Snakes and Ladders Optimization

Source: Flipkart Interview Question from Interview Street (taken from Chinmay - CSE IITB Blog)




Problem:

Find the smallest number of jumps (i.e. optimal number of dice throws) needed to win a snakes and ladders game. Assume you are given a board with all the necessary inputs like start/end positions of all ladders and snakes.



Comments

  1. Pratyush Rathore1:24 PM, December 26, 2012

    DAG, with each number as a node. A number x is linked to x + 1, x + 2, .. x + 6 with edge 1. A number with snake's head is linked only to the snakes tail with edge weight 0. A number with ladder's tail is linked only to the number with ladder's head with weight 0.
    BFS with destination = final point.

    Maximum number of edges from a vertex = 6. At worse, I travel each edge exactly once. So, at definitely it is O(n). Although, I am reasonably sure, the complexity in this case will come out to be much lesser.

    ReplyDelete
  2. dante8:11 PM, December 26, 2012

    this question also came during flipkart hiring process at other IITs , i also thought it was a DAG, but one can easily form a cycle here using a snake ,plus the edge weights were different so went with dijkstra later , (however wasn't able to code dijkstra during the time limit , so had to contend with BFS code which wasnt giving full score :/ )

    ReplyDelete
  3. timequalsmoney9:38 PM, October 20, 2013

    I would say it seems like an application of Djiktra's algorithm with source as 0 and destination as 100. Considering every move as unit cost, we just have to find the shortest path... And everything needed is given as input hence we have a graph with edges and weights.

    ReplyDelete

Post a Comment

Popular posts from this blog

Buying Dimsums

Source: Alok Goyal (Stellaris VP, Ex-Helion VC) puzzle blog Problem: A fast food restaurant sells dimsums in boxes of 7 and 3. What’s the greatest number of dimsums a person cannot buy. Generalize it for p and q where p and q are relatively prime. I loved the puzzle. Hope you enjoy it too.
Read more

Fraction Brainteaser

Source: Sent to me by Gaurav Sinha Problem: Siddhant writes a Maths test and correctly answers 5 out of 6 Arithmetic questions and 20 out of 28 Geometry questions.  In total, Siddhant scores 25 out of 34.  Vaibhav writes another Maths test and correctly answers 20 out of 25 Arithmetic questions and 6 out of 9 Geometry questions. in total, Vaibhav scores 26 out of 34. Note that a) Vaibhav scores more than Siddhant b) Siddhant score better than Vaibhav in both individual topics -  5/6 > 20/25 and 20/28 > 6/9 How is it possible? 
Read more

Consecutive Heads

Let's say A keep tossing a fair coin, until he get 2 consecutive heads, define X to be the number of tosses for this process; B keep tossing another fair coin, until he get 3 consecutive heads, define Y to be the number of the tosses for this process. 1) Calculate P{X>Y} 2) What's the expected value of X 3) What's the expected value of Y This is probably the hardest puzzle I have ever put on my blog. Hence, I will post its solution in the post directly rather than on comment. Solution: 1) (Solved by me finally after 13 months :)) Make a state diagram. Let the state be (a,b) where a is the number of consecutive heads streak "A" is on currently and b is the number of consecutive heads streak "B" is on currently. So, (0,3) (1,3) are final accepted states and (2,0) (2,1) (2,2) (2,3) are failure states. If you get tails, your contribution to the state reaches to "0" f(State) = P(X>Y | "State" configuration initially) ...
Read more