Paths in Matrix Whose Sum Is Divisible by K

arraydynamic programmingmatrix

Problem Statement

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 10 ^9 + 7 .

Examples

Example 1

Input: grid = [[5,2,4],[3,0,5],[0,7,2]], k = 3
Output: 2
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
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
Every integer is divisible by 1 so the sum of the elements on every possible path is divisible by k.

Constraints

m == grid.length

n == grid[i].length

1 <= m, n <= 5 * 10 ^4

1 <= m * n <= 5 * 10 ^4

0 <= grid[i][j] <= 100

1 <= k <= 50

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Hard

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicDynamic Programming