968. Binary Tree Cameras

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968. Binary Tree Cameras

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.

Example 1:

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

Example 2:

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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.

Constraints:

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

Hints/Notes

  • binary tree

Solution

Language: C++

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/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode() : val(0), left(nullptr), right(nullptr) {}
 *     TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
 *     TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left),
 * right(right) {}
 * };
 */
class Solution {
public:
    int res = 0;

    int minCameraCover(TreeNode* root) {
        setCamera(root, false, 0);
        return res;
    }

    // the meaning of the return value:
    // 1. -1: the node doesn't exist, or it's lit by its children
    // 2. 0: the node is leaf
    // 3. 1: the node has one camera
    int setCamera(TreeNode* root, bool hasParent, int depth) {
        if (!root) {
            return -1;
        }

        int l = setCamera(root->left, true, depth + 1);
        int r = setCamera(root->right, true, depth + 1);

        if (l == -1 && r == -1) {
            if (hasParent) {
                return 0;
            } else {
                res++;
                return 1;
            }
        }

        if (l == 0 || r == 0) {
            res++;
            return 1;
        }

        // the above conditions have ensured that there's
        // at least one 1 in l and r
        return -1;
        // if (l == 1 || r == 1) {
        //     return -1;
        // }
    }
};