147 lines
5.7 KiB
Python
147 lines
5.7 KiB
Python
from typing import List, Union
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import numpy as np
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# 解决百分比相加不为100%
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def fix_percentages(values: List[float], total: float) -> List[float]:
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"""
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修正百分比相加不为100%的问题。
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Args:
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values (list[float]): 百分比列表，元素个数与总和相同
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total (float): 总和
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Returns:
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list[float]: 修正后的百分比列表
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Examples:
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>>> values = [0.2, 0.3, 0.5]
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>>> total = 1
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>>> fix_percentages(values, total)
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[20.0, 30.0, 50.0]
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>>> values = [0.2, 0.3, 0.5]
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>>> total = 0.8
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>>> fix_percentages(values, total)
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[25.0, 37.5, 62.5]
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"""
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exact = [v / total * 100 for v in values]
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floor = [np.floor(p * 100) / 100 for p in exact] # 向下取整到2位小数
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remainders = [exact[i] - floor[i] for i in range(len(exact))]
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# 需要分配的百分点数（以0.01%为单位）
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to_distribute = int(round(10000 - sum(floor) * 100))
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# 按余数大小分配
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indices = sorted(range(len(remainders)), key=lambda i: remainders[i], reverse=True)
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fixed = floor.copy()
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for i in range(to_distribute):
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fixed[indices[i]] += 0.01
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return [round(p, 2) for p in fixed]
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# === 误差矫正 ===
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def correct_rounding_error(target_total:Union[int,float], adjusted_areas:List[float], original_areas:List[float]) -> List[int]:
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"""
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健壮的数值舍入误差矫正函数：将浮点型面积值四舍五入后，调整至目标总和。
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核心逻辑：基于原始数值的小数部分优先级，逐次增减1来抵消舍入误差，确保最终总和匹配目标值，
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同时避免调整后数值出现负数，防止无限循环。
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Args:
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target_total (int/float): 目标总和（最终舍入后数值的合计值），函数内部会转为整型
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adjusted_areas (list[float]): 经过比例调整后的浮点型面积列表（待舍入的原始数据）
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original_areas (list[float]): 调整前的原始浮点型面积列表（用于计算小数部分优先级）
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Returns:
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list[int]: 矫正后的整型面积列表，总和尽可能接近/等于target_total；
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若无法完全矫正，返回尽可能接近的结果并打印警告
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Raises:
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无显式抛出异常，所有异常会被捕获并打印错误信息，返回保底的四舍五入结果
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Notes:
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1. 误差矫正规则：
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- 误差>0（当前总和 < 目标总和）：优先给小数部分大的数值+1
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- 误差<0（当前总和 > 目标总和）：优先给小数部分小的数值-1
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2. 边界限制：调整时确保数值≥0（避免出现负数面积）
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3. 防无限循环：最大迭代次数为 len(adjusted_areas) * 10，超出则终止并提示剩余误差
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Examples:
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>>> target = 10
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>>> adjusted = [3.2, 2.8, 4.1] # 四舍五入后总和=3+3+4=10，无误差
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>>> original = [3.2, 2.8, 4.1]
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>>> correct_rounding_error(target, adjusted, original)
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[3, 3, 4]
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>>> target = 10
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>>> adjusted = [3.1, 2.1, 4.1] # 四舍五入后总和=3+2+4=9，误差+1
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>>> original = [3.1, 2.1, 4.1]
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>>> correct_rounding_error(target, adjusted, original)
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[3, 2, 5] # 优先给小数部分最大的4.1+1
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>>> target = 8
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>>> adjusted = [3.9, 2.9, 1.9] # 四舍五入后总和=4+3+2=9，误差-1
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>>> original = [3.9, 2.9, 1.9]
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>>> correct_rounding_error(target, adjusted, original)
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[3, 3, 2] # 优先给小数部分最小的1.9-1（实际小数1.9>2.9>3.9，故调整3.9）
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"""
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try:
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target_total = int(target_total)
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rounded_areas = [int(round(area)) for area in adjusted_areas]
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current_total = sum(rounded_areas)
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error = target_total - current_total
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if error == 0 or len(adjusted_areas) == 0:
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return rounded_areas
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# 使用循环分配直到误差为0或无法再分配
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remaining_error = error
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max_iterations = len(adjusted_areas) * 10 # 防止无限循环
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for _ in range(max_iterations):
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if remaining_error == 0:
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break
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# 每次迭代重新计算小数部分和排序
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decimal_parts = [float(area - int(area)) for area in original_areas]
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indices = list(range(len(adjusted_areas)))
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if remaining_error > 0:
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indices.sort(key=lambda i: decimal_parts[i], reverse=True)
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adjustment = 1
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else:
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indices.sort(key=lambda i: decimal_parts[i])
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adjustment = -1
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# 尝试分配一次调整
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adjusted = False
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for idx in indices:
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if (adjustment == 1 and rounded_areas[idx] >= 0) or (adjustment == -1 and rounded_areas[idx] > 0):
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rounded_areas[idx] += adjustment
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remaining_error -= adjustment
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adjusted = True
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break
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if not adjusted: # 无法再调整
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break
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if remaining_error != 0:
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print(f"警告：无法完全矫正误差，剩余: {remaining_error}")
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return rounded_areas
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except Exception as e:
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print(f"误差矫正出错: {e}")
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# 返回原始四舍五入结果作为保底
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return [int(round(area)) for area in adjusted_areas]
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if __name__ == '__main__':
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target = 10
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adjusted = [3.3, 3.9, 4.2] # 四舍五入后总和=3+3+4=10，无误差
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original = [3.25, 2.85, 4.15]
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print(correct_rounding_error(target, adjusted, original))
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