我正在寻找一种算法来为给定以下项目列表的记录设备生成最佳记录列表：
图片链接在这里 http://img692.imageshack.us/img692/7952/recordlist.png
目前的限制是：
将来可能会添加更多选项：
上下文如下：
另外我想知道是否有一种方法可以生成最优化的记录列表（发送到记录的程序的最高百分比），以防我们无法解决 100% 的冲突，而不管处理时间如何。
提前致谢。
class Recording
{
public int ProgrammeId { get; set; }
public string ProgrammeTitle { get; set; }
public DateTime StartTime { get; set; }
public DateTime EndTime { get; set; }
public int ChannelId { get; set; }
public string ChannelName { get; set; }
public int Weight { get { return 1; } } // Constant weight
}
一种贪婪的方法是按递增的顺序考虑程序start_time。如果某个程序与之前选择的程序兼容，请选择它：
public static IEnumerable<Recording> GreedySelection(IList<Recording> data)
{
data = data
.OrderBy(r => r.StartTime)
.ThenBy(r => r.EndTime)
.ToList();
DateTime? lastEnd = null;
foreach (var rec in data)
{
if (lastEnd == null || rec.StartTime >= lastEnd.Value)
{
yield return rec;
lastEnd = rec.EndTime;
}
}
}
要获得最佳加权解决方案，您可以使用动态规划：
public static IEnumerable<Recording> WeightedSelection(IList<Recording> data)
{
data = data
.OrderBy(r => r.EndTime)
.ThenBy(r => r.StartTime)
.ToList();
int count = data.Count;
var lastCompatible = new int?[count];
// Compute the closest program before in time, that is compatible.
// This nested loop might be optimizable in some way.
for (int i = 0; i < count; i++)
{
for (int j = i - 1; j >= 0; j--)
{
if (data[j].EndTime <= data[i].StartTime)
{
lastCompatible[i] = j;
break; // inner loop
}
}
}
// Dynamic programming to calculate the best path
var optimalWeight = new int[count];
var cameFrom = new int?[count];
for (int i = 0; i < count; i++)
{
int weightWithItem = data[i].Weight;
if (lastCompatible[i] != null)
{
weightWithItem += optimalWeight[lastCompatible[i].Value];
}
int weightWithoutItem = 0;
if (i > 0) weightWithoutItem = optimalWeight[i-1];
if (weightWithItem < weightWithoutItem)
{
optimalWeight[i] = weightWithoutItem;
cameFrom[i] = i - 1;
}
else
{
optimalWeight[i] = weightWithItem;
cameFrom[i] = lastCompatible[i];
}
}
// This will give the programs in reverse order.
for (int? i = count - 1; i != null; i = cameFrom[i.Value])
{
yield return data[i.Value];
}
}
并不是说这个版本包含权重，并试图最大化权重总和。如果所有权重都设置为一 (1)，则两种算法的结果大小将相同，因为大小等于权重。
贪心的结果：
ProgrammeTitle StartTime EndTime
Star Trek 2012-09-03 02:05 2012-09-03 03:05
Everybody Loves Raymond 2012-09-03 06:00 2012-09-03 07:00
CSI 2012-09-03 07:00 2012-09-03 08:00
Mythbusters 2012-09-03 08:00 2012-09-03 09:00
CSI 2012-09-03 10:00 2012-09-03 11:00
Mythbusters 2012-09-03 11:00 2012-09-03 12:00
Star Trek 2012-09-04 02:05 2012-09-04 03:05
Everybody Loves Raymond 2012-09-04 06:00 2012-09-04 07:00
CSI 2012-09-04 07:00 2012-09-04 08:00
Mythbusters 2012-09-04 08:00 2012-09-04 09:00
CSI 2012-09-04 10:00 2012-09-04 11:00
Mythbusters 2012-09-04 11:00 2012-09-04 12:00
动态结果（排序）：
ProgrammeTitle StartTime EndTime
Everybody Loves Raymond 2012-09-03 03:00 2012-09-03 04:00
Everybody Loves Raymond 2012-09-03 06:00 2012-09-03 07:00
CSI 2012-09-03 07:00 2012-09-03 08:00
CSI 2012-09-03 08:30 2012-09-03 09:30
CSI 2012-09-03 10:00 2012-09-03 11:00
Star Trek 2012-09-03 11:05 2012-09-03 12:05
Everybody Loves Raymond 2012-09-04 03:00 2012-09-04 04:00
Everybody Loves Raymond 2012-09-04 06:00 2012-09-04 07:00
CSI 2012-09-04 07:00 2012-09-04 08:00
CSI 2012-09-04 08:30 2012-09-04 09:30
CSI 2012-09-04 10:00 2012-09-04 11:00
Star Trek 2012-09-04 11:05 2012-09-04 12:05
算法基于此文档：