In an n*n grid, there is a snake that spans 2 cells and starts moving from the top left corner at (0, 0) and (0, 1). The grid has empty cells represented by zeros and blocked cells represented by ones. The snake wants to reach the lower right corner at (n-1, n-2) and (n-1, n-1).
In one move the snake can:
- Move one cell to the right if there are no blocked cells there. This move keeps the horizontal/vertical position of the snake as it is.
- Move down one cell if there are no blocked cells there. This move keeps the horizontal/vertical position of the snake as it is.
- Rotate clockwise if it's in a horizontal position and the two cells under it are both empty. In that case the snake moves from
(r, c)and(r, c+1)to(r, c)and(r+1, c).
- Rotate counterclockwise if it's in a vertical position and the two cells to its right are both empty. In that case the snake moves from
(r, c)and(r+1, c)to(r, c)and(r, c+1).
Return the minimum number of moves to reach the target.
If there is no way to reach the target, return -1.
Example 1:
Input: grid = [[0,0,0,0,0,1],
[1,1,0,0,1,0],
[0,0,0,0,1,1],
[0,0,1,0,1,0],
[0,1,1,0,0,0],
[0,1,1,0,0,0]]
Output: 11
Explanation:
One possible solution is [right, right, rotate clockwise, right, down, down, down, down, rotate counterclockwise, right, down].
Example 2:
Input: grid = [[0,0,1,1,1,1], [0,0,0,0,1,1], [1,1,0,0,0,1], [1,1,1,0,0,1], [1,1,1,0,0,1], [1,1,1,0,0,0]] Output: 9
Constraints:
2 <= n <= 1000 <= grid[i][j] <= 1- It is guaranteed that the snake starts at empty cells.
BFS.
class Solution:
def minimumMoves(self, grid: List[List[int]]) -> int:
def move(i1, j1, i2, j2):
if 0 <= i1 < n and 0 <= j1 < n and 0 <= i2 < n and 0 <= j2 < n:
a, b = i1 * n + j1, i2 * n + j2
status = 0 if i1 == i2 else 1
if (a, status) not in vis and grid[i1][j1] == 0 and grid[i2][j2] == 0:
q.append((a, b))
vis.add((a, status))
n = len(grid)
target = (n * n - 2, n * n - 1)
q = deque([(0, 1)])
vis = {(0, 0)}
ans = 0
while q:
for _ in range(len(q)):
a, b = q.popleft()
if (a, b) == target:
return ans
i1, j1 = a // n, a % n
i2, j2 = b // n, b % n
move(i1, j1 + 1, i2, j2 + 1)
move(i1 + 1, j1, i2 + 1, j2)
if i1 == i2 and i1 + 1 < n and grid[i1 + 1][j2] == 0:
move(i1, j1, i1 + 1, j1)
if j1 == j2 and j1 + 1 < n and grid[i2][j1 + 1] == 0:
move(i1, j1, i1, j1 + 1)
ans += 1
return -1class Solution {
private int n;
private int[][] grid;
private boolean[][] vis;
private Deque<int[]> q = new ArrayDeque<>();
public int minimumMoves(int[][] grid) {
this.grid = grid;
n = grid.length;
vis = new boolean[n * n][2];
int[] target = {n * n - 2, n * n - 1};
q.offer(new int[] {0, 1});
vis[0][0] = true;
int ans = 0;
while (!q.isEmpty()) {
for (int k = q.size(); k > 0; --k) {
var p = q.poll();
if (p[0] == target[0] && p[1] == target[1]) {
return ans;
}
int i1 = p[0] / n, j1 = p[0] % n;
int i2 = p[1] / n, j2 = p[1] % n;
move(i1, j1 + 1, i2, j2 + 1);
move(i1 + 1, j1, i2 + 1, j2);
if (i1 == i2 && i1 + 1 < n && grid[i1 + 1][j2] == 0) {
move(i1, j1, i1 + 1, j1);
}
if (j1 == j2 && j1 + 1 < n && grid[i2][j1 + 1] == 0) {
move(i1, j1, i1, j1 + 1);
}
}
++ans;
}
return -1;
}
private void move(int i1, int j1, int i2, int j2) {
if (i1 >= 0 && i1 < n && j1 >= 0 && j1 < n && i2 >= 0 && i2 < n && j2 >= 0 && j2 < n) {
int a = i1 * n + j1, b = i2 * n + j2;
int status = i1 == i2 ? 0 : 1;
if (!vis[a][status] && grid[i1][j1] == 0 && grid[i2][j2] == 0) {
q.offer(new int[] {a, b});
vis[a][status] = true;
}
}
}
}class Solution {
public:
int minimumMoves(vector<vector<int>>& grid) {
int n = grid.size();
auto target = make_pair(n * n - 2, n * n - 1);
queue<pair<int, int>> q;
q.emplace(0, 1);
bool vis[n * n][2];
memset(vis, 0, sizeof vis);
vis[0][0] = true;
auto move = [&](int i1, int j1, int i2, int j2) {
if (i1 >= 0 && i1 < n && j1 >= 0 && j1 < n && i2 >= 0 && i2 < n && j2 >= 0 && j2 < n) {
int a = i1 * n + j1, b = i2 * n + j2;
int status = i1 == i2 ? 0 : 1;
if (!vis[a][status] && grid[i1][j1] == 0 && grid[i2][j2] == 0) {
q.emplace(a, b);
vis[a][status] = true;
}
}
};
int ans = 0;
while (!q.empty()) {
for (int k = q.size(); k; --k) {
auto p = q.front();
q.pop();
if (p == target) {
return ans;
}
auto [a, b] = p;
int i1 = a / n, j1 = a % n;
int i2 = b / n, j2 = b % n;
move(i1, j1 + 1, i2, j2 + 1);
move(i1 + 1, j1, i2 + 1, j2);
if (i1 == i2 && i1 + 1 < n && grid[i1 + 1][j2] == 0) {
move(i1, j1, i1 + 1, j1);
}
if (j1 == j2 && j1 + 1 < n && grid[i2][j1 + 1] == 0) {
move(i1, j1, i1, j1 + 1);
}
}
++ans;
}
return -1;
}
};func minimumMoves(grid [][]int) int {
n := len(grid)
type pair struct{ a, b int }
target := pair{n*n - 2, n*n - 1}
q := []pair{pair{0, 1}}
vis := make([][2]bool, n*n)
vis[0][0] = true
move := func(i1, j1, i2, j2 int) {
if i1 >= 0 && i1 < n && j1 >= 0 && j1 < n && i2 >= 0 && i2 < n && j2 >= 0 && j2 < n {
a, b := i1*n+j1, i2*n+j2
status := 1
if i1 == i2 {
status = 0
}
if !vis[a][status] && grid[i1][j1] == 0 && grid[i2][j2] == 0 {
q = append(q, pair{a, b})
vis[a][status] = true
}
}
}
ans := 0
for len(q) > 0 {
for k := len(q); k > 0; k-- {
p := q[0]
q = q[1:]
if p == target {
return ans
}
a, b := p.a, p.b
i1, j1 := a/n, a%n
i2, j2 := b/n, b%n
move(i1, j1+1, i2, j2+1)
move(i1+1, j1, i2+1, j2)
if i1 == i2 && i1+1 < n && grid[i1+1][j2] == 0 {
move(i1, j1, i1+1, j1)
}
if j1 == j2 && j1+1 < n && grid[i2][j1+1] == 0 {
move(i1, j1, i1, j1+1)
}
}
ans++
}
return -1
}function minimumMoves(grid: number[][]): number {
const n = grid.length;
const target: number[] = [n * n - 2, n * n - 1];
const q: number[][] = [[0, 1]];
const vis = Array.from({ length: n * n }, () => Array(2).fill(false));
vis[0][0] = true;
const move = (i1: number, j1: number, i2: number, j2: number) => {
if (i1 >= 0 && i1 < n && j1 >= 0 && j1 < n && i2 >= 0 && i2 < n && j2 >= 0 && j2 < n) {
const a = i1 * n + j1;
const b = i2 * n + j2;
const status = i1 === i2 ? 0 : 1;
if (!vis[a][status] && grid[i1][j1] == 0 && grid[i2][j2] == 0) {
q.push([a, b]);
vis[a][status] = true;
}
}
};
let ans = 0;
while (q.length) {
for (let k = q.length; k; --k) {
const p: number[] = q.shift();
if (p[0] === target[0] && p[1] === target[1]) {
return ans;
}
const [i1, j1] = [~~(p[0] / n), p[0] % n];
const [i2, j2] = [~~(p[1] / n), p[1] % n];
move(i1, j1 + 1, i2, j2 + 1);
move(i1 + 1, j1, i2 + 1, j2);
if (i1 == i2 && i1 + 1 < n && grid[i1 + 1][j2] == 0) {
move(i1, j1, i1 + 1, j1);
}
if (j1 == j2 && j1 + 1 < n && grid[i2][j1 + 1] == 0) {
move(i1, j1, i1, j1 + 1);
}
}
++ans;
}
return -1;
}/**
* @param {number[][]} grid
* @return {number}
*/
var minimumMoves = function (grid) {
const n = grid.length;
const target = [n * n - 2, n * n - 1];
const q = [[0, 1]];
const vis = Array.from({ length: n * n }, () => Array(2).fill(false));
vis[0][0] = true;
const move = (i1, j1, i2, j2) => {
if (i1 >= 0 && i1 < n && j1 >= 0 && j1 < n && i2 >= 0 && i2 < n && j2 >= 0 && j2 < n) {
const a = i1 * n + j1;
const b = i2 * n + j2;
const status = i1 === i2 ? 0 : 1;
if (!vis[a][status] && grid[i1][j1] == 0 && grid[i2][j2] == 0) {
q.push([a, b]);
vis[a][status] = true;
}
}
};
let ans = 0;
while (q.length) {
for (let k = q.length; k; --k) {
const p = q.shift();
if (p[0] === target[0] && p[1] === target[1]) {
return ans;
}
const [i1, j1] = [~~(p[0] / n), p[0] % n];
const [i2, j2] = [~~(p[1] / n), p[1] % n];
move(i1, j1 + 1, i2, j2 + 1);
move(i1 + 1, j1, i2 + 1, j2);
if (i1 == i2 && i1 + 1 < n && grid[i1 + 1][j2] == 0) {
move(i1, j1, i1 + 1, j1);
}
if (j1 == j2 && j1 + 1 < n && grid[i2][j1 + 1] == 0) {
move(i1, j1, i1, j1 + 1);
}
}
++ans;
}
return -1;
};