minimum-cost-path-with-teleportations

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 bottom‐right 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.

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.

The minimum cost to reach bottom-right cell is 9.

Constraints:

• 2 <= m, n <= 80


• m == grid.length


• n == grid[i].length


• 0 <= grid[i][j] <= 104


• 0 <= k <= 10