# 752. Open the Lock

## Description

You have a lock in front of you with 4 circular wheels. Each wheel has 10 slots: '0', '1', '2', '3', '4', '5', '6', '7', '8', '9'. The wheels can rotate freely and wrap around: for example we can turn '9' to be '0', or '0' to be '9'. Each move consists of turning one wheel one slot.

The lock initially starts at '0000', a string representing the state of the 4 wheels.

You are given a list of deadends dead ends, meaning if the lock displays any of these codes, the wheels of the lock will stop turning and you will be unable to open it.

Given a target representing the value of the wheels that will unlock the lock, return the minimum total number of turns required to open the lock, or -1 if it is impossible.

Example 1:

Input: deadends = ["0201","0101","0102","1212","2002"], target = "0202"
Output: 6
Explanation:
A sequence of valid moves would be "0000" -> "1000" -> "1100" -> "1200" -> "1201" -> "1202" -> "0202".
Note that a sequence like "0000" -> "0001" -> "0002" -> "0102" -> "0202" would be invalid,
because the wheels of the lock become stuck after the display becomes the dead end "0102".


Example 2:

Input: deadends = ["8888"], target = "0009"
Output: 1
Explanation: We can turn the last wheel in reverse to move from "0000" -> "0009".


Example 3:

Input: deadends = ["8887","8889","8878","8898","8788","8988","7888","9888"], target = "8888"
Output: -1
Explanation: We cannot reach the target without getting stuck.


Constraints:

• 1 <= deadends.length <= 500
• deadends[i].length == 4
• target.length == 4
• target will not be in the list deadends.
• target and deadends[i] consist of digits only.

## Solutions

BFS.

• class Solution {
private String start;
private String target;
private Set<String> s = new HashSet<>();

public int openLock(String[] deadends, String target) {
if ("0000".equals(target)) {
return 0;
}
start = "0000";
this.target = target;
for (String d : deadends) {
}
if (s.contains(start)) {
return -1;
}
return bfs();
}

private int bfs() {
Map<String, Integer> m1 = new HashMap<>();
Map<String, Integer> m2 = new HashMap<>();
Deque<String> q1 = new ArrayDeque<>();
Deque<String> q2 = new ArrayDeque<>();
m1.put(start, 0);
m2.put(target, 0);
q1.offer(start);
q2.offer(target);
while (!q1.isEmpty() && !q2.isEmpty()) {
int t = q1.size() <= q2.size() ? extend(m1, m2, q1) : extend(m2, m1, q2);
if (t != -1) {
return t;
}
}
return -1;
}

private int extend(Map<String, Integer> m1, Map<String, Integer> m2, Deque<String> q) {
for (int n = q.size(); n > 0; --n) {
String p = q.poll();
int step = m1.get(p);
for (String t : next(p)) {
if (m1.containsKey(t) || s.contains(t)) {
continue;
}
if (m2.containsKey(t)) {
return step + 1 + m2.get(t);
}
m1.put(t, step + 1);
q.offer(t);
}
}
return -1;
}

private List<String> next(String t) {
List res = new ArrayList<>();
char[] chars = t.toCharArray();
for (int i = 0; i < 4; ++i) {
char c = chars[i];
chars[i] = c == '0' ? '9' : (char) (c - 1);
chars[i] = c == '9' ? '0' : (char) (c + 1);
chars[i] = c;
}
return res;
}
}

• class Solution {
public:
unordered_set<string> s;
string start;
string target;

int openLock(vector<string>& deadends, string target) {
if (target == "0000") return 0;
for (auto d : deadends) s.insert(d);
if (s.count("0000")) return -1;
this->start = "0000";
this->target = target;
return bfs();
}

int bfs() {
unordered_map<string, int> m1;
unordered_map<string, int> m2;
m1[start] = 0;
m2[target] = 0;
queue<string> q1{ {start} };
queue<string> q2{ {target} };
while (!q1.empty() && !q2.empty()) {
int t = q1.size() <= q2.size() ? extend(m1, m2, q1) : extend(m2, m1, q2);
if (t != -1) return t;
}
return -1;
}

int extend(unordered_map<string, int>& m1, unordered_map<string, int>& m2, queue<string>& q) {
for (int n = q.size(); n > 0; --n) {
string p = q.front();
int step = m1[p];
q.pop();
for (string t : next(p)) {
if (s.count(t) || m1.count(t)) continue;
if (m2.count(t)) return step + 1 + m2[t];
m1[t] = step + 1;
q.push(t);
}
}
return -1;
}

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;
}
};

• class Solution:
def openLock(self, deadends: List[str], target: str) -> int:
def next(s):
res = []
s = list(s)
for i in range(4):
c = s[i]
s[i] = '9' if c == '0' else str(int(c) - 1)
res.append(''.join(s))
s[i] = '0' if c == '9' else str(int(c) + 1)
res.append(''.join(s))
s[i] = c
return res

def extend(m1, m2, q):
for _ in range(len(q)):
p = q.popleft()
step = m1[p]
for t in next(p):
if t in s or t in m1:
continue
if t in m2:
return step + 1 + m2[t]
m1[t] = step + 1
q.append(t)
return -1

def bfs():
m1, m2 = {"0000": 0}, {target: 0}
q1, q2 = deque([('0000')]), deque([(target)])
while q1 and q2:
t = extend(m1, m2, q1) if len(q1) <= len(q2) else extend(m2, m1, q2)
if t != -1:
return t
return -1

if target == '0000':
return 0
if '0000' in s:
return -1
return bfs()


• func openLock(deadends []string, target string) int {
if target == "0000" {
return 0
}
s := make(map[string]bool)
for _, d := range deadends {
s[d] = true
}
if s["0000"] {
return -1
}
next := func(t string) []string {
s := []byte(t)
var res []string
for i, b := range s {
s[i] = b - 1
if s[i] < '0' {
s[i] = '9'
}
res = append(res, string(s))
s[i] = b + 1
if s[i] > '9' {
s[i] = '0'
}
res = append(res, string(s))
s[i] = b
}
return res
}

extend := func(m1, m2 map[string]int, q *[]string) int {
for n := len(*q); n > 0; n-- {
p := (*q)[0]
*q = (*q)[1:]
step, _ := m1[p]
for _, t := range next(p) {
if s[t] {
continue
}
if _, ok := m1[t]; ok {
continue
}
if v, ok := m2[t]; ok {
return step + 1 + v
}
m1[t] = step + 1
*q = append(*q, t)
}
}
return -1
}

bfs := func() int {
q1 := []string{"0000"}
q2 := []string{target}
m1 := map[string]int{"0000": 0}
m2 := map[string]int{target: 0}
for len(q1) > 0 && len(q2) > 0 {
t := -1
if len(q1) <= len(q2) {
t = extend(m1, m2, &q1)
} else {
t = extend(m2, m1, &q2)
}
if t != -1 {
return t
}
}
return -1
}

return bfs()
}