Solution3.cpp

class Solution {
public:
    string target;

    int openLock(vector<string>& deadends, string target) {
        if (target == "0000") return 0;
        unordered_set<string> s(deadends.begin(), deadends.end());
        if (s.count("0000")) return -1;
        string start = "0000";
        this->target = target;
        typedef pair<int, string> PIS;
        priority_queue<PIS, vector<PIS>, greater<PIS>> q;
        unordered_map<string, int> dist;
        dist[start] = 0;
        q.push({f(start), start});
        while (!q.empty()) {
            PIS t = q.top();
            q.pop();
            string state = t.second;
            int step = dist[state];
            if (state == target) return step;
            for (string& t : next(state)) {
                if (s.count(t)) continue;
                if (!dist.count(t) || dist[t] > step + 1) {
                    dist[t] = step + 1;
                    q.push({step + 1 + f(t), t});
                }
            }
        }
        return -1;
    }

    int f(string s) {
        int ans = 0;
        for (int i = 0; i < 4; ++i) {
            int a = s[i] - '0';
            int b = target[i] - '0';
            if (a < b) {
                int t = a;
                a = b;
                b = t;
            }
            ans += min(b - a, a + 10 - b);
        }
        return ans;
    }

    vector<string> next(string& t) {
        vector<string> res;
        for (int i = 0; i < 4; ++i) {
            char c = t[i];
            t[i] = c == '0' ? '9' : (char) (c - 1);
            res.push_back(t);
            t[i] = c == '9' ? '0' : (char) (c + 1);
            res.push_back(t);
            t[i] = c;
        }
        return res;
    }
};