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Number of Increasing Paths in a Grid
You are given an m x n integer matrix grid, where you can move from a cell to any adjacent cell in all 4 directions.
Return the number of strictly increasing paths in the grid such that you can start from any cell and end at any cell. Since the answer may be very large, return it modulo 10^9 + 7.
Two paths are considered different if they do not have exactly the same sequence of visited cells.
Example 1
1 1 3 4
Input
grid = [[1,1],[3,4]]Output
8The strictly increasing paths have lengths 1, 2, and 3, for a total of 4 + 3 + 1 = 8 paths.
Example 2
1 2
Input
grid = [[1],[2]]Output
3The strictly increasing paths are [1], [2], and [1 -> 2], for a total of 3 paths.
Constraints
- m == grid.length
- n == grid[i].length
- 1 <= m, n <= 1000
- 1 <= m * n <= 10^5
- 1 <= grid[i][j] <= 10^5