Tree DP Maximum Independent Set

Problem

Compute the size of a maximum independent set of a tree with dynamic programming.

Root the tree at node 0. For each node keep take[v] = 1 + sum of skip over children and skip[v] = sum of max(take, skip) over children, processing nodes in reverse BFS order. edges is a list of [u, v] pairs. Return the best value at the root.

Hint

A node taken forces every child skipped, but a skipped node lets each child choose freely.

Test cases

case 1

in: [4,[[0,1],[1,2],[2,3]]]

expected: 2

case 2

in: [4,[[0,1],[0,2],[0,3]]]

expected: 3

case 3

in: [1,[]]

expected: 1

case 4

in: [5,[[0,1],[1,2],[1,3],[3,4]]]

expected: 3

case 5

in: [3,[[0,1],[1,2]]]

expected: 2

Starter codePython

def tree_dp_max_independent_set(n, edges):
    # Your code here
    pass

5 test cases · run your code against them in the editor