Leetcode 684: redudant connection

January 17, 2018

Introduction

It is the second time to meet the peer again in less than one week. Julia chose to give a medium level algorithm for peer to solve, Leetcode 684: redudant connection.

Discussion

Here is the transcript for the discussion.

Highlights of good things in discussion

Peer did:

1. First the peer came out to check if the graph has a cycle

2. Second the peer drew a more complicated tree, and then try to add one edge to make it a cycle

3. Third the peer write down a list of graph algorithm he worked before.



I try not to give out hint explicitly. So what I talk is about the example a tree drawed by the peer how node 1 is connected to node 7.

What is the connected meaning for us? The nodes are connected.

Also, I added one more graph algorithm called Kruskal algorithm, and then share the wiki page for the algorithm. I talked about the algorithm for minimum spanning tree using disjoint set data structure. And then I asked if the peer knew the data structure before.

I explained the data structure, what is for, why we need this data structure. Since the path from one node to other node is not needed, all we care about is if two nodes are connected. We do not need to search a path from one node to other node.

At last, I tried to give the explanation how to solve it in less than five minutes.


Example 2:
Input: [[1,2], [2,3], [3,4], [1,4], [1,5]]
Output: [1,4]
Explanation: The given undirected graph will be like this:
5 - 1 - 2
    |   |
    4 - 3         
 

Julia's explantion:


At the beginning, each node has its own set.
{1}, {2}, {3}, {4}, {5}.

[1,2] first edge is to connect 1 to 2, so {2} likes to join {1].


{1} <- {2}, {3}, {4}, {5}.

we have {1, 2}, {3}, {4}, {5}.

[2,3] second edge is to connect 2 to 3, 2 is not the set, but 3 is not in the set.


{1, 2} <- {3}, {4}, {5}
we have {1, 2, 3}, {4}, {5}

[3,4] third edge is to connect 3 to 4, 3 is in the set, but 4 is not in the set.

{1, 2, 3} <-{4}, {5}
we have {1, 2, 3, 4}, {5}

[1, 4] fourth edge is to connect 1 to 4, 1 is in the set, and 4 is also in the set. Then we know that node 1 and node 4 are connected, but direct connected edge 1 to 4 is to be added. Then edge [1, 4] is to form a cycle.