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].

Definition

Class: WordLadder
Method: solve
Parameters: const tvector<string>& const string&, const string&
Returns: tvector<int>

Method signature:

   tvector<int> solve(const tvector<string>& words,
                       const string& from, const string& to);

(be sure your method is public)

Class

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

Notes

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.

Constraints

words contains at most 50 words.
All strings contain only lowercase, alphabetic characters.
All strings in word are the same length and are the same length as from and to.

Examples

```
[hot, dot, dog] hit cog 
```
Returns [5, 1]
The only ladder is hit hot dot dog cog which has length five.

[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

[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

```
[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
```
```
[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