From 4db2c6ab6153692fc61de10489c668c222b0265c Mon Sep 17 00:00:00 2001
From: Ilya Nikokoshev <ilya.nikokoshev@gmail.com>
Date: Fri, 12 Jan 2024 00:29:26 +0100
Subject: [PATCH] Add another coding problem

---
 dynamic-2d-path.py | 48 ++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 48 insertions(+)
 create mode 100644 dynamic-2d-path.py

diff --git a/dynamic-2d-path.py b/dynamic-2d-path.py
new file mode 100644
index 0000000..4ac4b43
--- /dev/null
+++ b/dynamic-2d-path.py
@@ -0,0 +1,48 @@
+from functools import cache
+from typing import Tuple
+
+
+def main():
+    n, m = (int(v) for v in input().split())
+    table = [[int(v) for v in input().split()] for _ in range(n)]
+    assert all(len(row) == m for row in table)
+
+    def neighbors(x, y):
+        if y < n:
+            yield "D", (x, y + 1)
+        if x < m:
+            yield "R", (x + 1, y)
+
+    def value_at(x, y):
+        return table[y - 1][x - 1]
+
+    initial = 1, 1
+    final = m, n
+
+    @cache
+    def answer(p) -> Tuple[int, list]:
+        def choices():
+            #  Ascend
+            if p == final:
+                yield value_at(*p), []
+
+            #  Go D or R
+            for dir, np in neighbors(*p):
+                pvalue, path = answer(np)
+                yield value_at(*p) + pvalue, (dir, path)
+
+        return max(choices())
+
+    def gen_path(path):
+        while path:
+            dir, path = path
+            yield dir
+
+    best_value, best_path = answer(initial)
+
+    print(best_value)
+    print(*gen_path(best_path))
+
+
+if __name__ == "__main__":
+    main()