# 433. 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


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'].

## Solutions

BFS or DFS.

• class Solution {
public int minMutation(String start, String end, String[] bank) {
Set<String> s = new HashSet<>();
for (String b : bank) {
}
Map<Character, String> mp = new HashMap<>(4);
mp.put('A', "TCG");
mp.put('T', "ACG");
mp.put('C', "ATG");
mp.put('G', "ATC");
Deque<Pair<String, Integer>> q = new LinkedList<>();
q.offer(new Pair<>(start, 0));
while (!q.isEmpty()) {
Pair<String, Integer> p = q.poll();
String t = p.getKey();
int step = p.getValue();
if (end.equals(t)) {
return step;
}
for (int i = 0; i < t.length(); ++i) {
for (char c : mp.get(t.charAt(i)).toCharArray()) {
String next = t.substring(0, i) + c + t.substring(i + 1);
if (s.contains(next)) {
q.offer(new Pair<>(next, step + 1));
s.remove(next);
}
}
}
}
return -1;
}
}

• class Solution {
public:
int minMutation(string start, string end, vector<string>& bank) {
unordered_set<string> s;
for (auto& b : bank) s.insert(b);
unordered_map<char, string> mp;
mp['A'] = "TCG";
mp['T'] = "ACG";
mp['C'] = "ATG";
mp['G'] = "ATC";
queue<pair<string, int>> q;
q.push({start, 0});
while (!q.empty()) {
auto p = q.front();
q.pop();
string t = p.first;
int step = p.second;
if (t == end) return step;
for (int i = 0; i < t.size(); ++i) {
for (char c : mp[t[i]]) {
string next = t.substr(0, i) + c + t.substr(i + 1, t.size() - i - 1);
if (s.count(next)) {
q.push({next, step + 1});
s.erase(next);
}
}
}
}
return -1;
}
};

• class Solution:
def minMutation(self, start: str, end: str, bank: List[str]) -> int:
s = set(bank)
q = deque([(start, 0)])
mp = {'A': 'TCG', 'T': 'ACG', 'C': 'ATG', 'G': 'ATC'}
while q:
t, step = q.popleft()
if t == end:
return step
for i, v in enumerate(t):
for j in mp[v]:
next = t[:i] + j + t[i + 1 :]
if next in s:
q.append((next, step + 1))
s.remove(next)
return -1


• func minMutation(start string, end string, bank []string) int {
s := make(map[string]bool)
for _, b := range bank {
s[b] = true
}
mp := make(map[byte]string)
mp['A'] = "TCG"
mp['T'] = "ACG"
mp['C'] = "ATG"
mp['G'] = "ATC"
type pair struct {
first  string
second int
}
q := []pair{ {start, 0} }
for len(q) > 0 {
p := q[0]
q = q[1:]
t, step := p.first, p.second
if t == end {
return step
}
for i := 0; i < len(t); i++ {
for _, c := range mp[t[i]] {
next := t[:i] + string(c) + t[i+1:]
if s[next] {
q = append(q, pair{next, step + 1})
s[next] = false
}
}
}
}
return -1
}

• function minMutation(start: string, end: string, bank: string[]): number {
const queue = [start];
let res = 0;
while (queue.length !== 0) {
const n = queue.length;
for (let i = 0; i < n; i++) {
const s1 = queue.shift();
if (s1 === end) {
return res;
}

for (let j = bank.length - 1; j >= 0; j--) {
const s2 = bank[j];
let count = 0;
for (let k = 0; k < 8; k++) {
if (s1[k] !== s2[k]) {
count++;
}
}
if (count <= 1) {
queue.push(...bank.splice(j, 1));
}
}
}
res++;
}
return -1;
}


• use std::collections::VecDeque;
impl Solution {
pub fn min_mutation(start: String, end: String, mut bank: Vec<String>) -> i32 {
let mut queue = vec![start].into_iter().collect::<VecDeque<String>>();
let mut res = 0;
while !queue.is_empty() {
let n = queue.len();
for _ in 0..n {
let s1 = queue.pop_front().unwrap();
if s1 == end {
return res;
}

for i in (0..bank.len()).rev() {
let s1 = s1.as_bytes();
let s2 = bank[i].as_bytes();
let mut count = 0;
for j in 0..8 {
if s1[j] != s2[j] {
count += 1;
}
}
if count <= 1 {
queue.push_back(bank.remove(i));
}
}
}
res += 1;
}
-1
}
}