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   Problem Statement  

 Problem Statement for WalkOverATree

Problem Statement

    

Given is a tree on n nodes. The nodes are numbered 0 through n-1. You are given the description of the tree as a int[] parent with n-1 elements. For each valid i, there is an edge between vertices (i+1) and parent[i].

A person is currently standing in node 0. In a single step, the person can move from its current node to any adjacent node. You are given an int L. The person is allowed to make at most L steps.

Return the maximum number of nodes the person can visit during the walk. Node 0 (where the walk starts) and the node where the walk ends count as visited. Each visited node is only counted once, even if it is visited multiple times.

 

Definition

    
Class:WalkOverATree
Method:maxNodesVisited
Parameters:int[], int
Returns:int
Method signature:int maxNodesVisited(int[] parent, int L)
(be sure your method is public)
    
 

Constraints

-parent will contain between 0 and 49 elements, inclusive.
-For each i, parent[i] will be between 0 and i, inclusive.
-L will be between 1 and 100, inclusive.
 

Examples

0)
    
{0, 0}
2
Returns: 2
The tree consists of edges 1-0 and 2-0. Our person will start in node 0 and can make at most L=2 steps. In two steps, the best we can do is visit one of the nodes 1 and 2.
1)
    
{0, 0}
3
Returns: 3
This is the same tree, only now we have L=3. In three steps the person can visit all three nodes: for example, by going from node 0 to node 1, back to node 0, and finally to node 2. Note that even though the person visited node 0 twice, we only count it once.
2)
    
{0, 1, 2, 3}
2
Returns: 3
3)
    
{0,0,0,0,2,4,2,3,1}
1
Returns: 2
4)
    
{0,0,1,2,3,2,3,1,3,0,1,8,6,8,0,5,15,0,9}
4
Returns: 5
5)
    
{0,0,0,1,1,3,5,1,4,5,2,2,10,5,10,10,11,13,8,3,18,15,20,20,23,8,11,26,4}
26
Returns: 17
6)
    
{0, 0, 2, 0}
100
Returns: 5
As the tree is very small and L large, the person can easily visit all nodes.
7)
    
{0, 0, 2}
4
Returns: 4

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This problem was used for:
       Single Round Match 666 Round 1 - Division I, Level One