Missionaries and Cannibals

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Problem Description

For some unknown reason, three cannibals and three missionaries are traveling together and come to river that they must cross.  There is a boat on their side of the river that can be used, but unfortunately, it only holds two people at a time.   And, while the cannibals will cooperatively share the task of river crossing, if the number of cannibals on either bank is greater than the number of missionaries at any time, old habits will kick in and the outnumbered missionaries will be eaten!

Can you plan the crossings necessary to successfully get all 6 travelers across the river in good condition?  
      

Background & Techniques

A few weeks ago, I received an email from a student studying C, (poor fellow!) inquiring about a program to solve this problem.  I sent him text description of the approach I'd take but decided not to code the program right away.  No sense of making his homework assignment too easy!    I guess it must have been due by now, so I coded it up, "just for fun". 

I skipped the animation in this version, but it does allow user play by specifying the boat occupants for each crossing.   And of course, the program will search for (and find) a solution.  Four solutions actually.

Moves are made by clicking one of the 5 possible combinations of boat occupants for the crossing (1 or 2 cannibals, 1 or 2 missionaries, or one of each).  The game is over when cannibals exceed missionaries on either bank or all six members are on the right bank.       

Non-programmers are welcome to read on, but may want to skip to the bottom of this page to download an executable version of the program.

The fun part in coding this puzzle is defining the search mechanism to find the moves that get all across the river safely.  

This is a typical graph search problem that is most easily solved by a recursive depth first search.    The first step in  these problems is to find a good data representation for the game states.  In this case, a state is defined by the number of cannibals and missionaries are on each bank, and where the boat is located.  Since there are only two positions for the boat and they alternate, we can always tell where the boat by whether the current move count is odd or even.  And we do not need to keep track of occupancy of both river banks - knowing one tells us the other.   So, a single pair of numbers representing left bank cannibals and missionary counts and the current move count is all we need.   

Google returns about a hundred hits for cannibals missionaries recursive depth first, so I won't re-chew that cabbage here.   There are a couple of tricks worth mentioning: 

  • A recursive search does not really needed to keep track of game states since each call just makes it's move and calls itself to make the next move.  But i wanted to allow manual play to be able to also retract a move and for that I used a "trick" that can simplify things at time - the Objects array associated with a stringlist can also hold a list of integers,  In this case, 10 times the number of left-bank  cannibals + the number of left-bank missionaries forms an integer that will  allow us to move back up the move list.             
  • The "Visited" array which keeps us from looping is a 4 X 4 X 2 array of boolean (true-false) values representing the 32 possible game states.   Cells are set to true when a move results in that state  (e.g. Visited[2,3,true] is set to true to indicate that we have 2 cannibals, 3 missionaries and the boat on the left bank).

Enjoy!

Running/Exploring the Program 

Suggestions for Further Explorations

Animated graphics of crossings.
Variations - multiple boats, more (or fewer) cannibals and missionaries. 

 

Original Date: April 25, 2004 

Modified: February 18, 2016

 
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