968. Binary Tree Cameras

1. Description

You are given the root of a binary tree. We install cameras on the tree nodes where each camera at a node can monitor its parent, itself, and its immediate children.
Return the minimum number of cameras needed to monitor all nodes of the tree.

2. Example

Example 1:

Input: root = [0,0,null,0,0]
Output: 1
Explanation: One camera is enough to monitor all nodes if placed as shown.

Example 2:

Input: root = [0,0,null,0,null,0,null,null,0]
Output: 2
Explanation: At least two cameras are needed to monitor all nodes of the tree. The above image shows one of the valid configurations of camera placement.

3. Constraints

  • The number of nodes in the tree is in the range [1, 1000].
  • Node.val == 0

4. Solutions

n is the number of nodes in root
Time complexity: O(n)
Space complexity: O(n)

class Solution {
public:
    int minCameraCover(TreeNode *root) {
        if (find_cover_(root) == 2) {
            ++result_;
        }

        return result_;
    }

private:
    int result_ = 0;

    int find_cover_(TreeNode *root) {
        // 0: there is a camera
        // 1: there is no camera but the node has been covered
        // 2: there is no camera and the node has not been covered
        if (root == nullptr) {
            // greedy, try to avoid the camera on the leaf node
            // hard to explain null node return value, so use the status rather than dp array
            return 1;
        } else {
            auto left = find_cover_(root->left);
            auto right = find_cover_(root->right);

            if (left == 2 || right == 2) {
                ++result_;
                return 0;
            } else if (left == 0 && right != 2 || left != 2 && right == 0) {
                return 1;
            } else {
                return 2;
            }
        }
    }
};
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