Add comprehensive doctests for binomial_coefficient function

Author: vishal-rathod-07

maths/binomial_coefficient.py

@@ -38,6 +38,107 @@ def binomial_coefficient(n: int, r: int) -> int:
     Traceback (most recent call last):
         ...
     TypeError: 'float' object cannot be interpreted as an integer
+
+    # Additional edge cases
+    >>> binomial_coefficient(0, 0)
+    1
+    >>> binomial_coefficient(1, 0)
+    1
+    >>> binomial_coefficient(1, 1)
+    1
+    >>> binomial_coefficient(2, 1)
+    2
+    >>> binomial_coefficient(3, 0)
+    1
+    >>> binomial_coefficient(3, 1)
+    3
+    >>> binomial_coefficient(3, 2)
+    3
+    >>> binomial_coefficient(3, 3)
+    1
+    >>> binomial_coefficient(4, 2)
+    6
+
+    # Test symmetry property: C(n,r) = C(n, n-r)
+    >>> binomial_coefficient(8, 3) == binomial_coefficient(8, 5)
+    True
+    >>> binomial_coefficient(7, 2) == binomial_coefficient(7, 5)
+    True
+    >>> binomial_coefficient(6, 1) == binomial_coefficient(6, 5)
+    True
+
+    # Test larger numbers
+    >>> binomial_coefficient(15, 3)
+    455
+    >>> binomial_coefficient(12, 4)
+    495
+    >>> binomial_coefficient(20, 2)
+    190
+    >>> binomial_coefficient(13, 6)
+    1716
+
+    # Test cases where r > n (should return 0)
+    >>> binomial_coefficient(1, 2)
+    0
+    >>> binomial_coefficient(2, 5)
+    0
+    >>> binomial_coefficient(4, 7)
+    0
+
+    # Test Pascal's triangle identity: C(n,r) = C(n-1,r-1) + C(n-1,r)
+    >>> (binomial_coefficient(5, 2) ==
+    ...  binomial_coefficient(4, 1) + binomial_coefficient(4, 2))
+    True
+    >>> (binomial_coefficient(6, 3) ==
+    ...  binomial_coefficient(5, 2) + binomial_coefficient(5, 3))
+    True
+    >>> (binomial_coefficient(7, 4) ==
+    ...  binomial_coefficient(6, 3) + binomial_coefficient(6, 4))
+    True
+
+    # Test performance with larger numbers
+    >>> binomial_coefficient(100, 2)
+    4950
+    >>> binomial_coefficient(50, 1)
+    50
+    >>> binomial_coefficient(25, 0)
+    1
+    >>> binomial_coefficient(30, 30)
+    1
+
+    # Test boundary conditions more thoroughly
+    >>> all(binomial_coefficient(n, 0) == 1 for n in range(10))
+    True
+    >>> all(binomial_coefficient(n, n) == 1 for n in range(10))
+    True
+    >>> all(binomial_coefficient(n, 1) == n for n in range(1, 10))
+    True
+
+    # Test some well-known binomial coefficients
+    >>> binomial_coefficient(4, 2)  # 4 choose 2
+    6
+    >>> binomial_coefficient(5, 3)  # 5 choose 3
+    10
+    >>> binomial_coefficient(6, 2)  # 6 choose 2
+    15
+    >>> binomial_coefficient(8, 4)  # 8 choose 4
+    70
+    >>> binomial_coefficient(9, 3)  # 9 choose 3
+    84
+
+    # Additional negative number tests
+    >>> binomial_coefficient(-1, 0)
+    Traceback (most recent call last):
+        ...
+    ValueError: n and r must be non-negative integers
+    >>> binomial_coefficient(0, -1)
+    Traceback (most recent call last):
+        ...
+    ValueError: n and r must be non-negative integers
+    >>> binomial_coefficient(-5, -3)
+    Traceback (most recent call last):
+        ...
+    ValueError: n and r must be non-negative integers
     """
     if n < 0 or r < 0:
         raise ValueError("n and r must be non-negative integers")