[Problem] Minimum Genetic Mutation

Description

A gene string can be represented by an 8-character long string, with choices from 'A', 'C', 'G', and 'T'.

Suppose we need to investigate a mutation from a gene string startGene to a gene string endGene where one mutation is defined as one single character changed in the gene string.

For example, "AACCGGTT" --> "AACCGGTA" is one mutation.
There is also a gene bank bank that records all the valid gene mutations. A gene must be in bank to make it a valid gene string.

Given the two gene strings startGene and endGene and the gene bank bank, return the minimum number of mutations needed to mutate from startGene to endGene. If there is no such a mutation, return -1.

Note that the starting point is assumed to be valid, so it might not be included in the bank.

Example 1:
Input: startGene = "AACCGGTT", endGene = "AACCGGTA", bank = ["AACCGGTA"]
Output: 1

Example 2:
Input: startGene = "AACCGGTT", endGene = "AAACGGTA", bank = ["AACCGGTA","AACCGCTA","AAACGGTA"]
Output: 2

Approach

Classic BFS problem, but we have to identify each of the genes as a independent node, where the neighbors of the each node would be the strings with one character difference. I implemented the function string_diff to faciliate this check process. The bank inside the problem simplifies the problem with time complexity, would have been an nightmare without it, phew!

• Without bank, each node would have 8 * 5 ^ 5 neighbors.

Solution

def string_diff(s1, s2):
    if len(s1) != len(s2): return False
    cnt = 0

    for i in range(len(s1)):
        if s1[i] != s2[i]: cnt += 1
    
    return cnt == 1

class Solution:

    def minMutation(self, startGene: str, endGene: str, bank: List[str]) -> int:
        genes = deque([(startGene, 0)])
        while genes:
            cur, cnt = genes.popleft()
            if cur in bank: 
                bank.remove(cur)

            if cur == endGene: 
                return cnt
            elif len(bank) == 0: 
                return -1

            for next_gene in bank:
                if string_diff(next_gene, cur):
                    genes.append((next_gene, cnt + 1))

        return -1