可能会有跨行重叠的情况

如果存在跨行重叠的情况，我们需要对每条记录进行跨行重叠的判断。以下是修改后的代码示例：

# 定义时间区间
start_time = datetime.datetime(2022, 1, 1, 0, 0, 0)
end_time = datetime.datetime(2022, 1, 31, 23, 59, 59)

# 读取记录
records = [
    {"id": 1, "start_time": "2022-01-10 12:00:00", "end_time": "2022-01-20 12:00:00"},
    {"id": 2, "start_time": "2022-01-05 12:00:00", "end_time": "2022-01-15 12:00:00"},
    {"id": 3, "start_time": "2022-01-25 12:00:00", "end_time": "2022-01-30 12:00:00"},
    {"id": 4, "start_time": "2022-01-15 12:00:00", "end_time": "2022-01-25 12:00:00"},
    {"id": 5, "start_time": "2022-01-01 00:00:00", "end_time": "2022-01-31 23:59:59"}
]

# 按照记录的起始时间排序
records = sorted(records, key=lambda x: datetime.datetime.strptime(x["start_time"], "%Y-%m-%d %H:%M:%S"))

# 判断每条记录是否在时间区间内
for i in range(len(records)):
    record_start_time = datetime.datetime.strptime(records[i]["start_time"], "%Y-%m-%d %H:%M:%S")
    record_end_time = datetime.datetime.strptime(records[i]["end_time"], "%Y-%m-%d %H:%M:%S")
    
    overlaps = False
    
    # 判断当前记录是否与前面的记录有跨行重叠
    for j in range(i):
        prev_record_start_time = datetime.datetime.strptime(records[j]["start_time"], "%Y-%m-%d %H:%M:%S")
        prev_record_end_time = datetime.datetime.strptime(records[j]["end_time"], "%Y-%m-%d %H:%M:%S")
        
        if record_start_time <= prev_record_end_time and record_end_time >= prev_record_start_time:
            overlaps = True
            break
    
    if start_time <= record_start_time <= end_time or start_time <= record_end_time <= end_time or overlaps:
        print(f"Record {records[i]['id']} is in the time range.")
    else:
        print(f"Record {records[i]['id']} is not in the time range.")

在上面的代码中，我们增加了一个for循环，用于判断当前记录是否与前面的记录有跨行重叠。如果有跨行重叠，我们将`overlaps`设置为`True`，表示当前记录与前面的记录有重叠部分。然后，我们再按照之前的方法判断每条记录是否在时间区间内，如果当前记录在时间区间内或与前面的记录有跨行重叠，则打印相应的结果。

请注意，上述代码仅作为示例，您需要根据自己的数据结构和要求进行修改。