# Word Reducing Puzzle

I recently found an interesting problem on the web, about reducing words, letter by letter until only one letter remains. Here is a formal definition:

We define word reduction as removing a single letter from a word while leaving the remaining letters in their original order so that the resulting sequence of characters is also a word. A good word can be reduced step-by-step until all that is left is a or i. Your program will answer the question: what is the biggest word in the given dictionary that can be reduced?

A typical example, not very long is this:

So I though this could be a good exercise for F#. Several good dictionaries, both small and big, can be found here.

My approach was to read the dictionary and build a list for each word length: one for 1-letter words, one for 2-letter words, etc. This could be a Dictionary<int, list>, and let’s call it simply dictionary. Then these lists could be traversed and create a second set of lists (let’s call this reducedwords), but only with the words that meet the defined reduction.

An good approach would be to take each list of words from the initial dictionary, starting with the list with words of 2 letters, and for each word to delete one letter at a time. Then check to see if the resulting word already exists in the list from reducedwords corresponding to a length smaller with 1. If it’s there, that this word could be reduced and should be added to the list from reducedwords corresponding to the current length. In other words, the algorithm would be:

Here is a function for reading a dictionary file:

One I have the dictionary read, I can apply the algorithm and generate a second Dictionary structure. The following function also returns length of the longest word(s) in the reduced dictionary. This is useful for printing.

Since the problem is about printing only the longest such reductions, I’ll only consider starting from the list of reduced words that has the longest words. That’s why I needed findReducedWords to return the length of longest reducible word.

To print these paths I apply the same algorithm as before. The only difference is that I build a list with the words in the reducing path, starting with the longest word and ending with a 1-letter word.

The only thing left to do is calling all these functions:

My results for this dictionary were:

### 1 Reply to “Word Reducing Puzzle”

1. Mayank says:

nice work bro…..

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