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 –

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If you’re using the int for BFS definition, it should either return node.minDist or if you’re printing as in this case, it should just be void. Something super minor but I figured it’s best if the code is updated. Thanks for all these wonderful questions 🙂