# Solving the River Crossing problem with SQL Graph

Solving the River Crossing problem with SQL Graph. Let’s see if we can solve this classic problem, using T-SQL and the graph capabilities in Azure SQL / SQL Server!

Are you are familiar with the classic “river crossing” problem? If not, an easy 4 minutes introduction using Wildebeest and Lions as the actors in the problem, is presented in this TED-Ed talk. If you observe carefully, the video briefly mentions using an enumeration approach to list all the possible transitions, and for each transition, the end state. It so happens that this is the classic algorithmic approach as well to solve such problems – to create a graph of all possible states (represented by vertices / nodes in the graph) and the transitions (represented by edges) which result into those states. If you search online, there are plenty of references showing you how to use Breadth-First-Search (BFS) to find the shortest path to solve the problem. David Kopec’s Classic Computer Science Problems books also present implementations of this problem in Python and other languages.

Let’s see if we can solve this classic problem, using T-SQL and the graph capabilities in Azure SQL / SQL Server!

## Governing Rules

Let’s present the main “rules” of this problem, as presented in the TED talk:

1. There are 3 wildebeest and 3 lions, all located on one bank (for completeness, we have the West bank, and the East bank) of a river. They are trying to cross the other river bank.
2. As it turns out, wildebeest are a natural prey for the lions. Therefore, there is a “rule” which states that if the number of wildebeest either equal, or outnumber the number of lions, on the same bank of the river, they are safe. In our context, we will call this a “safe” state.
3. Conversely, If the number of wildebeest are lesser than the number of lions, they are unsafe. In our context, we will refer to this as an “unsafe” or “disallowed” state, as we don’t want the wildebeest to come to harm!
4. Let’s also imagine, that these animals know how to use a raft, to cross the river However, the raft can only take 2 animals at any time, and obviously, the raft is not “autonomous”, and needs an animal or 2 animals on board to move from one bank of the river to the other.
5. At any given point in time, rules 2 and 3 must continuously be applied, even when 2 animals are on the raft!

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