cs: add «1289. Minimum Falling Path Sum II»

Signed-off-by: Matej Focko <me@mfocko.xyz>

cs/minimum-falling-path-sum-ii.cs

@@ -0,0 +1,44 @@
+public class Solution {
+    private int[,] PrepareDP(int[][] grid) {
+        int[,] dp = new int[grid.Length, grid.Length];
+
+        var y = grid.Length - 1;
+        for (var x = 0; x < grid.Length; ++x) {
+            dp[y, x] = grid[y][x];
+        }
+
+        return dp;
+    }
+
+    private void Compute(int[][] grid, int[,] dp, int y, int x0) {
+        var minimum = int.MaxValue;
+
+        for (var x = 0; x < grid.Length; ++x) {
+            // need to continue with different column
+            if (x == x0) {
+                continue;
+            }
+
+            minimum = Math.Min(minimum, dp[y + 1, x]);
+        }
+
+        dp[y, x0] = grid[y][x0] + minimum;
+    }
+
+    public int MinFallingPathSum(int[][] grid) {
+        var dp = PrepareDP(grid);
+
+        for (var y = grid.Length - 2; y >= 0; --y) {
+            for (var x = 0; x < grid.Length; ++x) {
+                Compute(grid, dp, y, x);
+            }
+        }
+
+        int minFallingPath = int.MaxValue;
+        for (var x = 0; x < grid.Length; ++x) {
+            minFallingPath = Math.Min(minFallingPath, dp[0, x]);
+        }
+
+        return minFallingPath;
+    }
+}