Problem Statement

A tree is a connected graph with no cycles. A rooted tree has one special vertex - the root (vertex 2 in the picture below).

Vertex w is an ancestor of vertex v if w lies on the shortest path from the root to v. Vertex w is a parent of vertex v if it is an ancestor of v and is directly connected to v. For example, vertices 0, 2 and 4 are ancestors of vertex 0, and vertex 4 is a parent of vertex 0. The lowest common ancestor (LCA) of vertices v and w is the common ancestor of v and w which is located as far from the root as possible. For example, the LCA of vertices 1 and 3 is vertex 2, and the LCA of vertices 5 and 0 is vertex 4.

You will be given a String[] lca, with each element of lca being a space-separated list of integers. The i-th integer in the j-th element of lca represents the LCA of vertices i and j (all indices are 0-based). Using this information, you are to reconstruct the whole rooted tree. Find parents for all the vertices and return them in a int[]. The i-th element of the result must represent the parent of vertex i (use -1 for the parent of the root).

Definition

Class:              InverseLca
Method:             getParents
Parameters:         String[]
Returns:            int[]
Method signature:   int[] getParents(String[] lca)
(be sure your method is public)

Constraints

• lca will contain between 1 and 25 elements, inclusive.
• Each element of lca will contain between 1 and 50 characters, inclusive.
• Each element of lca will contain exactly K single space separated non-negative integers, where K is the number of elements in lca.
• Each number in each element of lca will be between 0 and (K - 1) inclusive, where K is the number of elements in lca.
• Each number in each element of lca will contain no leading zeroes.
• The i-th number in the i-th element of lca will be equal to i.
• The i-th number in the j-th element of lca will be equal to the j-th number in the i-th element of lca.
• lca will represent a valid tree.

Examples

0)

{"0 0 0", 
 "0 1 0",
 "0 0 2"}
Returns: {-1, 0, 0 }
A simple tree with 3 vertices. Vertex 0 is the parent for both vertices 1 and 2.
1)

{"0 0 0",
 "0 1 1",
 "0 1 2"}
Returns: {-1, 0, 1 }

2)

{"0 2 2 2 4 4 2", 
 "2 1 2 2 2 2 6", 
 "2 2 2 2 2 2 2", 
 "2 2 2 3 2 2 2", 
 "4 2 2 2 4 4 2", 
 "4 2 2 2 4 5 2", 
 "2 6 2 2 2 2 6"}
Returns: {4, 6, -1, 2, 2, 4, 2 }
The example from the problem statement.
3)

{"0 0 0 0","0 1 0 1","0 0 2 0","0 1 0 3"}
Returns: {-1, 0, 0, 1 }

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