Minimum Number of Visited Cells in a Grid

Find the minimum number of cells visited to reach bottom-right in an m×n grid when from (i,j) you can jump right to any (i,k) with j<k<=j+grid[i][j] or down to any (k,j) with i<k<=i+grid[i][j]; this is a shortest-path problem with range-based moves that requires efficient enumeration of unvisited cells (m*n up to 1e5) to avoid scanning full ranges.