Minimum number of throws required to win Snake and Ladder game

Find minimum number of throws required to win given Snake and Ladder game.


For example,

For below game, minimum number of dice throws required is atleast 7 to win.

  Snake and Ladder Problem
 


 

The idea is to consider the snack and ladder board as directed graph and run BFS from starting node which is vertex 0 as per game rules. We construct a directed graph keeping in mind below conditions –

1. For any vertex in the graph v, we have an edge from v to v + 1, v + 2, v + 3, v + 4, v + 5, v + 6 as we can reach any of these nodes in one throw of dice from node v.

2. If any of these neighbors of v has a ladder or snake which takes you to position x, then x becomes the neighbor instead of the base of the ladder or head of the snake.

Now the problem is transformed into a Shortest path between two nodes in a directed graph problem. We represent the snake and ladder board using a map.

 
C++ implementation –
 

Download   Run Code

Output:

7

Image credits: shutterstock.com

 
Thanks for reading.




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