From 3d2012c4ba3a9d9ddd80e518f0b5b9ba6c52df7d Mon Sep 17 00:00:00 2001
From: Maxim Smolskiy <mithridatus@mail.ru>
Date: Sat, 1 Apr 2023 15:20:08 +0300
Subject: [PATCH] Add Project Euler problem 94 solution 1 (#8599)

Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
---
 DIRECTORY.md                          |  2 ++
 project_euler/problem_094/__init__.py |  0
 project_euler/problem_094/sol1.py     | 44 +++++++++++++++++++++++++++
 3 files changed, 46 insertions(+)
 create mode 100644 project_euler/problem_094/__init__.py
 create mode 100644 project_euler/problem_094/sol1.py

diff --git a/DIRECTORY.md b/DIRECTORY.md
index 18c573909..c781b17bf 100644
--- a/DIRECTORY.md
+++ b/DIRECTORY.md
@@ -937,6 +937,8 @@
     * [Sol1](project_euler/problem_091/sol1.py)
   * Problem 092
     * [Sol1](project_euler/problem_092/sol1.py)
+  * Problem 094
+    * [Sol1](project_euler/problem_094/sol1.py)
   * Problem 097
     * [Sol1](project_euler/problem_097/sol1.py)
   * Problem 099
diff --git a/project_euler/problem_094/__init__.py b/project_euler/problem_094/__init__.py
new file mode 100644
index 000000000..e69de29bb
diff --git a/project_euler/problem_094/sol1.py b/project_euler/problem_094/sol1.py
new file mode 100644
index 000000000..a41292fe2
--- /dev/null
+++ b/project_euler/problem_094/sol1.py
@@ -0,0 +1,44 @@
+"""
+Project Euler Problem 94: https://projecteuler.net/problem=94
+
+It is easily proved that no equilateral triangle exists with integral length sides and
+integral area. However, the almost equilateral triangle 5-5-6 has an area of 12 square
+units.
+
+We shall define an almost equilateral triangle to be a triangle for which two sides are
+equal and the third differs by no more than one unit.
+
+Find the sum of the perimeters of all almost equilateral triangles with integral side
+lengths and area and whose perimeters do not exceed one billion (1,000,000,000).
+"""
+
+
+def solution(max_perimeter: int = 10**9) -> int:
+    """
+    Returns the sum of the perimeters of all almost equilateral triangles with integral
+    side lengths and area and whose perimeters do not exceed max_perimeter
+
+    >>> solution(20)
+    16
+    """
+
+    prev_value = 1
+    value = 2
+
+    perimeters_sum = 0
+    i = 0
+    perimeter = 0
+    while perimeter <= max_perimeter:
+        perimeters_sum += perimeter
+
+        prev_value += 2 * value
+        value += prev_value
+
+        perimeter = 2 * value + 2 if i % 2 == 0 else 2 * value - 2
+        i += 1
+
+    return perimeters_sum
+
+
+if __name__ == "__main__":
+    print(f"{solution() = }")