Minimum Genetic Mutation

Minimum Genetic Mutation

1. What is this problem about?

The Minimum Genetic Mutation problem is a fascinating string transformation challenge. You are given a starting gene string, an end gene string, and a "bank" of valid gene mutations. A gene string is 8 characters long and consists of the letters 'A', 'C', 'G', and 'T'. One mutation is defined as changing a single character in the gene string. The goal is to find the minimum number of mutations needed to transform the start gene into the end gene, such that every intermediate gene in the process is present in the mutation bank.

2. Why is this asked in interviews?

This question is a favorite at top-tier companies like Microsoft, Twitter, and Google because it perfectly demonstrates the application of graph traversal algorithms to string problems. The Minimum Genetic Mutation interview question evaluates whether a candidate can model a set of strings as a graph, where each string is a node and an edge exists between two strings if they differ by exactly one character. It tests your ability to find the shortest path in an unweighted graph.

3. Algorithmic pattern used

The primary algorithmic pattern used is Breadth-First Search (BFS). Since we are looking for the minimum number of steps in an unweighted state-space, BFS is the optimal choice as it explores all possibilities level by level. At each step, we generate all possible single-character mutations of the current gene. If a mutation exists in the bank and hasn't been visited yet, we add it to the queue. This "Breadth-First Search, Hash Table interview pattern" ensures that the first time we reach the end gene, we have found the shortest path.

4. Example explanation

Start: "AACCGGTT", End: "AACCGGTA", Bank: ["AACCGGTA"]

1. Initial state: Queue = ["AACCGGTT"], steps = 0.
2. Level 1: Pop "AACCGGTT". Try changing each of the 8 positions to A, C, G, or T.
3. One possibility is "AACCGGTA" (changing the last 'T' to 'A').
4. "AACCGGTA" is in the bank. Add to queue.
5. Next step: Pop "AACCGGTA". It matches the end string. Result: 1 mutation. If "AACCGGTA" was not in the bank, we could not have reached it in one step.

5. Common mistakes candidates make

A common pitfall in the Minimum Genetic Mutation coding problem is using Depth-First Search (DFS) instead of BFS. While DFS can find a path, it doesn't guarantee the shortest path without extra complexity (like tracking the minimum steps globally). Another mistake is not using a Hash Set for the bank, which leads to slow lookups ($O(N)$ instead of $O(1)$) and potentially exceeding the time limit. Candidates also often forget to mark visited genes, leading to infinite loops in the search space.

6. Interview preparation tip

Whenever you encounter a "shortest path" or "minimum steps to transform" problem where each step has a constant cost, think BFS immediately. Practice building the "neighbor" function efficiently—either by iterating through the bank or by generating all possible 1-char mutations and checking if they exist in the bank. This "String Transformation interview pattern" is very common in technical assessments.