How many different words can you make from letter tiles?
In many tech interviews, candidates are often asked about problems related to combinations, permutations, or string manipulation. One common problem that arises is determining how many different combinations of words can be formed using a set of letter tiles, considering various constraints like duplicates and length. This challenge tests your understanding of algorithms, data structures, and logical thinking.
Let’s take a concrete example to illustrate how we can solve this problem. Assume we have a set of letter tiles: A, A, B, and C. We want to know how many distinct words can we create using these tiles.
First, we need to understand that generating combinations of letters while accounting for duplicate letters requires a method to track which letters have been used. One of the best approaches for this problem is to use recursion combined with backtracking.
Here’s a simple implementation in Python:
Python
In this code, we define a function generate_words which takes a list of tiles. We use a Counter from the collections module to tally the number of each letter. The helper function backtrack generates the different combinations of letters. It checks if the current letter is available to use before adding it to the current path. If a letter is used, we decrement its count, and once we've explored that path, we increment the count back, restoring the state for the next iteration.
The result set gathers all unique combinations of letters that can be formed. The if path: condition ensures that we do not include the empty string in our results.
In this example, when you run the function with the letter tiles ['A', 'A', 'B', 'C'], it will output distinct words formed like {'A', 'AB', 'BA', 'C', 'AC', 'CA', 'AA', 'ABC', ...} and calculate their number count.
This approach efficiently explores all possible letter combinations while preventing duplicates from forming in our result set. The recursive backtracking method is particularly suitable for problems involving permutations and combinations of a set of elements, especially when duplicates are present.
Using this solution, you can adapt it for different lengths of combinations or constraints based on the specific requirements of an interview question or project scenario. This method not only demonstrates a solid understanding of recursion but also highlights your capability to solve complex coding problems thoughtfully.
