From 61e1dd27b0db00302cec75fca5365d08e81ab707 Mon Sep 17 00:00:00 2001
From: poloso <osoriopabl@gmail.com>
Date: Thu, 28 Oct 2021 15:31:32 -0500
Subject: [PATCH] [mypy] Fix type annotation in euler_method.py (#5649)

* [mypy] Fix type annotation in euler_method.py

In line with issue #4052.

* updating DIRECTORY.md

Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
---
 DIRECTORY.md          |  1 +
 maths/euler_method.py | 27 +++++++++++++++++----------
 2 files changed, 18 insertions(+), 10 deletions(-)

diff --git a/DIRECTORY.md b/DIRECTORY.md
index a8986f195..434cddbfd 100644
--- a/DIRECTORY.md
+++ b/DIRECTORY.md
@@ -186,6 +186,7 @@
     * [Swap Nodes](https://github.com/TheAlgorithms/Python/blob/master/data_structures/linked_list/swap_nodes.py)
   * Queue
     * [Circular Queue](https://github.com/TheAlgorithms/Python/blob/master/data_structures/queue/circular_queue.py)
+    * [Circular Queue Linked List](https://github.com/TheAlgorithms/Python/blob/master/data_structures/queue/circular_queue_linked_list.py)
     * [Double Ended Queue](https://github.com/TheAlgorithms/Python/blob/master/data_structures/queue/double_ended_queue.py)
     * [Linked Queue](https://github.com/TheAlgorithms/Python/blob/master/data_structures/queue/linked_queue.py)
     * [Priority Queue Using List](https://github.com/TheAlgorithms/Python/blob/master/data_structures/queue/priority_queue_using_list.py)
diff --git a/maths/euler_method.py b/maths/euler_method.py
index 7c7801986..155ef28d1 100644
--- a/maths/euler_method.py
+++ b/maths/euler_method.py
@@ -1,18 +1,25 @@
+from typing import Callable
+
 import numpy as np
 
 
-def explicit_euler(ode_func, y0, x0, step_size, x_end):
-    """
-    Calculate numeric solution at each step to an ODE using Euler's Method
+def explicit_euler(
+    ode_func: Callable, y0: float, x0: float, step_size: float, x_end: float
+) -> np.ndarray:
+    """Calculate numeric solution at each step to an ODE using Euler's Method
 
-    https://en.wikipedia.org/wiki/Euler_method
+    For reference to Euler's method refer to https://en.wikipedia.org/wiki/Euler_method.
 
-    Arguments:
-    ode_func -- The ode as a function of x and y
-    y0 -- the initial value for y
-    x0 -- the initial value for x
-    stepsize -- the increment value for x
-    x_end -- the end value for x
+    Args:
+        ode_func (Callable):  The ordinary differential equation
+            as a function of x and y.
+        y0 (float): The initial value for y.
+        x0 (float): The initial value for x.
+        step_size (float): The increment value for x.
+        x_end (float): The final value of x to be calculated.
+
+    Returns:
+        np.ndarray: Solution of y for every step in x.
 
     >>> # the exact solution is math.exp(x)
     >>> def f(x, y):