Add doctests, type hints; fix bug for dynamic_programming/minimum_partition.py (TheAlgorithms#10012)

* Add doctests, type hints; fix bug

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---------

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

Author: 2 people

dynamic_programming/minimum_partition.py

@@ -3,21 +3,33 @@
 """
 
 
-def find_min(arr):
+def find_min(arr: list[int]) -> int:
+    """
+    >>> find_min([1, 2, 3, 4, 5])
+    1
+    >>> find_min([5, 5, 5, 5, 5])
+    5
+    >>> find_min([5, 5, 5, 5])
+    0
+    >>> find_min([3])
+    3
+    >>> find_min([])
+    0
+    """
     n = len(arr)
     s = sum(arr)
 
     dp = [[False for x in range(s + 1)] for y in range(n + 1)]
 
-    for i in range(1, n + 1):
+    for i in range(n + 1):
         dp[i][0] = True
 
     for i in range(1, s + 1):
         dp[0][i] = False
 
     for i in range(1, n + 1):
         for j in range(1, s + 1):
-            dp[i][j] = dp[i][j - 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]]
@@ -28,3 +40,9 @@ def find_min(arr):
             break
 
     return diff
+
+
+if __name__ == "__main__":
+    from doctest import testmod
+
+    testmod()