[mypy] fix mypy error in Project Euler Problem 092 solution 1 (#5357)

* fix mypy error

* updating DIRECTORY.md

* simplify code

* run black

* fix doc consistency

* Fix doc

* fix doc

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

DIRECTORY.md

@@ -211,6 +211,9 @@
   * Histogram Equalization
     * [Histogram Stretch](https://github.com/TheAlgorithms/Python/blob/master/digital_image_processing/histogram_equalization/histogram_stretch.py)
   * [Index Calculation](https://github.com/TheAlgorithms/Python/blob/master/digital_image_processing/index_calculation.py)
+  * Morphological Operations
+    * [Dilation Operation](https://github.com/TheAlgorithms/Python/blob/master/digital_image_processing/morphological_operations/dilation_operation.py)
+    * [Erosion Operation](https://github.com/TheAlgorithms/Python/blob/master/digital_image_processing/morphological_operations/erosion_operation.py)
   * Resize
     * [Resize](https://github.com/TheAlgorithms/Python/blob/master/digital_image_processing/resize/resize.py)
   * Rotation
@@ -778,6 +781,8 @@
     * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_089/sol1.py)
   * Problem 091
     * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_091/sol1.py)
+  * Problem 092
+    * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_092/sol1.py)
   * Problem 097
     * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_097/sol1.py)
   * Problem 099

project_euler/problem_092/sol1.py

@@ -17,7 +17,7 @@ def next_number(number: int) -> int:
     Returns the next number of the chain by adding the square of each digit
     to form a neww number.
     For example if number = 12, next_number() will return 1^2 + 2^2 = 5.
-    Therefore 5 is the next number of the chain.
+    Therefore, 5 is the next number of the chain.
     >>> next_number(44)
     32
     >>> next_number(10)
@@ -25,22 +25,22 @@ def next_number(number: int) -> int:
     >>> next_number(32)
     13
     """
-    num = 0
+    sum_of_digits_squared = 0
-    for i in range(len(str(number))):
+    while number:
-        num += int(str(number)[i]) ** 2
+        sum_of_digits_squared += (number % 10) ** 2
+        number //= 10
 
-    return num
+    return sum_of_digits_squared
 
 
 def chain(number: int) -> bool:
     """
-    Generates the chain of numbers until the nest number generated is 1 0r 89.
+    The function generates the chain of numbers until the next number is 1 or 89.
-    for example, if starting number is 44, then the function generates the
+    For example, if starting number is 44, then the function generates the
-    following chain of  numbers.
+    following chain of numbers:
-    chain: 44 → 32 → 13 → 10 → 1 → 1
+    44 → 32 → 13 → 10 → 1 → 1.
-    once the next number generated is 1 or 89, the function
+    Once the next number generated is 1 or 89, the function returns whether
-    Returns True if the next number generated by next_number() if 1.
+    or not the the next number generated by next_number() is 1.
-    Returns False if the next number generated by next_number() is 89.
     >>> chain(10)
     True
     >>> chain(58)
@@ -51,43 +51,26 @@ def chain(number: int) -> bool:
     while number != 1 and number != 89:
         number = next_number(number)
 
-    if number == 1:
+    return number == 1
-        return True
-
-    elif number == 89:
-        return False
 
 
 def solution(number: int = 10000000) -> int:
     """
-    The function returns the total numbers that end up in 89 after the chain generation.
+    The function returns the number of integers that end up being 89 in each chain.
     The function accepts a range number and the function checks all the values
     under value number.
-    if the chain generation leads to the end number as 1 or 89. If the chain()
-    returns True, then total is incremented, implying that the number we
-    started with ended up with 1 else total2 is incremented, implying that
-    the number we started with ended up in 89 after chain generation.
-    But the function returns total2 as the requirement of question is
-    to find out how many ended up in 89.
 
     >>> solution(100)
     80
     >>> solution(10000000)
     8581146
     """
-    total = 0
+    return sum(1 for i in range(1, number) if not chain(i))
-    total2 = 0
-    for i in range(1, number):
-        val = chain(i)
-
-        if val is True:
-            total += 1
-
-        elif val is False:
-            total2 += 1
-
-    return total2
 
 
 if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
+
     print(f"{solution() = }")