From a2efba59bfb0dd5920cfa05572fc7843ea454d28 Mon Sep 17 00:00:00 2001
From: Mindaugas <76015221+mindaugl@users.noreply.github.com>
Date: Thu, 12 Mar 2026 23:00:28 +0200
Subject: [PATCH] Add euler project problem 15 additional solution (#12774)

* Add euler project problem 15 additional solution by explicitly counting the paths.

* Update sol2.py

* updating DIRECTORY.md

* updating DIRECTORY.md

* Trigger CI

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

---------

Co-authored-by: Maxim Smolskiy <mithridatus@mail.ru>
Co-authored-by: MaximSmolskiy <MaximSmolskiy@users.noreply.github.com>
Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
---
 DIRECTORY.md                      |  6 ++++++
 project_euler/problem_015/sol2.py | 32 +++++++++++++++++++++++++++++++
 2 files changed, 38 insertions(+)
 create mode 100644 project_euler/problem_015/sol2.py

diff --git a/DIRECTORY.md b/DIRECTORY.md
index a73c630bc..ca454bd5f 100644
--- a/DIRECTORY.md
+++ b/DIRECTORY.md
@@ -469,6 +469,11 @@
 
 ## Geometry
   * [Geometry](geometry/geometry.py)
+  * [Graham Scan](geometry/graham_scan.py)
+  * [Jarvis March](geometry/jarvis_march.py)
+  * Tests
+    * [Test Graham Scan](geometry/tests/test_graham_scan.py)
+    * [Test Jarvis March](geometry/tests/test_jarvis_march.py)
 
 ## Graphics
   * [Bezier Curve](graphics/bezier_curve.py)
@@ -981,6 +986,7 @@
     * [Sol2](project_euler/problem_014/sol2.py)
   * Problem 015
     * [Sol1](project_euler/problem_015/sol1.py)
+    * [Sol2](project_euler/problem_015/sol2.py)
   * Problem 016
     * [Sol1](project_euler/problem_016/sol1.py)
     * [Sol2](project_euler/problem_016/sol2.py)
diff --git a/project_euler/problem_015/sol2.py b/project_euler/problem_015/sol2.py
new file mode 100644
index 000000000..903095e14
--- /dev/null
+++ b/project_euler/problem_015/sol2.py
@@ -0,0 +1,32 @@
+"""
+Problem 15: https://projecteuler.net/problem=15
+
+Starting in the top left corner of a 2x2 grid, and only being able to move to
+the right and down, there are exactly 6 routes to the bottom right corner.
+How many such routes are there through a 20x20 grid?
+"""
+
+
+def solution(n: int = 20) -> int:
+    """
+    Solve by explicitly counting the paths with dynamic programming.
+
+    >>> solution(6)
+    924
+    >>> solution(2)
+    6
+    >>> solution(1)
+    2
+    """
+
+    counts = [[1 for _ in range(n + 1)] for _ in range(n + 1)]
+
+    for i in range(1, n + 1):
+        for j in range(1, n + 1):
+            counts[i][j] = counts[i - 1][j] + counts[i][j - 1]
+
+    return counts[n][n]
+
+
+if __name__ == "__main__":
+    print(solution())