Find the Fewest Valid Single-Character Gene Mutations

# Find the Fewest Valid Single-Character Gene Mutations A gene is a string of eight characters from `A`, `C`, `G`, and `T`. One mutation changes exactly one character to a different character. Given `startGene`, `endGene`, and a list `bank` of valid genes, return the minimum number of mutations needed to reach `endGene`. Every gene entered after the starting point must occur in `bank`. The starting gene is valid even if absent from the bank. Return `-1` when no valid sequence reaches the target. ### Function `int minMutation(string startGene, string endGene, vector<string>& bank)` ### Example 1 ```text Input: startGene = "GGGGGGGG", endGene = "GGGGTTGG", bank = ["GGGGTGGG","GGGGTTGG"] Output: 2 ``` The listed intermediate changes position `4`, and the target then changes position `5`. The start and target differ at two positions, so fewer than two mutations cannot suffice. ### Example 2 ```text Input: startGene = "AAAAAAAA", endGene = "AAAAAATT", bank = ["AAAAAATT"] Output: -1 ``` The target differs at two positions, and no bank gene is available for the first single-character mutation. ### Constraints - `0 <= bank.length <= 10`. - Every input gene has length `8`. - All characters are from `A`, `C`, `G`, and `T`. ### Clarifications A step must change exactly one position; changing two at once is forbidden. If start and target already match, zero mutations are needed because the starting point is valid. Bank entries are valid destinations, not a prescribed order of visits. ### What a Strong Answer Covers - Single-character adjacency and bank membership after each mutation. - Minimum steps rather than merely finding some sequence. - An empty bank, equal endpoints, and an unreachable target. - Correctness, termination, and resource bounds.