998. Check Completeness of a Binary Tree

• Difficulty: Medium

• Topics: Tree

• Similar Questions:

Problem:

Given a binary tree, determine if it is a complete binary tree.

Definition of a complete binary tree from Wikipedia:
In a complete binary tree every level, except possibly the last, is completely filled, and all nodes in the last level are as far left as possible. It can have between 1 and 2^h nodes inclusive at the last level h.

Example 1:

Input: [1,2,3,4,5,6]
Output: true
Explanation: Every level before the last is full (ie. levels with node-values {1} and {2, 3}), and all nodes in the last level ({4, 5, 6}) are as far left as possible.

Input: [1,2,3,4,5,null,7]
Output: false
Explanation: The node with value 7 isn't as far left as possible.

Note:

1. The tree will have between 1 and 100 nodes.

Solutions:

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
 * };
 */
class Solution {
public:
    bool isCompleteTree(TreeNode* root) {
        if (root == nullptr)    return true;
        queue<TreeNode*> q;
        q.push(root);

        int level = 0;
        bool lastLevel = false;
        while (!q.empty()) {
            int n = q.size();
            if ((1 << level) != n) {
                lastLevel = true;
            }
            for (int i = 0; i < n; ++i) {
                TreeNode* node = q.front(); q.pop();
                if (!node->left && node->right) return false;
                if (node->left) {
                    if (lastLevel)  return false;
                    q.push(node->left);
                } else {
                    lastLevel = true;
                }

                if (node->right) {
                    if (lastLevel)  return false;
                    q.push(node->right);
                } else {
                    lastLevel = true;
                }
            }
            ++level;
        }

        return true;
    }
};