You are given a m x n 2D integer array grid and an integer k. You start at the top-left cell (0, 0) and your goal is to reach the bottomâright cell (m - 1, n - 1).
There are two types of moves available:
Normal move: You can move right or down from your current cell (i, j), i.e. you can move to (i, j + 1) (right) or (i + 1, j) (down). The cost is the value of the destination cell.
Teleportation: You can teleport from any cell (i, j), to any cell (x, y) such that grid[x][y] <= grid[i][j]; the cost of this move is 0. You may teleport at most k times.
Return the minimum total cost to reach cell (m - 1, n - 1) from (0, 0).
Example 1:
Input: grid = [[1,3,3],[2,5,4],[4,3,5]], k = 2
Output: 7
Explanation:
Initially we are at (0, 0) and cost is 0.
| Current Position | Move | New Position | Total Cost |
|---|---|---|---|
(0, 0) |
Move Down | (1, 0) |
0 + 2 = 2 |
(1, 0) |
Move Right | (1, 1) |
2 + 5 = 7 |
(1, 1) |
Teleport to (2, 2) |
(2, 2) |
7 + 0 = 7 |
The minimum cost to reach bottom-right cell is 7.
Example 2:
Input: grid = [[1,2],[2,3],[3,4]], k = 1
Output: 9
Explanation:
Initially we are at (0, 0) and cost is 0.
| Current Position | Move | New Position | Total Cost |
|---|---|---|---|
(0, 0) |
Move Down | (1, 0) |
0 + 2 = 2 |
(1, 0) |
Move Right | (1, 1) |
2 + 3 = 5 |
(1, 1) |
Move Down | (2, 1) |
5 + 4 = 9 |
The minimum cost to reach bottom-right cell is 9.
Constraints:
2 <= m, n <= 80m == grid.lengthn == grid[i].length0 <= grid[i][j] <= 1040 <= k <= 10