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1091. Shortest Path in Binary Matrix

Description

Given an n x n binary matrix grid, return the length of the shortest clear path in the matrix. If there is no clear path, return -1.

A clear path in a binary matrix is a path from the top-left cell (i.e., (0, 0)) to the bottom-right cell (i.e., (n - 1, n - 1)) such that:

  • All the visited cells of the path are 0.
  • All the adjacent cells of the path are 8-directionally connected (i.e., they are different and they share an edge or a corner).

The length of a clear path is the number of visited cells of this path.

 

Example 1:

Input: grid = [[0,1],[1,0]]
Output: 2

Example 2:

Input: grid = [[0,0,0],[1,1,0],[1,1,0]]
Output: 4

Example 3:

Input: grid = [[1,0,0],[1,1,0],[1,1,0]]
Output: -1

 

Constraints:

  • n == grid.length
  • n == grid[i].length
  • 1 <= n <= 100
  • grid[i][j] is 0 or 1

Solutions

Solution 1

Thinking

The eight-connected path has unit weights, so BFS by layer is the shortest length. \(n\le 100\) lets us mark visited cells in the grid. A blocked origin has no path.

Enqueue \((0,0)\) and mark it \(1\). Each layer expands the eight neighbors that are still \(0\). Reaching \((n-1,n-1)\) yields the current layer index.

If the queue empties first, the answer is \(-1\).

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class Solution:
    def shortestPathBinaryMatrix(self, grid: List[List[int]]) -> int:
        if grid[0][0]:
            return -1
        n = len(grid)
        grid[0][0] = 1
        q = deque([(0, 0)])
        ans = 1
        while q:
            for _ in range(len(q)):
                i, j = q.popleft()
                if i == j == n - 1:
                    return ans
                for x in range(i - 1, i + 2):
                    for y in range(j - 1, j + 2):
                        if 0 <= x < n and 0 <= y < n and grid[x][y] == 0:
                            grid[x][y] = 1
                            q.append((x, y))
            ans += 1
        return -1

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class Solution {
    public int shortestPathBinaryMatrix(int[][] grid) {
        if (grid[0][0] == 1) {
            return -1;
        }
        int n = grid.length;
        grid[0][0] = 1;
        Deque<int[]> q = new ArrayDeque<>();
        q.offer(new int[] {0, 0});
        for (int ans = 1; !q.isEmpty(); ++ans) {
            for (int k = q.size(); k > 0; --k) {
                var p = q.poll();
                int i = p[0], j = p[1];
                if (i == n - 1 && j == n - 1) {
                    return ans;
                }
                for (int x = i - 1; x <= i + 1; ++x) {
                    for (int y = j - 1; y <= j + 1; ++y) {
                        if (x >= 0 && x < n && y >= 0 && y < n && grid[x][y] == 0) {
                            grid[x][y] = 1;
                            q.offer(new int[] {x, y});
                        }
                    }
                }
            }
        }
        return -1;
    }
}

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class Solution {
public:
    int shortestPathBinaryMatrix(vector<vector<int>>& grid) {
        if (grid[0][0]) {
            return -1;
        }
        int n = grid.size();
        grid[0][0] = 1;
        queue<pair<int, int>> q;
        q.emplace(0, 0);
        for (int ans = 1; !q.empty(); ++ans) {
            for (int k = q.size(); k; --k) {
                auto [i, j] = q.front();
                q.pop();
                if (i == n - 1 && j == n - 1) {
                    return ans;
                }
                for (int x = i - 1; x <= i + 1; ++x) {
                    for (int y = j - 1; y <= j + 1; ++y) {
                        if (x >= 0 && x < n && y >= 0 && y < n && !grid[x][y]) {
                            grid[x][y] = 1;
                            q.emplace(x, y);
                        }
                    }
                }
            }
        }
        return -1;
    }
};

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func shortestPathBinaryMatrix(grid [][]int) int {
    if grid[0][0] == 1 {
        return -1
    }
    n := len(grid)
    grid[0][0] = 1
    q := [][2]int{{0, 0}}
    for ans := 1; len(q) > 0; ans++ {
        for k := len(q); k > 0; k-- {
            p := q[0]
            i, j := p[0], p[1]
            q = q[1:]
            if i == n-1 && j == n-1 {
                return ans
            }
            for x := i - 1; x <= i+1; x++ {
                for y := j - 1; y <= j+1; y++ {
                    if x >= 0 && x < n && y >= 0 && y < n && grid[x][y] == 0 {
                        grid[x][y] = 1
                        q = append(q, [2]int{x, y})
                    }
                }
            }
        }
    }
    return -1
}

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function shortestPathBinaryMatrix(grid: number[][]): number {
    if (grid[0][0]) {
        return -1;
    }
    const max = grid.length - 1;
    grid[0][0] = 1;
    let q: number[][] = [[0, 0]];
    for (let ans = 1; q.length > 0; ++ans) {
        const nq: number[][] = [];
        for (const [i, j] of q) {
            if (i === max && j === max) {
                return ans;
            }
            for (let x = i - 1; x <= i + 1; ++x) {
                for (let y = j - 1; y <= j + 1; ++y) {
                    if (grid[x]?.[y] === 0) {
                        grid[x][y] = 1;
                        nq.push([x, y]);
                    }
                }
            }
        }
        q = nq;
    }
    return -1;
}

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use std::collections::VecDeque;
impl Solution {
    pub fn shortest_path_binary_matrix(mut grid: Vec<Vec<i32>>) -> i32 {
        let n = grid.len();
        let mut queue = VecDeque::new();
        queue.push_back([0, 0]);
        let mut res = 0;
        while !queue.is_empty() {
            res += 1;
            for _ in 0..queue.len() {
                let [i, j] = queue.pop_front().unwrap();
                if grid[i][j] == 1 {
                    continue;
                }
                if i == n - 1 && j == n - 1 {
                    return res;
                }
                grid[i][j] = 1;
                for x in -1..=1 {
                    for y in -1..=1 {
                        let x = x + (i as i32);
                        let y = y + (j as i32);
                        if x < 0 || x == (n as i32) || y < 0 || y == (n as i32) {
                            continue;
                        }
                        queue.push_back([x as usize, y as usize]);
                    }
                }
            }
        }
        -1
    }
}

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