#2617
Minimum Number of Visited Cells in a Grid
hard · verified · 23.6% accepted · 416 likes · top 3%
array · dynamic programming · stack · breadth-first search · union-find · heap (priority queue) · matrix · monotonic stack
Description
You are given a 0-indexed m x n integer matrix grid. Your initial position is at the top-left cell (0, 0).
Starting from the cell (i, j), you can move to one of the following cells:
- Cells (i, k) with j < k <= grid[i][j] + j (rightward movement), or
- Cells (k, j) with i < k <= grid[i][j] + i (downward movement).
Return the minimum number of cells you need to visit to reach the bottom-right cell (m - 1, n - 1). If there is no valid path, return -1.
Example 1:
Input: grid = [[3,4,2,1],[4,2,3,1],[2,1,0,0],[2,4,0,0]]
Output: 4
Explanation: The image above shows one of the paths that visits exactly 4 cells.
Example 2:
Input: grid = [[3,4,2,1],[4,2,1,1],[2,1,1,0],[3,4,1,0]]
Output: 3
Explanation: The image above shows one of the paths that visits exactly 3 cells.
Example 3:
Input: grid = [[2,1,0],[1,0,0]]
Output: -1
Explanation: It can be proven that no path exists.
Solution