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* ci: Add `B023` to `.flake8` ignores * refactor: Return `bool`/raise Exception * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * revert: Remove previous branch commit * Update data_structures/binary_tree/segment_tree_other.py Co-authored-by: Christian Clauss <cclauss@me.com> * feat: Apply `__repr__` changes * chore: Fix failing tests * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * Update data_structures/binary_tree/segment_tree_other.py Co-authored-by: Christian Clauss <cclauss@me.com> * test: Fix doctests * random.choice(population_score[:N_SELECTED])[0] * Update basic_string.py Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com> Co-authored-by: Christian Clauss <cclauss@me.com>
117 lines
4.1 KiB
Python
117 lines
4.1 KiB
Python
def points_to_polynomial(coordinates: list[list[int]]) -> str:
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"""
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coordinates is a two dimensional matrix: [[x, y], [x, y], ...]
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number of points you want to use
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>>> print(points_to_polynomial([]))
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Traceback (most recent call last):
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...
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ValueError: The program cannot work out a fitting polynomial.
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>>> print(points_to_polynomial([[]]))
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Traceback (most recent call last):
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...
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ValueError: The program cannot work out a fitting polynomial.
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>>> print(points_to_polynomial([[1, 0], [2, 0], [3, 0]]))
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f(x)=x^2*0.0+x^1*-0.0+x^0*0.0
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>>> print(points_to_polynomial([[1, 1], [2, 1], [3, 1]]))
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f(x)=x^2*0.0+x^1*-0.0+x^0*1.0
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>>> print(points_to_polynomial([[1, 3], [2, 3], [3, 3]]))
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f(x)=x^2*0.0+x^1*-0.0+x^0*3.0
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>>> print(points_to_polynomial([[1, 1], [2, 2], [3, 3]]))
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f(x)=x^2*0.0+x^1*1.0+x^0*0.0
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>>> print(points_to_polynomial([[1, 1], [2, 4], [3, 9]]))
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f(x)=x^2*1.0+x^1*-0.0+x^0*0.0
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>>> print(points_to_polynomial([[1, 3], [2, 6], [3, 11]]))
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f(x)=x^2*1.0+x^1*-0.0+x^0*2.0
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>>> print(points_to_polynomial([[1, -3], [2, -6], [3, -11]]))
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f(x)=x^2*-1.0+x^1*-0.0+x^0*-2.0
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>>> print(points_to_polynomial([[1, 5], [2, 2], [3, 9]]))
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f(x)=x^2*5.0+x^1*-18.0+x^0*18.0
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"""
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if len(coordinates) == 0 or not all(len(pair) == 2 for pair in coordinates):
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raise ValueError("The program cannot work out a fitting polynomial.")
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if len({tuple(pair) for pair in coordinates}) != len(coordinates):
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raise ValueError("The program cannot work out a fitting polynomial.")
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set_x = {x for x, _ in coordinates}
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if len(set_x) == 1:
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return f"x={coordinates[0][0]}"
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if len(set_x) != len(coordinates):
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raise ValueError("The program cannot work out a fitting polynomial.")
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x = len(coordinates)
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count_of_line = 0
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matrix: list[list[float]] = []
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# put the x and x to the power values in a matrix
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while count_of_line < x:
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count_in_line = 0
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a = coordinates[count_of_line][0]
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count_line: list[float] = []
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while count_in_line < x:
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count_line.append(a ** (x - (count_in_line + 1)))
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count_in_line += 1
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matrix.append(count_line)
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count_of_line += 1
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count_of_line = 0
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# put the y values into a vector
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vector: list[float] = []
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while count_of_line < x:
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vector.append(coordinates[count_of_line][1])
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count_of_line += 1
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count = 0
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while count < x:
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zahlen = 0
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while zahlen < x:
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if count == zahlen:
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zahlen += 1
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if zahlen == x:
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break
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bruch = matrix[zahlen][count] / matrix[count][count]
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for counting_columns, item in enumerate(matrix[count]):
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# manipulating all the values in the matrix
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matrix[zahlen][counting_columns] -= item * bruch
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# manipulating the values in the vector
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vector[zahlen] -= vector[count] * bruch
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zahlen += 1
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count += 1
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count = 0
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# make solutions
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solution: list[str] = []
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while count < x:
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solution.append(str(vector[count] / matrix[count][count]))
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count += 1
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count = 0
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solved = "f(x)="
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while count < x:
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remove_e: list[str] = solution[count].split("E")
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if len(remove_e) > 1:
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solution[count] = f"{remove_e[0]}*10^{remove_e[1]}"
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solved += f"x^{x - (count + 1)}*{solution[count]}"
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if count + 1 != x:
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solved += "+"
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count += 1
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return solved
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if __name__ == "__main__":
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print(points_to_polynomial([]))
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print(points_to_polynomial([[]]))
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print(points_to_polynomial([[1, 0], [2, 0], [3, 0]]))
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print(points_to_polynomial([[1, 1], [2, 1], [3, 1]]))
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print(points_to_polynomial([[1, 3], [2, 3], [3, 3]]))
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print(points_to_polynomial([[1, 1], [2, 2], [3, 3]]))
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print(points_to_polynomial([[1, 1], [2, 4], [3, 9]]))
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print(points_to_polynomial([[1, 3], [2, 6], [3, 11]]))
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print(points_to_polynomial([[1, -3], [2, -6], [3, -11]]))
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print(points_to_polynomial([[1, 5], [2, 2], [3, 9]]))
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