:meth:`x.__trunc__() <object.__trunc__>`.
+.. function:: comb(n, k)
+
+ Return the number of ways to choose *k* items from *n* items without repetition
+ and without order.
+
+ Also called the binomial coefficient. It is mathematically equal to the expression
+ ``n! / (k! (n - k)!)``. It is equivalent to the coefficient of k-th term in
+ polynomial expansion of the expression ``(1 + x) ** n``.
+
+ Raises :exc:`TypeError` if the arguments not integers.
+ Raises :exc:`ValueError` if the arguments are negative or if k > n.
+
+ .. versionadded:: 3.8
+
+
Note that :func:`frexp` and :func:`modf` have a different call/return pattern
than their C equivalents: they take a single argument and return a pair of
values, rather than returning their second return value through an 'output
self.assertAllClose(fraction_examples, rel_tol=1e-8)
self.assertAllNotClose(fraction_examples, rel_tol=1e-9)
+ def testComb(self):
+ comb = math.comb
+ factorial = math.factorial
+ # Test if factorial defintion is satisfied
+ for n in range(100):
+ for k in range(n + 1):
+ self.assertEqual(comb(n, k), factorial(n)
+ // (factorial(k) * factorial(n - k)))
+
+ # Test for Pascal's identity
+ for n in range(1, 100):
+ for k in range(1, n):
+ self.assertEqual(comb(n, k), comb(n - 1, k - 1) + comb(n - 1, k))
+
+ # Test corner cases
+ for n in range(100):
+ self.assertEqual(comb(n, 0), 1)
+ self.assertEqual(comb(n, n), 1)
+
+ for n in range(1, 100):
+ self.assertEqual(comb(n, 1), n)
+ self.assertEqual(comb(n, n - 1), n)
+
+ # Test Symmetry
+ for n in range(100):
+ for k in range(n // 2):
+ self.assertEqual(comb(n, k), comb(n, n - k))
+
+ # Raises TypeError if any argument is non-integer or argument count is
+ # not 2
+ self.assertRaises(TypeError, comb, 10, 1.0)
+ self.assertRaises(TypeError, comb, 10, "1")
+ self.assertRaises(TypeError, comb, "10", 1)
+ self.assertRaises(TypeError, comb, 10.0, 1)
+
+ self.assertRaises(TypeError, comb, 10)
+ self.assertRaises(TypeError, comb, 10, 1, 3)
+ self.assertRaises(TypeError, comb)
+
+ # Raises Value error if not k or n are negative numbers
+ self.assertRaises(ValueError, comb, -1, 1)
+ self.assertRaises(ValueError, comb, -10*10, 1)
+ self.assertRaises(ValueError, comb, 1, -1)
+ self.assertRaises(ValueError, comb, 1, -10*10)
+
+ # Raises value error if k is greater than n
+ self.assertRaises(ValueError, comb, 1, 10**10)
+ self.assertRaises(ValueError, comb, 0, 1)
+
+
+
def test_main():
from doctest import DocFileSuite
--- /dev/null
+Implement :func:`math.comb` that returns binomial coefficient, that computes\r
+the number of ways to choose k items from n items without repetition and\r
+without order.\r
+Patch by Yash Aggarwal and Keller Fuchs.\r
exit:
return return_value;
}
-/*[clinic end generated code: output=aeed62f403b90199 input=a9049054013a1b77]*/
+
+PyDoc_STRVAR(math_comb__doc__,
+"comb($module, /, n, k)\n"
+"--\n"
+"\n"
+"Number of ways to choose *k* items from *n* items without repetition and without order.\n"
+"\n"
+"Also called the binomial coefficient. It is mathematically equal to the expression\n"
+"n! / (k! * (n - k)!). It is equivalent to the coefficient of k-th term in\n"
+"polynomial expansion of the expression (1 + x)**n.\n"
+"\n"
+"Raises TypeError if the arguments are not integers.\n"
+"Raises ValueError if the arguments are negative or if k > n.");
+
+#define MATH_COMB_METHODDEF \
+ {"comb", (PyCFunction)(void(*)(void))math_comb, METH_FASTCALL|METH_KEYWORDS, math_comb__doc__},
+
+static PyObject *
+math_comb_impl(PyObject *module, PyObject *n, PyObject *k);
+
+static PyObject *
+math_comb(PyObject *module, PyObject *const *args, Py_ssize_t nargs, PyObject *kwnames)
+{
+ PyObject *return_value = NULL;
+ static const char * const _keywords[] = {"n", "k", NULL};
+ static _PyArg_Parser _parser = {NULL, _keywords, "comb", 0};
+ PyObject *argsbuf[2];
+ PyObject *n;
+ PyObject *k;
+
+ args = _PyArg_UnpackKeywords(args, nargs, NULL, kwnames, &_parser, 2, 2, 0, argsbuf);
+ if (!args) {
+ goto exit;
+ }
+ if (!PyLong_Check(args[0])) {
+ _PyArg_BadArgument("comb", 1, "int", args[0]);
+ goto exit;
+ }
+ n = args[0];
+ if (!PyLong_Check(args[1])) {
+ _PyArg_BadArgument("comb", 2, "int", args[1]);
+ goto exit;
+ }
+ k = args[1];
+ return_value = math_comb_impl(module, n, k);
+
+exit:
+ return return_value;
+}
+/*[clinic end generated code: output=00aa76356759617a input=a9049054013a1b77]*/
}
+/*[clinic input]
+math.comb
+
+ n: object(subclass_of='&PyLong_Type')
+ k: object(subclass_of='&PyLong_Type')
+
+Number of ways to choose *k* items from *n* items without repetition and without order.
+
+Also called the binomial coefficient. It is mathematically equal to the expression
+n! / (k! * (n - k)!). It is equivalent to the coefficient of k-th term in
+polynomial expansion of the expression (1 + x)**n.
+
+Raises TypeError if the arguments are not integers.
+Raises ValueError if the arguments are negative or if k > n.
+
+[clinic start generated code]*/
+
+static PyObject *
+math_comb_impl(PyObject *module, PyObject *n, PyObject *k)
+/*[clinic end generated code: output=bd2cec8d854f3493 input=565f340f98efb5b5]*/
+{
+ PyObject *val = NULL,
+ *temp_obj1 = NULL,
+ *temp_obj2 = NULL,
+ *dump_var = NULL;
+ int overflow, cmp;
+ long long i, terms;
+
+ cmp = PyObject_RichCompareBool(n, k, Py_LT);
+ if (cmp < 0) {
+ goto fail_comb;
+ }
+ else if (cmp > 0) {
+ PyErr_Format(PyExc_ValueError,
+ "n must be an integer greater than or equal to k");
+ goto fail_comb;
+ }
+
+ /* b = min(b, a - b) */
+ dump_var = PyNumber_Subtract(n, k);
+ if (dump_var == NULL) {
+ goto fail_comb;
+ }
+ cmp = PyObject_RichCompareBool(k, dump_var, Py_GT);
+ if (cmp < 0) {
+ goto fail_comb;
+ }
+ else if (cmp > 0) {
+ k = dump_var;
+ dump_var = NULL;
+ }
+ else {
+ Py_DECREF(dump_var);
+ dump_var = NULL;
+ }
+
+ terms = PyLong_AsLongLongAndOverflow(k, &overflow);
+ if (terms < 0 && PyErr_Occurred()) {
+ goto fail_comb;
+ }
+ else if (overflow > 0) {
+ PyErr_Format(PyExc_OverflowError,
+ "minimum(n - k, k) must not exceed %lld",
+ LLONG_MAX);
+ goto fail_comb;
+ }
+ else if (overflow < 0 || terms < 0) {
+ PyErr_Format(PyExc_ValueError,
+ "k must be a positive integer");
+ goto fail_comb;
+ }
+
+ if (terms == 0) {
+ return PyNumber_Long(_PyLong_One);
+ }
+
+ val = PyNumber_Long(n);
+ for (i = 1; i < terms; ++i) {
+ temp_obj1 = PyLong_FromSsize_t(i);
+ if (temp_obj1 == NULL) {
+ goto fail_comb;
+ }
+ temp_obj2 = PyNumber_Subtract(n, temp_obj1);
+ if (temp_obj2 == NULL) {
+ goto fail_comb;
+ }
+ dump_var = val;
+ val = PyNumber_Multiply(val, temp_obj2);
+ if (val == NULL) {
+ goto fail_comb;
+ }
+ Py_DECREF(dump_var);
+ dump_var = NULL;
+ Py_DECREF(temp_obj2);
+ temp_obj2 = PyLong_FromUnsignedLongLong((unsigned long long)(i + 1));
+ if (temp_obj2 == NULL) {
+ goto fail_comb;
+ }
+ dump_var = val;
+ val = PyNumber_FloorDivide(val, temp_obj2);
+ if (val == NULL) {
+ goto fail_comb;
+ }
+ Py_DECREF(dump_var);
+ Py_DECREF(temp_obj1);
+ Py_DECREF(temp_obj2);
+ }
+
+ return val;
+
+fail_comb:
+ Py_XDECREF(val);
+ Py_XDECREF(dump_var);
+ Py_XDECREF(temp_obj1);
+ Py_XDECREF(temp_obj2);
+
+ return NULL;
+}
+
+
static PyMethodDef math_methods[] = {
{"acos", math_acos, METH_O, math_acos_doc},
{"acosh", math_acosh, METH_O, math_acosh_doc},
{"tanh", math_tanh, METH_O, math_tanh_doc},
MATH_TRUNC_METHODDEF
MATH_PROD_METHODDEF
+ MATH_COMB_METHODDEF
{NULL, NULL} /* sentinel */
};
projects / python / commitdiff