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773. Sliding Puzzle

Description

On an 2 x 3 board, there are five tiles labeled from 1 to 5, and an empty square represented by 0. A move consists of choosing 0 and a 4-directionally adjacent number and swapping it.

The state of the board is solved if and only if the board is [[1,2,3],[4,5,0]].

Given the puzzle board board, return the least number of moves required so that the state of the board is solved. If it is impossible for the state of the board to be solved, return -1.

 

Example 1:

Input: board = [[1,2,3],[4,0,5]]
Output: 1
Explanation: Swap the 0 and the 5 in one move.

Example 2:

Input: board = [[1,2,3],[5,4,0]]
Output: -1
Explanation: No number of moves will make the board solved.

Example 3:

Input: board = [[4,1,2],[5,0,3]]
Output: 5
Explanation: 5 is the smallest number of moves that solves the board.
An example path:
After move 0: [[4,1,2],[5,0,3]]
After move 1: [[4,1,2],[0,5,3]]
After move 2: [[0,1,2],[4,5,3]]
After move 3: [[1,0,2],[4,5,3]]
After move 4: [[1,2,0],[4,5,3]]
After move 5: [[1,2,3],[4,5,0]]

 

Constraints:

  • board.length == 2
  • board[i].length == 3
  • 0 <= board[i][j] <= 5
  • Each value board[i][j] is unique.

Solutions

Solution 1

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class Solution:
    def slidingPuzzle(self, board: List[List[int]]) -> int:
        t = [None] * 6

        def gets():
            for i in range(2):
                for j in range(3):
                    t[i * 3 + j] = str(board[i][j])
            return ''.join(t)

        def setb(s):
            for i in range(2):
                for j in range(3):
                    board[i][j] = int(s[i * 3 + j])

        def f():
            res = []
            i, j = next((i, j) for i in range(2) for j in range(3) if board[i][j] == 0)
            for a, b in [[0, -1], [0, 1], [1, 0], [-1, 0]]:
                x, y = i + a, j + b
                if 0 <= x < 2 and 0 <= y < 3:
                    board[i][j], board[x][y] = board[x][y], board[i][j]
                    res.append(gets())
                    board[i][j], board[x][y] = board[x][y], board[i][j]
            return res

        start = gets()
        end = "123450"
        if start == end:
            return 0
        vis = {start}
        q = deque([(start)])
        ans = 0
        while q:
            ans += 1
            for _ in range(len(q)):
                x = q.popleft()
                setb(x)
                for y in f():
                    if y == end:
                        return ans
                    if y not in vis:
                        vis.add(y)
                        q.append(y)
        return -1

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class Solution {
    private String[] t = new String[6];
    private int[][] board;

    public int slidingPuzzle(int[][] board) {
        this.board = board;
        String start = gets();
        String end = "123450";
        if (end.equals(start)) {
            return 0;
        }
        Set<String> vis = new HashSet<>();
        Deque<String> q = new ArrayDeque<>();
        q.offer(start);
        vis.add(start);
        int ans = 0;
        while (!q.isEmpty()) {
            ++ans;
            for (int n = q.size(); n > 0; --n) {
                String x = q.poll();
                setb(x);
                for (String y : next()) {
                    if (y.equals(end)) {
                        return ans;
                    }
                    if (!vis.contains(y)) {
                        vis.add(y);
                        q.offer(y);
                    }
                }
            }
        }
        return -1;
    }

    private String gets() {
        for (int i = 0; i < 2; ++i) {
            for (int j = 0; j < 3; ++j) {
                t[i * 3 + j] = String.valueOf(board[i][j]);
            }
        }
        return String.join("", t);
    }

    private void setb(String s) {
        for (int i = 0; i < 2; ++i) {
            for (int j = 0; j < 3; ++j) {
                board[i][j] = s.charAt(i * 3 + j) - '0';
            }
        }
    }

    private int[] find0() {
        for (int i = 0; i < 2; ++i) {
            for (int j = 0; j < 3; ++j) {
                if (board[i][j] == 0) {
                    return new int[] {i, j};
                }
            }
        }
        return new int[] {0, 0};
    }

    private List<String> next() {
        int[] p = find0();
        int i = p[0], j = p[1];
        int[] dirs = {-1, 0, 1, 0, -1};
        List<String> res = new ArrayList<>();
        for (int k = 0; k < 4; ++k) {
            int x = i + dirs[k];
            int y = j + dirs[k + 1];
            if (x >= 0 && x < 2 && y >= 0 && y < 3) {
                swap(i, j, x, y);
                res.add(gets());
                swap(i, j, x, y);
            }
        }
        return res;
    }

    private void swap(int i, int j, int x, int y) {
        int t = board[i][j];
        board[i][j] = board[x][y];
        board[x][y] = t;
    }
}

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class Solution {
public:
    int slidingPuzzle(vector<vector<int>>& board) {
        string start = gets(board);
        string end = "123450";
        if (start == end) return 0;
        unordered_set<string> vis;
        vis.insert(start);
        queue<string> q{{start}};
        int ans = 0;
        while (!q.empty()) {
            ++ans;
            for (int n = q.size(); n > 0; --n) {
                string x = q.front();
                q.pop();
                setb(x, board);
                for (string y : next(board)) {
                    if (y == end) return ans;
                    if (!vis.count(y)) {
                        vis.insert(y);
                        q.push(y);
                    }
                }
            }
        }
        return -1;
    }

    string gets(vector<vector<int>>& board) {
        string s = "";
        for (int i = 0; i < 2; ++i)
            for (int j = 0; j < 3; ++j)
                s.push_back('0' + board[i][j]);
        return s;
    }

    void setb(string s, vector<vector<int>>& board) {
        for (int i = 0; i < 2; ++i)
            for (int j = 0; j < 3; ++j)
                board[i][j] = s[i * 3 + j] - '0';
    }

    vector<string> next(vector<vector<int>>& board) {
        vector<string> res;
        auto p = find0(board);
        int i = p.first, j = p.second;
        vector<int> dirs = {-1, 0, 1, 0, -1};
        for (int k = 0; k < 4; ++k) {
            int x = i + dirs[k], y = j + dirs[k + 1];
            if (x >= 0 && x < 2 && y >= 0 && y < 3) {
                swap(i, j, x, y, board);
                res.push_back(gets(board));
                swap(i, j, x, y, board);
            }
        }
        return res;
    }

    void swap(int i, int j, int x, int y, vector<vector<int>>& board) {
        int t = board[i][j];
        board[i][j] = board[x][y];
        board[x][y] = t;
    }

    pair<int, int> find0(vector<vector<int>>& board) {
        for (int i = 0; i < 2; ++i)
            for (int j = 0; j < 3; ++j)
                if (board[i][j] == 0)
                    return {i, j};
        return {0, 0};
    }
};

Solution 2

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class Solution:
    def slidingPuzzle(self, board: List[List[int]]) -> int:
        m, n = 2, 3
        seq = []
        start, end = '', '123450'
        for i in range(m):
            for j in range(n):
                if board[i][j] != 0:
                    seq.append(board[i][j])
                start += str(board[i][j])

        def check(seq):
            n = len(seq)
            cnt = sum(seq[i] > seq[j] for i in range(n) for j in range(i, n))
            return cnt % 2 == 0

        def f(s):
            ans = 0
            for i in range(m * n):
                if s[i] != '0':
                    num = ord(s[i]) - ord('1')
                    ans += abs(i // n - num // n) + abs(i % n - num % n)
            return ans

        if not check(seq):
            return -1
        q = [(f(start), start)]
        dist = {start: 0}
        while q:
            _, state = heappop(q)
            if state == end:
                return dist[state]
            p1 = state.index('0')
            i, j = p1 // n, p1 % n
            s = list(state)
            for a, b in [[0, -1], [0, 1], [1, 0], [-1, 0]]:
                x, y = i + a, j + b
                if 0 <= x < m and 0 <= y < n:
                    p2 = x * n + y
                    s[p1], s[p2] = s[p2], s[p1]
                    next = ''.join(s)
                    s[p1], s[p2] = s[p2], s[p1]
                    if next not in dist or dist[next] > dist[state] + 1:
                        dist[next] = dist[state] + 1
                        heappush(q, (dist[next] + f(next), next))
        return -1

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class Solution {
    private int m = 2;
    private int n = 3;

    public int slidingPuzzle(int[][] board) {
        String start = "";
        String end = "123450";
        String seq = "";
        for (int i = 0; i < m; ++i) {
            for (int j = 0; j < n; ++j) {
                start += board[i][j];
                if (board[i][j] != 0) {
                    seq += board[i][j];
                }
            }
        }
        if (!check(seq)) {
            return -1;
        }
        PriorityQueue<Pair<Integer, String>> q
            = new PriorityQueue<>(Comparator.comparingInt(Pair::getKey));
        Map<String, Integer> dist = new HashMap<>();
        dist.put(start, 0);
        q.offer(new Pair<>(f(start), start));
        int[] dirs = {-1, 0, 1, 0, -1};
        while (!q.isEmpty()) {
            String state = q.poll().getValue();
            int step = dist.get(state);
            if (end.equals(state)) {
                return step;
            }
            int p1 = state.indexOf("0");
            int i = p1 / n, j = p1 % n;
            char[] s = state.toCharArray();
            for (int k = 0; k < 4; ++k) {
                int x = i + dirs[k], y = j + dirs[k + 1];
                if (x >= 0 && x < m && y >= 0 && y < n) {
                    int p2 = x * n + y;
                    swap(s, p1, p2);
                    String next = String.valueOf(s);
                    if (!dist.containsKey(next) || dist.get(next) > step + 1) {
                        dist.put(next, step + 1);
                        q.offer(new Pair<>(step + 1 + f(next), next));
                    }
                    swap(s, p1, p2);
                }
            }
        }
        return -1;
    }

    private void swap(char[] arr, int i, int j) {
        char t = arr[i];
        arr[i] = arr[j];
        arr[j] = t;
    }

    private int f(String s) {
        int ans = 0;
        for (int i = 0; i < m * n; ++i) {
            if (s.charAt(i) != '0') {
                int num = s.charAt(i) - '1';
                ans += Math.abs(i / n - num / n) + Math.abs(i % n - num % n);
            }
        }
        return ans;
    }

    private boolean check(String s) {
        int n = s.length();
        int cnt = 0;
        for (int i = 0; i < n; ++i) {
            for (int j = i + 1; j < n; ++j) {
                if (s.charAt(i) > s.charAt(j)) {
                    ++cnt;
                }
            }
        }
        return cnt % 2 == 0;
    }
}

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class Solution {
public:
    int m = 2;
    int n = 3;

    int slidingPuzzle(vector<vector<int>>& board) {
        string start, seq;
        string end = "123450";
        for (int i = 0; i < m; ++i) {
            for (int j = 0; j < n; ++j) {
                start += char(board[i][j] + '0');
                if (board[i][j] != 0) seq += char(board[i][j] + '0');
            }
        }
        if (!check(seq)) return -1;
        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});
        vector<int> dirs = {-1, 0, 1, 0, -1};
        while (!q.empty()) {
            PIS t = q.top();
            q.pop();
            string state = t.second;
            int step = dist[state];
            if (state == end) return step;
            int p1 = state.find('0');
            int i = p1 / n, j = p1 % n;
            for (int k = 0; k < 4; ++k) {
                int x = i + dirs[k], y = j + dirs[k + 1];
                if (x < 0 || x >= m || y < 0 || y >= n) continue;
                int p2 = x * n + y;
                swap(state[p1], state[p2]);
                if (!dist.count(state) || dist[state] > step + 1) {
                    dist[state] = step + 1;
                    q.push({step + 1 + f(state), state});
                }
                swap(state[p1], state[p2]);
            }
        }
        return -1;
    }

    bool check(string s) {
        int n = s.size();
        int cnt = 0;
        for (int i = 0; i < n; ++i)
            for (int j = i; j < n; ++j)
                if (s[i] > s[j])
                    ++cnt;
        return cnt % 2 == 0;
    }

    int f(string s) {
        int ans = 0;
        for (int i = 0; i < m * n; ++i) {
            if (s[i] == '0') continue;
            int num = s[i] - '1';
            ans += abs(num / n - i / n) + abs(num % n - i % n);
        }
        return ans;
    }
};

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