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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

Solution 1

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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

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class Solution {
    public int minMutation(String start, String end, String[] bank) {
        Set<String> s = new HashSet<>();
        for (String b : bank) {
            s.add(b);
        }
        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;
    }
}

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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;
    }
};

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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
}

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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;
}

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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
    }
}

Solution 2

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class Solution:
    def minMutation(self, start: str, end: str, bank: List[str]) -> int:
        def dfs(start, t):
            if start == end:
                nonlocal ans
                ans = min(ans, t)
                return
            for i, x in enumerate(start):
                for y in 'ACGT':
                    if x != y:
                        nxt = start[:i] + y + start[i + 1 :]
                        if nxt in s:
                            s.remove(nxt)
                            dfs(nxt, t + 1)

        s = set(bank)
        ans = inf
        dfs(start, 0)
        return -1 if ans == inf else ans

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class Solution {
    private int ans;
    private Set<String> s;
    private static final char[] seq = {'A', 'C', 'G', 'T'};

    public int minMutation(String start, String end, String[] bank) {
        s = new HashSet<>();
        for (String b : bank) {
            s.add(b);
        }
        ans = Integer.MAX_VALUE;
        dfs(start, end, 0);
        s.remove(start);
        return ans == Integer.MAX_VALUE ? -1 : ans;
    }

    private void dfs(String start, String end, int t) {
        if (start.equals(end)) {
            ans = Math.min(ans, t);
            return;
        }
        for (int i = 0; i < start.length(); ++i) {
            for (char c : seq) {
                if (start.charAt(i) == c) {
                    continue;
                }
                String nxt = start.substring(0, i) + c + start.substring(i + 1);
                if (s.contains(nxt)) {
                    s.remove(nxt);
                    dfs(nxt, end, t + 1);
                }
            }
        }
    }
}

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class Solution {
public:
    int ans;
    string seq = "ACGT";

    int minMutation(string start, string end, vector<string>& bank) {
        unordered_set<string> s;
        for (auto& b : bank) s.insert(b);
        ans = INT_MAX;
        s.erase(start);
        dfs(start, end, s, 0);
        return ans == INT_MAX ? -1 : ans;
    }

    void dfs(string& start, string& end, unordered_set<string>& s, int t) {
        if (start == end) {
            ans = min(ans, t);
            return;
        }
        for (int i = 0; i < start.size(); ++i) {
            for (char& c : seq) {
                if (start[i] == c) continue;
                string nxt = start.substr(0, i) + c + start.substr(i + 1, start.size() - i - 1);
                if (s.count(nxt)) {
                    s.erase(nxt);
                    dfs(nxt, end, s, t + 1);
                }
            }
        }
    }
};

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func minMutation(start string, end string, bank []string) int {
    s := make(map[string]bool)
    for _, b := range bank {
        s[b] = true
    }
    ans := math.MaxInt32
    s[start] = false
    seq := []rune{'A', 'C', 'G', 'T'}
    var dfs func(start string, t int)
    dfs = func(start string, t int) {
        if start == end {
            if ans > t {
                ans = t
            }
            return
        }
        for i, x := range start {
            for _, y := range seq {
                if x == y {
                    continue
                }
                nxt := start[:i] + string(y) + start[i+1:]
                if s[nxt] {
                    s[nxt] = false
                    dfs(nxt, t+1)
                }
            }
        }
    }
    dfs(start, 0)
    if ans == math.MaxInt32 {
        return -1
    }
    return ans
}

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