Tree DP Minimum Vertex Cover

Problem

Compute the size of a minimum vertex cover of a tree with dynamic programming.

Root the tree at node 0. For each node keep take[v] = 1 + sum of min over children and skip[v] = sum of take over children, because an uncovered edge forces the child into the cover. Return the better of take and skip at the root. edges is a list of [u, v] pairs.

Hint

If a node stays out of the cover, every child must be inside it.

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: 1

case 3

in: [1,[]]

expected: 0

case 4

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

expected: 2

case 5

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

expected: 1

Starter codePython

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

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