             = 2

        for(i = 0; i < 2; i++)
          - 0 < 2
          - true

          node = q.front()
          node = 9

          if node->left
            - node->left = nil
            - false

          if node->right
            - node->right = nil
            - false

          q.pop()
          q = [20]

          tmp.push_back(node->val)
          tmp.push_back(9)

          i++
          i = 1

        for(i < 2)
          - 1 < 2
          - true

          node = q.front()
          node = 20

          if node->left
            - node->left = 15
            - q.push(node->left)
            - q = [20, 15]

          if node->right
            - node->left = 7
            - q.push(node->right)
            - q = [20, 15, 7]

          q.pop()
          q = [15, 7]

          tmp.push_back(node->val)
          tmp.push_back(20)
          tmp = [9, 20]

          i++
          i = 2

        for(i < 2)
          - 2 < 2
          - false

        result.push_back(tmp)
        result = [[3], [9, 20]]

Step 6: loop !q.empty()
        q = [15, 7]
        q.empty() = false
        !false = true

        vector<int> tmp
        size = q.size()
             = 2

        for(i = 0; i < 2; i++)
          - 0 < 2
          - true

          node = q.front()
          node = 15

          if node->left
            - node->left = nil
            - false

          if node->right
            - node->right = nil
            - false

          q.pop()
          q = [7]

          tmp.push_back(node->val)
          tmp.push_back(15)

          i++
          i = 1

        for(i < 2)
          - 1 < 2
          - true

          node = q.front()
          node = 7

          if node->left
            - node->left = nil
            - false

          if node->right
            - node->right = nil
            - false

          q.pop()
          q = []

          tmp.push_back(node->val)
          tmp.push_back(7)
          tmp = [15, 7]

          i++
          i = 2

        for(i < 2)
          - 2 < 2
          - false

        result.push_back(tmp)
        result = [[3], [9, 20], [15, 7]]

Step 7: loop !q.empty()
        q = []
        q.empty() = true
        !true = false

Step 8: return result

So we return the result as [[3], [9, 20], [15, 7]].
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