题目

https://www.geeksforgeeks.org/largest-independent-set-problem-dp-26/

给一个binary tree，我们定义non-connected set是指互不直接相连的node的集合，求这种non-connected set最多有几个node。

例子

                   10
               /        \
            20           30
          /    \           \
        40      50          60      
              /    \
            70      80

Largest non-connected set in the binary tree. A subset of all tree nodes is an independent set if there is no edge between any two nodes of the subset.

Non-connected set:

|10, 40, 50, 60| = 4
|10, 40, 70, 80, 60| = <--- largest non-connected set
|20, 30, 70, 80| = 4

{10, 40, 60, 70, 80} and size is 5.

解法

public class Solution {
    public int lisp(Node root) {
        int[] candidates = findLiss(root);
        return Math.max(candidates[0], candidates[1]);
    } 

    private int[] findLiss(TreeNode node) {
        int[] size = new int[2]; // size[0]表示exclude，size[1]表示include
        if (root == null) {
            return new int[2];
        }
        int[] left = findLiss(root.left);
        int[] right = findLiss(root.right);
        size[0] = Math.max(left[0], left[1]) + Math.max(right[0], right[1]);
        size[1] = 1 + left[0] + right[0];
       
        return size;
    }
}