




'''simple docstring'''







def 		snake_case_				(_a      :				list[list[int]]	):
    if len(_a	) == 0 or not all(len(_a	) == 2 for pair in coordinates	):
        raise ValueError('''The program cannot work out a fitting polynomial.'''	)

    if len({tuple(_a	) for pair in coordinates}	) != len(_a	):
        raise ValueError('''The program cannot work out a fitting polynomial.'''	)

    UpperCAmelCase     			=						{x for x, _ in coordinates}
    if len(_a	) == 1:
        return F"x={coordinates[0][0]}"

    if len(_a	) != len(_a	):
        raise ValueError('''The program cannot work out a fitting polynomial.'''	)

    UpperCAmelCase     			=						len(_a	)

    UpperCAmelCase     			=						0
    UpperCAmelCase     			=						[]
    # put the x and x to the power values in a matrix
    while count_of_line < x:
        UpperCAmelCase     			=						0
        UpperCAmelCase     			=						coordinates[count_of_line][0]
        UpperCAmelCase     			=						[]
        while count_in_line < x:
            count_line.append(a ** (x - (count_in_line + 1))	)
            count_in_line += 1
        matrix.append(_a	)
        count_of_line += 1

    UpperCAmelCase     			=						0
    # put the y values into a vector
    UpperCAmelCase     			=						[]
    while count_of_line < x:
        vector.append(coordinates[count_of_line][1]	)
        count_of_line += 1

    UpperCAmelCase     			=						0

    while count < x:
        UpperCAmelCase     			=						0
        while zahlen < x:
            if count == zahlen:
                zahlen += 1
            if zahlen == x:
                break
            UpperCAmelCase     			=						matrix[zahlen][count] / matrix[count][count]
            for counting_columns, item in enumerate(matrix[count]	):
                # manipulating all the values in the matrix
                matrix[zahlen][counting_columns] -= item * bruch
            # manipulating the values in the vector
            vector[zahlen] -= vector[count] * bruch
            zahlen += 1
        count += 1

    UpperCAmelCase     			=						0
    # make solutions
    UpperCAmelCase     			=						[]
    while count < x:
        solution.append(str(vector[count] / matrix[count][count]	)	)
        count += 1

    UpperCAmelCase     			=						0
    UpperCAmelCase     			=						'''f(x)='''

    while count < x:
        UpperCAmelCase     			=						solution[count].split('''E'''	)
        if len(_a	) > 1:
            UpperCAmelCase     			=						F"{remove_e[0]}*10^{remove_e[1]}"
        solved += F"x^{x - (count + 1)}*{solution[count]}"
        if count + 1 != x:
            solved += "+"
        count += 1

    return solved


if __name__ == "__main__":
   print(points_to_polynomial([]))
   print(points_to_polynomial([[]]))
   print(points_to_polynomial([[1, 0], [2, 0], [3, 0]]))
   print(points_to_polynomial([[1, 1], [2, 1], [3, 1]]))
   print(points_to_polynomial([[1, 3], [2, 3], [3, 3]]))
   print(points_to_polynomial([[1, 1], [2, 2], [3, 3]]))
   print(points_to_polynomial([[1, 1], [2, 4], [3, 9]]))
   print(points_to_polynomial([[1, 3], [2, 6], [3, 11]]))
   print(points_to_polynomial([[1, -3], [2, -6], [3, -11]]))
   print(points_to_polynomial([[1, 5], [2, 2], [3, 9]]))










'''simple docstring'''







def 		snake_case_				(_a      :				float       ,  _a      :				float       ,  _a      :				float	):
    if hue < 0 or hue > 3_6_0:
        raise Exception('''hue should be between 0 and 360'''	)

    if saturation < 0 or saturation > 1:
        raise Exception('''saturation should be between 0 and 1'''	)

    if value < 0 or value > 1:
        raise Exception('''value should be between 0 and 1'''	)

    UpperCAmelCase     			=						value * saturation
    UpperCAmelCase     			=						hue / 6_0
    UpperCAmelCase     			=						chroma * (1 - abs(hue_section % 2 - 1	))
    UpperCAmelCase     			=						value - chroma

    if hue_section >= 0 and hue_section <= 1:
        UpperCAmelCase     			=						round(2_5_5 * (chroma + match_value)	)
        UpperCAmelCase     			=						round(2_5_5 * (second_largest_component + match_value)	)
        UpperCAmelCase     			=						round(2_5_5 * (match_value)	)
    elif hue_section > 1 and hue_section <= 2:
        UpperCAmelCase     			=						round(2_5_5 * (second_largest_component + match_value)	)
        UpperCAmelCase     			=						round(2_5_5 * (chroma + match_value)	)
        UpperCAmelCase     			=						round(2_5_5 * (match_value)	)
    elif hue_section > 2 and hue_section <= 3:
        UpperCAmelCase     			=						round(2_5_5 * (match_value)	)
        UpperCAmelCase     			=						round(2_5_5 * (chroma + match_value)	)
        UpperCAmelCase     			=						round(2_5_5 * (second_largest_component + match_value)	)
    elif hue_section > 3 and hue_section <= 4:
        UpperCAmelCase     			=						round(2_5_5 * (match_value)	)
        UpperCAmelCase     			=						round(2_5_5 * (second_largest_component + match_value)	)
        UpperCAmelCase     			=						round(2_5_5 * (chroma + match_value)	)
    elif hue_section > 4 and hue_section <= 5:
        UpperCAmelCase     			=						round(2_5_5 * (second_largest_component + match_value)	)
        UpperCAmelCase     			=						round(2_5_5 * (match_value)	)
        UpperCAmelCase     			=						round(2_5_5 * (chroma + match_value)	)
    else:
        UpperCAmelCase     			=						round(2_5_5 * (chroma + match_value)	)
        UpperCAmelCase     			=						round(2_5_5 * (match_value)	)
        UpperCAmelCase     			=						round(2_5_5 * (second_largest_component + match_value)	)

    return [red, green, blue]





def 		snake_case_				(_a      :				int       ,  _a      :				int       ,  _a      :				int	):
    if red < 0 or red > 2_5_5:
        raise Exception('''red should be between 0 and 255'''	)

    if green < 0 or green > 2_5_5:
        raise Exception('''green should be between 0 and 255'''	)

    if blue < 0 or blue > 2_5_5:
        raise Exception('''blue should be between 0 and 255'''	)

    UpperCAmelCase     			=						red / 2_5_5
    UpperCAmelCase     			=						green / 2_5_5
    UpperCAmelCase     			=						blue / 2_5_5
    UpperCAmelCase     			=						max(_a       ,  _a       ,  _a	)
    UpperCAmelCase     			=						value - min(_a       ,  _a       ,  _a	)
    UpperCAmelCase     			=						0 if value == 0 else chroma / value

    if chroma == 0:
        UpperCAmelCase     			=						0.0
    elif value == float_red:
        UpperCAmelCase     			=						6_0 * (0 + (float_green - float_blue) / chroma)
    elif value == float_green:
        UpperCAmelCase     			=						6_0 * (2 + (float_blue - float_red) / chroma)
    else:
        UpperCAmelCase     			=						6_0 * (4 + (float_red - float_green) / chroma)

    UpperCAmelCase     			=						(hue + 3_6_0) % 3_6_0

    return [hue, saturation, value]







def 		snake_case_				(_a      :				list[float]       ,  _a      :				list[float]	):
    UpperCAmelCase     			=						abs(hsv_a[0] - hsv_a[0]	) < 0.2
    UpperCAmelCase     			=						abs(hsv_a[1] - hsv_a[1]	) < 0.002
    UpperCAmelCase     			=						abs(hsv_a[2] - hsv_a[2]	) < 0.002

    return check_hue and check_saturation and check_value




