Watch 10 video solutions for Paths in Matrix Whose Sum Is Divisible by K, a hard level problem involving Array, Dynamic Programming, Matrix. This walkthrough by NeetCodeIO has 23,675 views views. Want to try solving it yourself? Practice on FleetCode or read the detailed text solution.
You are given a 0-indexed m x n integer matrix grid and an integer k. You are currently at position (0, 0) and you want to reach position (m - 1, n - 1) moving only down or right.
Return the number of paths where the sum of the elements on the path is divisible by k. Since the answer may be very large, return it modulo 109 + 7.
Example 1:
Input: grid = [[5,2,4],[3,0,5],[0,7,2]], k = 3 Output: 2 Explanation: There are two paths where the sum of the elements on the path is divisible by k. The first path highlighted in red has a sum of 5 + 2 + 4 + 5 + 2 = 18 which is divisible by 3. The second path highlighted in blue has a sum of 5 + 3 + 0 + 5 + 2 = 15 which is divisible by 3.
Example 2:
Input: grid = [[0,0]], k = 5 Output: 1 Explanation: The path highlighted in red has a sum of 0 + 0 = 0 which is divisible by 5.
Example 3:
Input: grid = [[7,3,4,9],[2,3,6,2],[2,3,7,0]], k = 1 Output: 10 Explanation: Every integer is divisible by 1 so the sum of the elements on every possible path is divisible by k.
Constraints:
m == grid.lengthn == grid[i].length1 <= m, n <= 5 * 1041 <= m * n <= 5 * 1040 <= grid[i][j] <= 1001 <= k <= 50