Minimum Genetic Mutation Python Solution

LeetCode 433, Medium. Topics: Hash Table, String, Breadth-First Search, Bidirectional Search. View on LeetCode. Generate this problem as a practice environment: tested reference solution, 17 parametrized pytest cases, and a playground notebook:

lcpy gen -n 433   # by problem number
lcpy gen -s minimum_genetic_mutation   # by problem name

Problem

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 mutation, return -1. Note that the starting point is assumed to be valid, so it might not be included in the bank.

Examples

Input: startGene = "AACCGGTT", endGene = "AACCGGTA", bank = ["AACCGGTA"]
Output: 1
Explanation: One mutation changes the last gene from 'T' to 'A'.

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

Constraints

0 <= bank.length <= 10
startGene.length == endGene.length == bank[i].length == 8
startGene, endGene, and bank[i] consist of only the characters [‘A’, ‘C’, ‘G’, ‘T’].

Solution

Reference implementation from solution.py on GitHub, full suite in test_solution.py:

from collections import deque


class Solution:
    # Time: O(8^2 * n) where n = len(bank), each gene expands 8*4 neighbors
    # Space: O(n)
    def min_mutation(self, start_gene: str, end_gene: str, bank: list[str]) -> int:
        valid = set(bank)
        if start_gene == end_gene:
            return 0
        if end_gene not in valid:
            return -1
        queue: deque[tuple[str, int]] = deque([(start_gene, 0)])
        visited = {start_gene}
        while queue:
            gene, steps = queue.popleft()
            if gene == end_gene:
                return steps
            for i in range(len(gene)):
                for c in "ACGT":
                    if c == gene[i]:
                        continue
                    nxt = gene[:i] + c + gene[i + 1 :]
                    if nxt in valid and nxt not in visited:
                        visited.add(nxt)
                        queue.append((nxt, steps + 1))
        return -1

Complexity

Time	Space
O(8^2 * n) where n = len(bank), each gene expands 8*4 neighbors	O(n)

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Minimum Genetic Mutation Python Solution

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