订单编号    总价
order001    80

------解决方案--------------------

作为一个LINQ的新手，这样的题目很有挑战性。想了一个下午，终于想出来了，还请各位LINQ的高手进一步简化和改良，以进一步提高效率，消除冗余。

附上完整的测试代码：
C# code
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Collections;

namespace PaymentRecord
{
    class Program
    {
        static void Main(string[] args)
        {
            ArrayList orders = new ArrayList();
            orders.Add(new Order { _id = 1, _total = 80M });
            orders.Add(new Order { _id = 2, _total = 100M });
            orders.Add(new Order { _id = 3, _total = 20.5M });

            ArrayList payments = new ArrayList();
            payments.Add(new Payment { _id = 1, _payment = 20M, _date = DateTime.Parse("2011/06/02") });
            payments.Add(new Payment { _id = 1, _payment = 40M, _date = DateTime.Parse("2011/06/04") });
            payments.Add(new Payment { _id = 1, _payment = 10M, _date = DateTime.Parse("2011/06/12") });
            payments.Add(new Payment { _id = 2, _payment = 30M, _date = DateTime.Parse("2011/06/08") });

            var payrecords_1 = orders.OfType<Order>()
                .GroupJoin(payments.OfType<Payment>(),
                o => o._id,
                p => p._id,
                (o, ps) => ps.DefaultIfEmpty().Select(p => new
                {
                    id = o._id,
                    total = o._total,
                    payment = (p != null) ? p._payment : 0,
                    paydate = (p != null) ? p._date : (new DateTime(0))
                }))
                    .SelectMany(r => r);

            var payrecords_2 = payrecords_1.Select(s => new
            {
                id = s.id,
                total = s.total,
                payment = s.payment,
                remain = s.total - payrecords_1.Where(p => (p.id == s.id) && (p.paydate <= s.paydate))
                .Sum(sum => sum.payment),
                paydate = s.paydate
            });

            foreach (var item in payrecords_2)
                Console.WriteLine(item);
        }

        class Order { public int _id; public decimal _total; }
        class Payment { public int _id; public decimal _payment; public DateTime _date; }
    }
}