diff --git a/algorithms/maths/polynomial.py b/algorithms/maths/polynomial.py
index 07a0c3b8a..81faf2b7e 100644
--- a/algorithms/maths/polynomial.py
+++ b/algorithms/maths/polynomial.py
@@ -438,10 +438,7 @@ def __floordiv__(self, other: Union[int, float, Fraction, Monomial]):
# def __truediv__(self, other: Union[int, float, Fraction, Monomial, Polynomial]) -> Polynomial:
def __truediv__(self, other: Union[int, float, Fraction, Monomial]):
"""
- For Polynomials, only division by a monomial
- is defined.
-
- TODO: Implement polynomial / polynomial.
+ For Polynomial division, no remainder is provided. Must use poly_long_division() to capture remainder
"""
if isinstance(other, int) or isinstance(other, float) or isinstance(other, Fraction):
return self.__truediv__( Monomial({}, other) )
@@ -449,17 +446,11 @@ def __truediv__(self, other: Union[int, float, Fraction, Monomial]):
poly_temp = reduce(lambda acc, val: acc + val, map(lambda x: x / other, [z for z in self.all_monomials()]), Polynomial([Monomial({}, 0)]))
return poly_temp
elif isinstance(other, Polynomial):
- if Monomial({}, 0) in other.all_monomials():
- if len(other.all_monomials()) == 2:
- temp_set = {x for x in other.all_monomials() if x != Monomial({}, 0)}
- only = temp_set.pop()
- return self.__truediv__(only)
- elif len(other.all_monomials()) == 1:
- temp_set = {x for x in other.all_monomials()}
- only = temp_set.pop()
- return self.__truediv__(only)
-
- raise ValueError('Can only divide a polynomial by an int, float, Fraction, or a Monomial.')
+ # Call long division
+ quotient, remainder = self.poly_long_division(other)
+ return quotient # Return just the quotient, remainder is ignored here
+
+ raise ValueError('Can only divide a polynomial by an int, float, Fraction, Monomial, or Polynomial.')
return
@@ -526,7 +517,59 @@ def subs(self, substitutions: Union[int, float, Fraction, Dict[int, Union[int, f
def __str__(self) -> str:
"""
- Get a string representation of
- the polynomial.
+ Get a properly formatted string representation of the polynomial.
+ """
+ sorted_monos = sorted(self.all_monomials(), key=lambda m: sorted(m.variables.items(), reverse=True),
+ reverse=True)
+ return ' + '.join(str(m) for m in sorted_monos if m.coeff != Fraction(0, 1))
+
+ def poly_long_division(self, other: 'Polynomial') -> tuple['Polynomial', 'Polynomial']:
"""
- return ' + '.join(str(m) for m in self.all_monomials() if m.coeff != Fraction(0, 1))
+ Perform polynomial long division
+ Returns (quotient, remainder)
+ """
+ if not isinstance(other, Polynomial):
+ raise ValueError("Can only divide by another Polynomial.")
+
+ if len(other.all_monomials()) == 0:
+ raise ValueError("Cannot divide by zero polynomial.")
+
+ quotient = Polynomial([])
+ remainder = self.clone()
+
+ divisor_monos = sorted(other.all_monomials(), key=lambda m: sorted(m.variables.items(), reverse=True),
+ reverse=True)
+ divisor_lead = divisor_monos[0]
+
+ while remainder.all_monomials() and max(remainder.variables(), default=-1) >= max(other.variables(),
+ default=-1):
+ remainder_monos = sorted(remainder.all_monomials(), key=lambda m: sorted(m.variables.items(), reverse=True),
+ reverse=True)
+ remainder_lead = remainder_monos[0]
+
+ if not all(remainder_lead.variables.get(var, 0) >= divisor_lead.variables.get(var, 0) for var in
+ divisor_lead.variables):
+ break
+
+ lead_quotient = remainder_lead / divisor_lead
+ quotient = quotient + Polynomial([lead_quotient]) # Convert Monomial to Polynomial
+
+ remainder = remainder - (
+ Polynomial([lead_quotient]) * other) # Convert Monomial to Polynomial before multiplication
+
+ return quotient, remainder
+
+dividend = Polynomial([
+ Monomial({1: 3}, 4), # 4(a_1)^3
+ Monomial({1: 2}, 3), # 3(a_1)^2
+ Monomial({1: 1}, -2), # -2(a_1)
+ Monomial({}, 5) # +5
+])
+
+divisor = Polynomial([
+ Monomial({1: 1}, 2), # 2(a_1)
+ Monomial({}, -1) # -1
+])
+
+quotient = dividend / divisor
+print("Quotient:", quotient)
diff --git a/algorithms/sort/bead_sort.py b/algorithms/sort/bead_sort.py
new file mode 100644
index 000000000..0d949fa82
--- /dev/null
+++ b/algorithms/sort/bead_sort.py
@@ -0,0 +1,26 @@
+"""
+Bead Sort (also known as Gravity Sort) is a natural sorting algorithm that simulates how beads would settle under gravity on an abacus. It is most useful for sorting positive integers, especially when the range of numbers isn't excessively large. However, it is not a comparison-based sort and is generally impractical for large inputs due to its reliance on physical modeling.
+Time Complexity
+- Best Case: O(n) if the numbers are already sorted
+- Average Case: O(n^2) because each bead needs to be placed and then fall under gravity
+- Worst Case: O(n^2) since each bead must "fall" individually
+"""
+
+def bead_sort(arr):
+ if any(num < 0 for num in arr):
+ raise ValueError("Bead sort only works with non-negative integers.")
+
+ max_num = max(arr) if arr else 0
+ grid = [[0] * len(arr) for _ in range(max_num)]
+
+ # Drop beads (place beads in columns)
+ for col, num in enumerate(arr):
+ for row in range(num):
+ grid[row][col] = 1
+
+ # Let the beads "fall" (count beads in each row)
+ for row in grid:
+ sum_beads = sum(row)
+ for col in range(len(arr)):
+ row[col] = 1 if col < sum_beads else 0
+
diff --git a/tests/test_array.py b/tests/test_array.py
index f1ad11693..b73ecb17b 100644
--- a/tests/test_array.py
+++ b/tests/test_array.py
@@ -9,7 +9,7 @@
missing_ranges,
move_zeros,
plus_one_v1, plus_one_v2, plus_one_v3,
- remove_duplicates
+ remove_duplicates,
rotate_v1, rotate_v2, rotate_v3,
summarize_ranges,
three_sum,
diff --git a/tests/test_polynomial.py b/tests/test_polynomial.py
index 4ba2ba6b7..ab5674017 100644
--- a/tests/test_polynomial.py
+++ b/tests/test_polynomial.py
@@ -105,27 +105,6 @@ def test_polynomial_multiplication(self):
]))
return
- def test_polynomial_division(self):
-
- # Should raise a ValueError if the divisor is not a monomial
- # or a polynomial with only one term.
- self.assertRaises(ValueError, lambda x, y: x / y, self.p5, self.p3)
- self.assertRaises(ValueError, lambda x, y: x / y, self.p6, self.p4)
-
- self.assertEqual(self.p3 / self.p2, Polynomial([
- Monomial({}, 1),
- Monomial({1: 1, 2: -1}, 0.75)
- ]))
- self.assertEqual(self.p7 / self.m1, Polynomial([
- Monomial({1: -1, 2: -3}, 2),
- Monomial({1: 0, 2: -4}, 1.5)
- ]))
- self.assertEqual(self.p7 / self.m1, Polynomial([
- Monomial({1: -1, 2: -3}, 2),
- Monomial({2: -4}, 1.5)
- ]))
- return
-
def test_polynomial_variables(self):
# The zero polynomial has no variables.
@@ -172,4 +151,51 @@ def test_polynomial_clone(self):
self.assertEqual(self.p5.clone(), Polynomial([
Monomial({1: -1, 3: 2}, 1)
]))
- return
\ No newline at end of file
+ return
+
+ def test_polynomial_long_division(self):
+ """
+ Test polynomial long division
+ """
+
+ # Dividend: 4a_1^3 + 3a_1^2 - 2a_1 + 5
+ dividend = Polynomial([
+ Monomial({1: 3}, 4), # 4(a_1)^3
+ Monomial({1: 2}, 3), # 3(a_1)^2
+ Monomial({1: 1}, -2), # -2(a_1)
+ Monomial({}, 5) # +5
+ ])
+
+ # Divisor: 2a_1 - 1
+ divisor = Polynomial([
+ Monomial({1: 1}, 2), # 2(a_1)
+ Monomial({}, -1) # -1
+ ])
+
+ # Expected Quotient: 2a_1^2 + (5/2)a_1 + 1/4
+ expected_quotient = Polynomial([
+ Monomial({1: 2}, 2), # 2(a_1)^2
+ Monomial({1: 1}, Fraction(5, 2)), # (5/2)(a_1)
+ Monomial({}, Fraction(1, 4)) # +1/4
+ ])
+
+ # Expected Remainder: 21/4
+ expected_remainder = Polynomial([
+ Monomial({}, Fraction(21, 4)) # 21/4
+ ])
+
+ quotient_long_div, remainder_long_div = dividend.poly_long_division(divisor)
+
+ quotient_truediv = dividend / divisor # Calls __truediv__, which returns only the quotient
+
+ # Check if quotient from poly_long_division matches expected
+ self.assertEqual(quotient_long_div, expected_quotient)
+
+ # Check if remainder from poly_long_division matches expected
+ self.assertEqual(remainder_long_div, expected_remainder)
+
+ # Check if quotient from __truediv__ matches quotient from poly_long_division
+ self.assertEqual(quotient_truediv, quotient_long_div)
+
+ return
+
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