Add Project Euler problem 94 solution 1

DIRECTORY.md

@@ -317,6 +317,7 @@
  * [Longest Sub Array](dynamic_programming/longest_sub_array.py)
  * [Matrix Chain Order](dynamic_programming/matrix_chain_order.py)
  * [Max Non Adjacent Sum](dynamic_programming/max_non_adjacent_sum.py)
+ * [Max Product Subarray](dynamic_programming/max_product_subarray.py)
  * [Max Sub Array](dynamic_programming/max_sub_array.py)
  * [Max Sum Contiguous Subsequence](dynamic_programming/max_sum_contiguous_subsequence.py)
  * [Min Distance Up Bottom](dynamic_programming/min_distance_up_bottom.py)
@@ -936,6 +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

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() = }")