added doctests for dynamicprogramming/minimum_partition (TheAlgorithms#10033)

* added doctests

* added doctests

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

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

* Add doctests to integer_partition.py

* Update minimum_partition.py

---------

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Christian Clauss <[email protected]>

Author: 3 people

Diff for: dynamic_programming/integer_partition.py

@@ -3,10 +3,34 @@
 partitions into exactly k parts plus the number of partitions into at least k-1 parts.
 Subtracting 1 from each part of a partition of n into k parts gives a partition of n-k
 into k parts. These two facts together are used for this algorithm.
+* https://en.wikipedia.org/wiki/Partition_(number_theory)
+* https://en.wikipedia.org/wiki/Partition_function_(number_theory)
 """
 
 
 def partition(m: int) -> int:
+    """
+    >>> partition(5)
+    7
+    >>> partition(7)
+    15
+    >>> partition(100)
+    190569292
+    >>> partition(1_000)
+    24061467864032622473692149727991
+    >>> partition(-7)
+    Traceback (most recent call last):
+        ...
+    IndexError: list index out of range
+    >>> partition(0)
+    Traceback (most recent call last):
+        ...
+    IndexError: list assignment index out of range
+    >>> partition(7.8)
+    Traceback (most recent call last):
+        ...
+    TypeError: 'float' object cannot be interpreted as an integer
+    """
     memo: list[list[int]] = [[0 for _ in range(m)] for _ in range(m + 1)]
     for i in range(m + 1):
         memo[i][0] = 1

Diff for: dynamic_programming/minimum_partition.py

@@ -3,7 +3,7 @@
 """
 
 
-def find_min(arr: list[int]) -> int:
+def find_min(numbers: list[int]) -> int:
     """
     >>> find_min([1, 2, 3, 4, 5])
     1
@@ -15,9 +15,37 @@ def find_min(arr: list[int]) -> int:
     3
     >>> find_min([])
     0
+    >>> find_min([1, 2, 3, 4])
+    0
+    >>> find_min([0, 0, 0, 0])
+    0
+    >>> find_min([-1, -5, 5, 1])
+    0
+    >>> find_min([-1, -5, 5, 1])
+    0
+    >>> find_min([9, 9, 9, 9, 9])
+    9
+    >>> find_min([1, 5, 10, 3])
+    1
+    >>> find_min([-1, 0, 1])
+    0
+    >>> find_min(range(10, 0, -1))
+    1
+    >>> find_min([-1])
+    Traceback (most recent call last):
+        --
+    IndexError: list assignment index out of range
+    >>> find_min([0, 0, 0, 1, 2, -4])
+    Traceback (most recent call last):
+        ...
+    IndexError: list assignment index out of range
+    >>> find_min([-1, -5, -10, -3])
+    Traceback (most recent call last):
+        ...
+    IndexError: list assignment index out of range
     """
-    n = len(arr)
-    s = sum(arr)
+    n = len(numbers)
+    s = sum(numbers)
 
     dp = [[False for x in range(s + 1)] for y in range(n + 1)]
 
@@ -31,8 +59,8 @@ def find_min(arr: list[int]) -> int:
         for j in range(1, s + 1):
             dp[i][j] = dp[i - 1][j]
 
-            if arr[i - 1] <= j:
-                dp[i][j] = dp[i][j] or dp[i - 1][j - arr[i - 1]]
+            if numbers[i - 1] <= j:
+                dp[i][j] = dp[i][j] or dp[i - 1][j - numbers[i - 1]]
 
     for j in range(int(s / 2), -1, -1):
         if dp[n][j] is True: