From 8bbe8caa256882ef2ebdbb3274e6f99f804716bd Mon Sep 17 00:00:00 2001
From: Scarfinos <158184182+Scarfinos@users.noreply.github.com>
Date: Fri, 27 Dec 2024 23:40:35 +0100
Subject: [PATCH] Improve test coverage for matrix exponentiation (#12388)

* #9943 : Adding coverage test for basic_graphs.py

* #9943 : Adding coverage test for basic_graphs.py

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

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

* Solve problem of line too long

* Improving coverage for matrix_exponentiation.py

* fix more than one file

* Update matrix_exponentiation.py

* Update matrix_exponentiation.py

---------

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Maxim Smolskiy <mithridatus@mail.ru>
---
 maths/matrix_exponentiation.py | 36 ++++++++++++++++++++++++++++++----
 1 file changed, 32 insertions(+), 4 deletions(-)

diff --git a/maths/matrix_exponentiation.py b/maths/matrix_exponentiation.py
index 7c37151c8..7cdac9d34 100644
--- a/maths/matrix_exponentiation.py
+++ b/maths/matrix_exponentiation.py
@@ -39,6 +39,21 @@ def modular_exponentiation(a, b):
 
 
 def fibonacci_with_matrix_exponentiation(n, f1, f2):
+    """
+    Returns the nth number of the Fibonacci sequence that
+    starts with f1 and f2
+    Uses the matrix exponentiation
+    >>> fibonacci_with_matrix_exponentiation(1, 5, 6)
+    5
+    >>> fibonacci_with_matrix_exponentiation(2, 10, 11)
+    11
+    >>> fibonacci_with_matrix_exponentiation(13, 0, 1)
+    144
+    >>> fibonacci_with_matrix_exponentiation(10, 5, 9)
+    411
+    >>> fibonacci_with_matrix_exponentiation(9, 2, 3)
+    89
+    """
     # Trivial Cases
     if n == 1:
         return f1
@@ -50,21 +65,34 @@ def fibonacci_with_matrix_exponentiation(n, f1, f2):
 
 
 def simple_fibonacci(n, f1, f2):
+    """
+    Returns the nth number of the Fibonacci sequence that
+    starts with f1 and f2
+    Uses the definition
+    >>> simple_fibonacci(1, 5, 6)
+    5
+    >>> simple_fibonacci(2, 10, 11)
+    11
+    >>> simple_fibonacci(13, 0, 1)
+    144
+    >>> simple_fibonacci(10, 5, 9)
+    411
+    >>> simple_fibonacci(9, 2, 3)
+    89
+    """
     # Trivial Cases
     if n == 1:
         return f1
     elif n == 2:
         return f2
 
-    fn_1 = f1
-    fn_2 = f2
     n -= 2
 
     while n > 0:
-        fn_1, fn_2 = fn_1 + fn_2, fn_1
+        f2, f1 = f1 + f2, f2
         n -= 1
 
-    return fn_1
+    return f2
 
 
 def matrix_exponentiation_time():