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:

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.

 

Constraints:

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

 

Solutions

Solution: Greedy + Depth-First Search

• Time complexity: O(n)
• Space complexity: O(h)

 

JavaScript

/**
 * Definition for a binary tree node.
 * function TreeNode(val, left, right) {
 *     this.val = (val===undefined ? 0 : val)
 *     this.left = (left===undefined ? null : left)
 *     this.right = (right===undefined ? null : right)
 * }
 */
/**
 * @param {TreeNode} root
 * @return {number}
 */
const minCameraCover = function (root) {
  const LEAF = 0;
  const CAMERA = 1;
  const PARENT = 2;
  let result = 0;

  const setupCamera = node => {
    if (!node) return PARENT;
    const left = setupCamera(node.left);
    const right = setupCamera(node.right);

    if (left === LEAF || right === LEAF) {
      result += 1;
      return CAMERA;
    }
    return left === CAMERA || right === CAMERA ? PARENT : LEAF;
  };

  const node = setupCamera(root);

  return result + (node === LEAF ? 1 : 0);
};