Graph 1, Word Ladders II

Problem Statement

A word ladder is a sequence of words in which each word can be transformed into the next word by changing one letter. For example, the word ladder below changes 'lot' to 'log'.
   lot dot dog log
This is not the shortest word-ladder between 'lot' and 'log' since the former can be immediately changed to the latter yielding a word ladder of length two:
  lot log
The first and last words in a word ladder are the anchor rungs of the ladder. Any other words are interior rungs. For example, there are three interior rungs in the ladder below between 'smile' and 'evote'.
   smile smite smote emote evote
In this problem you'll write a method that has parameters representing potential interior rungs: a vector of strings (these by nonsense or English words), and the anchor rungs --- two strings. Your code must determine the shortest word ladder between the anchor rungs that uses at least one interior rung, and the number of such ladders. Return a vector containing two ints: the first is the length of the shortest valid word ladder and the second is the number of shortest ladders. If there are no valid ladders return [0,0].



class WordLadder { public: tvector<int> solve(const tvector<string>& words, const string& from, const string& to) { // fill in code here } };


The parameters from and to are the anchor rungs, they must be connected by at least one interior rung from words or there are no valid word ladders.



  1. [hot, dot, dog] hit cog 
    Returns [5, 1]

    The only ladder is hit hot dot dog cog which has length five.

  2. [hot, dot, dog, lot, log] hit cog 
    Returns [5, 2]

    Now there are two length-five ladders:

      hit hot dot dog cog
      hit hot lot log cog
  3. [rain, ruin, gain, grin, grit, main, pain, pair, pail, mail] sail ruip 
    Returns: [6, 2]

    There are two ladders of length six and no shorter ladders.

      sail mail main rain ruin ruip
      sail pail pain rain ruin ruip

  4. [most, mist, fist, fish,] lost cost 
    Returns [3, 1]

    Although lost is directly connected to cost, a valid word ladder must contain an interior rung so the shortest ladder is

       lost most cost
  5. [mist, fist, fish,] lost cost 
    Returns [0, 0]

    Although lost is directly connected to cost, a valid word ladder must contain an interior rung, there is no such ladder.

Owen L. Astrachan
Last modified: Fri Apr 9 09:55:57 EDT 2004