Optimization problem_10 in project_euler (#2453)

* optimization for problem09 in project_euler

* added benchmark code

* fixup! Format Python code with psf/black push

* Update project_euler/problem_09/sol1.py

Co-authored-by: Christian Clauss <cclauss@me.com>

* updating DIRECTORY.md

* Update project_euler/problem_09/sol1.py

* fixup! Format Python code with psf/black push

Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Co-authored-by: Christian Clauss <cclauss@me.com>

DIRECTORY.md

@@ -713,6 +713,7 @@
 ## Strings
   * [Aho Corasick](https://github.com/TheAlgorithms/Python/blob/master/strings/aho_corasick.py)
   * [Boyer Moore Search](https://github.com/TheAlgorithms/Python/blob/master/strings/boyer_moore_search.py)
+  * [Can String Be Rearranged As Palindrome](https://github.com/TheAlgorithms/Python/blob/master/strings/can_string_be_rearranged_as_palindrome.py)
   * [Capitalize](https://github.com/TheAlgorithms/Python/blob/master/strings/capitalize.py)
   * [Check Anagrams](https://github.com/TheAlgorithms/Python/blob/master/strings/check_anagrams.py)
   * [Check Pangram](https://github.com/TheAlgorithms/Python/blob/master/strings/check_pangram.py)

project_euler/problem_09/sol1.py

@@ -16,7 +16,6 @@ def solution():
      1. a < b < c
      2. a**2 + b**2 = c**2
      3. a + b + c = 1000
-
     # The code below has been commented due to slow execution affecting Travis.
     # >>> solution()
     # 31875000
@@ -30,6 +29,40 @@ def solution():
                             return a * b * c
 
 
+def solution_fast():
+    """
+     Returns the product of a,b,c which are Pythagorean Triplet that satisfies
+     the following:
+     1. a < b < c
+     2. a**2 + b**2 = c**2
+     3. a + b + c = 1000
+
+    # The code below has been commented due to slow execution affecting Travis.
+    # >>> solution_fast()
+    # 31875000
+    """
+    for a in range(300):
+        for b in range(400):
+            c = 1000 - a - b
+            if a < b < c and (a ** 2) + (b ** 2) == (c ** 2):
+                return a * b * c
+
+
+def benchmark() -> None:
+    """
+    Benchmark code comparing two different version function.
+    """
+    import timeit
+
+    print(
+        timeit.timeit("solution()", setup="from __main__ import solution", number=1000)
+    )
+    print(
+        timeit.timeit(
+            "solution_fast()", setup="from __main__ import solution_fast", number=1000
+        )
+    )
+
+
 if __name__ == "__main__":
-    print("Please Wait...")
+    benchmark()
-    print(solution())

project_euler/problem_09/sol3.py

@@ -25,11 +25,10 @@ def solution():
     # 31875000
     """
     return [
-        a * b * c
+        a * b * (1000 - a - b)
         for a in range(1, 999)
         for b in range(a, 999)
-        for c in range(b, 999)
+        if (a * a + b * b == (1000 - a - b) ** 2)
-        if (a * a + b * b == c * c) and (a + b + c == 1000)
     ][0]
 
 

strings/can_string_be_rearranged_as_palindrome.py

@@ -8,7 +8,9 @@ from timeit import timeit
 # Counter is faster for long strings and non-Counter is faster for short strings.
 
 
-def can_string_be_rearranged_as_palindrome_counter(input_str: str = "",) -> bool:
+def can_string_be_rearranged_as_palindrome_counter(
+    input_str: str = "",
+) -> bool:
     """
     A Palindrome is a String that reads the same forward as it does backwards.
     Examples of Palindromes mom, dad, malayalam