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Author: NinePiece2

Solutions/2521-paths-in-matrix-whose-sum-is-divisible-by-k/README.md

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+<p>You are given a <strong>0-indexed</strong> <code>m x n</code> integer matrix <code>grid</code> and an integer <code>k</code>. You are currently at position <code>(0, 0)</code> and you want to reach position <code>(m - 1, n - 1)</code> moving only <strong>down</strong> or <strong>right</strong>.</p>
+
+<p>Return<em> the number of paths where the sum of the elements on the path is divisible by </em><code>k</code>. Since the answer may be very large, return it <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>
+
+<p>&nbsp;</p>
+<p><strong class="example">Example 1:</strong></p>
+<img src="https://assets.leetcode.com/uploads/2022/08/13/image-20220813183124-1.png" style="width: 437px; height: 200px;" />
+<pre>
+<strong>Input:</strong> grid = [[5,2,4],[3,0,5],[0,7,2]], k = 3
+<strong>Output:</strong> 2
+<strong>Explanation:</strong> 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.
+</pre>
+
+<p><strong class="example">Example 2:</strong></p>
+<img src="https://assets.leetcode.com/uploads/2022/08/17/image-20220817112930-3.png" style="height: 85px; width: 132px;" />
+<pre>
+<strong>Input:</strong> grid = [[0,0]], k = 5
+<strong>Output:</strong> 1
+<strong>Explanation:</strong> The path highlighted in red has a sum of 0 + 0 = 0 which is divisible by 5.
+</pre>
+
+<p><strong class="example">Example 3:</strong></p>
+<img src="https://assets.leetcode.com/uploads/2022/08/12/image-20220812224605-3.png" style="width: 257px; height: 200px;" />
+<pre>
+<strong>Input:</strong> grid = [[7,3,4,9],[2,3,6,2],[2,3,7,0]], k = 1
+<strong>Output:</strong> 10
+<strong>Explanation:</strong> Every integer is divisible by 1 so the sum of the elements on every possible path is divisible by k.
+</pre>
+
+<p>&nbsp;</p>
+<p><strong>Constraints:</strong></p>
+
+<ul>
+	<li><code>m == grid.length</code></li>
+	<li><code>n == grid[i].length</code></li>
+	<li><code>1 &lt;= m, n &lt;= 5 * 10<sup>4</sup></code></li>
+	<li><code>1 &lt;= m * n &lt;= 5 * 10<sup>4</sup></code></li>
+	<li><code>0 &lt;= grid[i][j] &lt;= 100</code></li>
+	<li><code>1 &lt;= k &lt;= 50</code></li>
+</ul>

Solutions/2521-paths-in-matrix-whose-sum-is-divisible-by-k/solution.py

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+class Solution:
+    def numberOfPaths(self, grid: List[List[int]], k: int) -> int:
+        m, n = len(grid), len(grid[0])
+
+        @cache
+        def dfs(i: int, j: int, sum_val: int) -> int:
+            if i < 0 or i >= m or j < 0 or j >= n:
+                return 0
+            sum_val = (sum_val + grid[i][j]) % k
+            if i == m - 1 and j == n - 1:
+                return int(sum_val == 0)
+            return (dfs(i + 1, j, sum_val) + dfs(i, j + 1, sum_val)) % (10**9 + 7)
+        
+        
+        result = dfs(0, 0, 0)
+        dfs.cache_clear()
+        return result