1293. Shortest Path in a Grid with Obstacles Elimination
1. Description
You are given an m x n integer matrix grid where each cell is either 0 (empty) or 1 (obstacle). You can move up, down, left, or right from and to an empty cell in one step.
Return the minimum number of steps to walk from the upper left corner (0, 0) to the lower right corner (m - 1, n - 1) given that you can eliminate at most k obstacles. If it is not possible to find such walk return -1.
2. Example
Example 1
Input: grid = [[0,0,0],[1,1,0],[0,0,0],[0,1,1],[0,0,0]], k = 1
Output: 6
Explanation:
The shortest path without eliminating any obstacle is 10.
The shortest path with one obstacle elimination at position (3,2) is 6. Such path is (0,0) -> (0,1) -> (0,2) -> (1,2) -> (2,2) -> (3,2) -> (4,2).
Example 2
Input: grid = [[0,1,1],[1,1,1],[1,0,0]], k = 1
Output: -1
Explanation: We need to eliminate at least two obstacles to find such a walk.
3. Constraints
- m == grid.length
- n == grid[i].length
- 1 <= m, n <= 40
- 1 <= k <= m * n
- grid[i][j] is either 0 or 1.
- grid[0][0] == grid[m - 1][n - 1] == 0
4. Solutions
Breadth-First Search
m = grid.size(), n = grid.front().size()
Time complexity: O(mnk)
Space complexity: O(mn)
class Solution {
public:
int shortestPath(const vector<vector<int>> &grid, int k) {
const int m = grid.size(), n = grid.front().size();
vector<vector<int>> bombs(m, vector<int>(n, -1));
bombs[0][0] = k;
queue<tuple<int, int, int>> tasks{{{0, 0, k}}};
int steps = 0;
array<pair<int, int>, 4> directions{{{1, 0}, {0, 1}, {-1, 0}, {0, -1}}};
while (!tasks.empty()) {
for (int size = tasks.size(); size > 0; --size) {
auto [row, col, bomb] = tasks.front();
tasks.pop();
if (row == m - 1 && col == n - 1) {
return steps;
}
for (auto [i, j] : directions) {
int next_row = row + i, next_col = col + j;
if (0 <= next_row && next_row < m && 0 <= next_col && next_col < n) {
int next_bomb = bomb - grid[next_row][next_col];
if (next_bomb >= 0 && next_bomb > bombs[next_row][next_col]) {
bombs[next_row][next_col] = next_bomb;
tasks.push({next_row, next_col, next_bomb});
}
}
}
}
++steps;
}
return -1;
}
};