以下是一个示例代码，解决了计算不同ID的日期范围之间重叠天数的总和的问题：

from datetime import datetime, timedelta

# 定义日期范围类
class DateRange:
    def __init__(self, start_date, end_date):
        self.start_date = start_date
        self.end_date = end_date

    def get_overlap_days(self, other_range):
        overlap_start = max(self.start_date, other_range.start_date)
        overlap_end = min(self.end_date, other_range.end_date)
        overlap = (overlap_end - overlap_start).days + 1
        return max(0, overlap)


def calculate_overlap_days(date_ranges):
    total_overlap_days = 0
    for i in range(len(date_ranges)):
        for j in range(i + 1, len(date_ranges)):
            overlap_days = date_ranges[i].get_overlap_days(date_ranges[j])
            total_overlap_days += overlap_days
    return total_overlap_days


# 示例数据
date_range1 = DateRange(datetime(2022, 1, 1), datetime(2022, 1, 5))
date_range2 = DateRange(datetime(2022, 1, 4), datetime(2022, 1, 8))
date_range3 = DateRange(datetime(2022, 1, 10), datetime(2022, 1, 15))

date_ranges = [date_range1, date_range2, date_range3]

# 计算重叠天数总和
overlap_days = calculate_overlap_days(date_ranges)
print("Total overlap days:", overlap_days)

在这个示例中，我们定义了一个DateRange类来表示日期范围，该类包含起始日期和结束日期。然后，我们使用get_overlap_days方法来计算两个日期范围之间的重叠天数。最后，我们使用calculate_overlap_days函数来计算不同ID的日期范围之间重叠天数的总和。

请注意，此示例假设日期范围是闭区间，即包括起始日期和结束日期。如果你的需求是半开区间（包括起始日期但不包括结束日期），你可以相应地调整计算重叠天数的逻辑。