dev-elle-up / bipartition-graph

An exercise working with graphs

Partitioning a Graph

In this exercise you will take in an adjacency list and determine if you can break the map into two sections where no two elements from the same section are adjacent. This is a variation on the graph coloring problem as it can be extended to breaking the graph into k groups, each labeled with a color.

Learning Goals

In this exercise you should be able to:

• Work with an adjacency list to process a graph.
• Navigate a graph through a traversal

Description

Given a set of N puppies (numbered 1, 2, ..., N), we would like to split them into two groups of any size to use two play areas.

Some dogs have a history of fighting with specific other dogs and shouldn't be put into the same play area.

Formally, if dislikes[i] = [a, b], it means it is not allowed to put the people numbered a and b into the same group.

Return true if and only if it is possible to split everyone into two groups in this way.

Example 1

Input: dislikes = [ [],
                    [2, 3],
                    [1, 4],
                    [1],
                    [2]
                  ]
Output: true

Explanation: group1 [0, 1, 4], group2 [2, 3]

Example 2

Input: dislikes = [ [],
                    [2, 3],
                    [1, 3],
                    [1, 2]
                  ]
Output: false

Explanation: All the nodes 1-3 are interconnected and so there is no way to split them up.

Example 3

Input: dislikes = [ [],
                    [2, 5],
                    [1, 3],
                    [2, 4],
                    [3, 5],
                    [1, 4]
                  ]
Output: false

Note

The graph is undirected, so if dog 1 dislikes dog 2, then dog 2 also dislikes dog 1.

Source

• Leetocde 886. Possible Bipartition