From 8d94f7745f81c8f7c33bdd3d0c0740861b9c98e7 Mon Sep 17 00:00:00 2001
From: Kamil <32775019+quant12345@users.noreply.github.com>
Date: Sun, 1 Oct 2023 23:14:58 +0500
Subject: [PATCH] Euler072 - application of vector operations to reduce
 calculation time and refactoring numpy (#9229)

* Replacing the generator with numpy vector operations from lu_decomposition.

* Revert "Replacing the generator with numpy vector operations from lu_decomposition."

This reverts commit ad217c66165898d62b76cc89ba09c2d7049b6448.

* Application of vector operations  to reduce calculation time and refactoring numpy.

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

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

---------

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
---
 project_euler/problem_072/sol1.py | 11 +++++++----
 1 file changed, 7 insertions(+), 4 deletions(-)

diff --git a/project_euler/problem_072/sol1.py b/project_euler/problem_072/sol1.py
index a2a0eeeb3..5a28be564 100644
--- a/project_euler/problem_072/sol1.py
+++ b/project_euler/problem_072/sol1.py
@@ -21,6 +21,8 @@ Sum of phi(d), for all d|n = n. This result can be used to find phi(n) using a s
 Time: 1 sec
 """
 
+import numpy as np
+
 
 def solution(limit: int = 1_000_000) -> int:
     """
@@ -33,14 +35,15 @@ def solution(limit: int = 1_000_000) -> int:
     304191
     """
 
-    phi = [i - 1 for i in range(limit + 1)]
+    # generating an array from -1 to limit
+    phi = np.arange(-1, limit)
 
     for i in range(2, limit + 1):
         if phi[i] == i - 1:
-            for j in range(2 * i, limit + 1, i):
-                phi[j] -= phi[j] // i
+            ind = np.arange(2 * i, limit + 1, i)  # indexes for selection
+            phi[ind] -= phi[ind] // i
 
-    return sum(phi[2 : limit + 1])
+    return np.sum(phi[2 : limit + 1])
 
 
 if __name__ == "__main__":