计算时间序列的滑动 window 最大值
Calculate max on a sliding window for TimeSeries
输入：
public class MyObject
{
public double Value { get; set; }
public DateTime Date { get; set; }
}
生成测试对象的方法：
public static MyObject[] GetTestObjects()
{
var rnd = new Random();
var date = new DateTime(2021, 1, 1, 0, 0, 0);
var result = new List<MyObject>();
for (int i = 0; i < 50000; i++)
{
//this is to simulate real data having gaps
if (rnd.Next(100) < 25)
{
continue;
}
var myObject = new MyObject()
{
Value = rnd.NextDouble(),
Date = date.AddMinutes(15 * i)
};
result.Add(myObject);
}
return result.ToArray();
}
鉴于此，我需要为每个 myObject 计算前 12 个月的最大值。我只能考虑 InParallel，但也许有优化的解决方案？
抱歉不清楚，这是我现在用来得到我想要的东西：
public MyObject[] BruteForceBackward(MyObject[] testData)
{
return testData.AsParallel().Select(point =>
{
var max = testData.Where(x => x.Date <= point.Date && x.Date >= point.Date.AddYears(-1)).Max(x => x.Value);
return new MyObject() { Date = point.Date, Value = point.Value / max };
}).OrderBy(r => r.Date).ToArray();
}
这可行，但它很慢并且会占用处理器资源（想象一下，你有 100k 个对象），我相信一定有更好的东西
假设您的意思是您需要从 result 开始的过去 12 个月中每个月的最大值 Value，那么您可以使用 LINQ：
var beginDateTime = DateTime.Now.AddMonths(-12);
var ans = result.Where(r => r.Date >= beginDateTime).GroupBy(r => r.Date.Month).Select(mg => mg.MaxBy(r => r.Value)).ToList();
运行 一些时间，我知道在 result 之后放置 AsParallel 将 运行 时间从大约 16 毫秒（第一个 运行）更改为大约 32 毫秒，所以它实际上更慢。 Where 之后和 GroupBy 之后大约 23 毫秒（并行处理 12 个组）大致相同。至少在我的 PC 上，没有足够的数据或复杂的并行操作，但 GroupBy 不是最有效的。
使用数组并测试每个元素，我在大约 1.2 毫秒内得到了结果：
var maxMOs = new MyObject[12];
foreach (var r in result.Where(r => r.Date >= beginDateTime)) {
var monthIndex = r.Date.Month-1;
if (maxMOs[monthIndex] == null || r.Value > maxMOs[monthIndex].Value)
maxMOs[monthIndex] = r;
}
请注意，结果不是按时间顺序排列的；如果需要，您可以将 monthIndex 偏移到今天的月份以对结果进行排序。
var maxMOs = new MyObject[12];
var offset = DateTime.Now.Month-11;
foreach (var r in result.Where(r => r.Date >= beginDateTime)) {
var monthIndex = r.Date.Month-offset;
if (maxMOs[monthIndex] == null || r.Value > maxMOs[monthIndex].Value)
maxMOs[monthIndex] = r;
}
微优化（主要用于重复 运行nings）是反转测试并使用空传播运算符：
if (!(r.Value <= maxMOs[monthIndex]?.Value))
这在第一个 运行 上节省了大约 0.2 毫秒，但在随后的 运行 上最多节省了 0.5 毫秒。
我有一个类似的项目，我必须根据大量传感器数据计算这些东西。
一般来说，您希望减少遍历所有数据的循环次数。充其量，您只想触摸每个元素一次。
进程数组（相当于BruteForceBackwards）
public static MyObject[] FlowThroughForward(ref MyObject[] testData)
{
// generate return array
MyObject[] returnData = new MyObject[testData.Length];
// keep track to minimize processing
double currentMaximum = 0;
List<MyObject> maximumValues = new List<MyObject>();
// go through the elements
for (int i = 0; i < testData.Length; i++)
{
// calculate the oldest date to keep in tracking list
DateTime targetDate = testData[i].Date.AddYears(-1);
// maximum logic
if (testData[i].Value >= currentMaximum)
{
// new maximum found, clear tracking list
// this is the best case scenario
maximumValues.Clear();
currentMaximum = testData[i].Value;
}
else
{
// unfortunately, no new maximum was found
// go backwards the maximum tracking list and check for smaller values
// clear the list of all smaller values. The list should therefore always
// be in descending order
for (int b = maximumValues.Count - 1; b >= 0; b--)
{
if (maximumValues[b].Value <= testData[i].Value)
{
// a lower value has been found. We have a newer, higher value
// clear this waste value from the tracking list
maximumValues.RemoveAt(b);
}
else
{
// there are no more lower values.
// stop looking for smaller values to save time
break;
}
}
}
// append new value to tracking list, no matter if higher or lower
// all future values might be lower
maximumValues.Add(testData[i]);
// check if the oldest value is too old to be kept in the tracking list
while (maximumValues[0].Date < targetDate)
{
// oldest value is to be removed
maximumValues.RemoveAt(0);
// update maximum
currentMaximum = maximumValues[0].Value;
}
// add object to result list
returnData[i] = new MyObject() { Date = testData[i].Date, Value = testData[i].Value / currentMaximum }; ;
}
return returnData;
}
实时数据或流数据
注意：如果列表非常大，则传递完整数组的方法可能会出现内存问题。在这种情况下：一次传递一个值，将它们从最旧的值传递到最新的值。一次存储一个值。
此功能也可用于实时数据。
测试方法包含在代码中。
static void Main(string[] args)
{
int length = 50000;
Stopwatch stopWatch1 = new Stopwatch();
stopWatch1.Start();
var myObject = new MyObject();
var result = new List<MyObject>();
var date = new DateTime(2021, 1, 1, 0, 0, 0);
for (int i = 0; i < length; i++)
{
//this is to simulate real data having gaps
if (rnd.Next(100) < 25)
{
continue;
}
myObject.Value = rnd.NextDouble();
myObject.Date = date.AddMinutes(15 * i);
result.Add(CalculateNextObject(ref myObject));
}
stopWatch1.Stop();
Console.WriteLine("test code executed in " + stopWatch1.ElapsedMilliseconds + " ms");
Thread.Sleep(1000000);
}
private static Random rnd = new Random();
private static double currentMaximum = 0;
private static List<MyObject> maximumValues = new List<MyObject>();
public static MyObject CalculateNextObject(ref MyObject input)
{
// calculate the oldest date to keep in tracking list
DateTime targetDate = input.Date.AddYears(-1);
// maximum logic
if (input.Value >= currentMaximum)
{
// new maximum found, clear tracking list
// this is the best case scenario
maximumValues.Clear();
currentMaximum = input.Value;
}
else
{
// unfortunately, no new maximum was found
// go backwards the maximum tracking list and check for smaller values
// clear the list of all smaller values. The list should therefore always
// be in descending order
for (int b = maximumValues.Count - 1; b >= 0; b--)
{
if (maximumValues[b].Value <= input.Value)
{
// a lower value has been found. We have a newer, higher value
// clear this waste value from the tracking list
maximumValues.RemoveAt(b);
}
else
{
// there are no more lower values.
// stop looking for smaller values to save time
break;
}
}
}
// append new value to tracking list, no matter if higher or lower
// all future values might be lower
maximumValues.Add(input);
// check if the oldest value is too old to be kept in the tracking list
while (maximumValues[0].Date < targetDate)
{
// oldest value is to be removed
maximumValues.RemoveAt(0);
// update maximum
currentMaximum = maximumValues[0].Value;
}
// add object to result list
MyObject returnData = new MyObject() { Date = input.Date, Value = input.Value / currentMaximum };
return returnData;
}
测试方法
static void Main(string[] args)
{
MyObject[] testData = GetTestObjects();
Stopwatch stopWatch1 = new Stopwatch();
Stopwatch stopWatch2 = new Stopwatch();
stopWatch1.Start();
MyObject[] testresults1 = BruteForceBackward(testData);
stopWatch1.Stop();
Console.WriteLine("BruteForceBackward executed in " + stopWatch1.ElapsedMilliseconds + " ms");
stopWatch2.Start();
MyObject[] testresults2 = FlowThroughForward(ref testData);
stopWatch2.Stop();
Console.WriteLine("FlowThroughForward executed in " + stopWatch2.ElapsedMilliseconds + " ms");
Console.WriteLine();
Console.WriteLine("Comparing some random test results: ");
var rnd = new Random();
for (int i = 0; i < 10; i++)
{
int index = rnd.Next(0, testData.Length);
Console.WriteLine("Index: " + index + " brute: " + testresults1[index].Value + " flow: " + testresults2[index].Value);
}
Thread.Sleep(1000000);
}
测试结果
测试是在 32 核的机器上进行的，所以理论上多线程方法应该有优势，但你会看到 ;)
Function
Function Time
time %
BruteForceBackward
5334 ms
99.9%
FlowThroughForward
5 ms
0.094%
性能提升系数：~time/1000
带数据验证的控制台输出：
BruteForceBackward executed in 5264 ms
FlowThroughForward executed in 5 ms
Comparing some random test results:
Index: 25291 brute: 0.989688139105413 flow: 0.989688139105413
Index: 11945 brute: 0.59670821976193 flow: 0.59670821976193
Index: 30282 brute: 0.413238225210297 flow: 0.413238225210297
Index: 33898 brute: 0.38258761939139 flow: 0.38258761939139
Index: 8824 brute: 0.833512217105447 flow: 0.833512217105447
Index: 22092 brute: 0.648052464067263 flow: 0.648052464067263
Index: 24633 brute: 0.35859417692481 flow: 0.35859417692481
Index: 24061 brute: 0.540642018793402 flow: 0.540642018793402
Index: 34219 brute: 0.498785766613022 flow: 0.498785766613022
Index: 2396 brute: 0.151471808392111 flow: 0.151471808392111
Cpu 由于并行化，Bruteforce 向后的使用率要高得多。
最坏的情况是价值长期下降。代码仍然可以大大优化，但我想这应该足够了。为了进一步优化，当 removing/adding 元素变为 maximumValues.
时，可能会减少列表洗牌
这是一个类似于 julian bechtold 的答案的解决方案。不同之处在于最大值（和所有相关变量）隐藏在远离主要实现的地方，在一个单独的 class 中，其目的只是为了跟踪过去一年的最大值。算法是一样的，我只是在这里和那里使用了一些 Linq 表达式。
我们跟踪以下最大值class：
public class MaxSlidingWindow
{
private readonly List<MyObject> _maximumValues;
private double _max;
public MaxSlidingWindow()
{
_maximumValues = new List<MyObject>();
_max = double.NegativeInfinity;
}
public double Max => _max;
public void Add(MyObject myObject)
{
if (myObject.Value >= _max)
{
_maximumValues.Clear();
_max = myObject.Value;
}
else
{
RemoveValuesSmallerThan(myObject.Value);
}
_maximumValues.Add(myObject);
RemoveObservationsBefore(myObject.Date.AddYears(-1));
_max = _maximumValues[0].Value;
}
private void RemoveObservationsBefore(DateTime targetDate)
{
var toRemoveFromFront = 0;
while (_maximumValues[toRemoveFromFront].Date < targetDate && toRemoveFromFront <= maximumValues3.Count -1)
{
toRemoveFromFront++;
}
_maximumValues.RemoveRange(0, toRemoveFromFront);
}
private void RemoveValuesSmallerThan(double targetValue)
{
var maxEntry = _maximumValues.Count - 1;
var toRemoveFromBack = 0;
while (toRemoveFromBack <= maxEntry && _maximumValues[maxEntry - toRemoveFromBack].Value <= targetValue)
{
toRemoveFromBack++;
}
_maximumValues.RemoveRange(maxEntry - toRemoveFromBack + 1, toRemoveFromBack);
}
}
可以这样使用：
public static MyObject[] GetTestObjects_MaxSlidingWindow()
{
var rnd = new Random();
var date = new DateTime(2021, 1, 1, 0, 0, 0);
var result = new List<MyObject>();
var maxSlidingWindow = new MaxSlidingWindow();
for (int i = 0; i < 50000; i++)
{
//this is to simulate real data having gaps
if (rnd.Next(100) < 25)
{
continue;
}
var myObject = new MyObject()
{
Value = rnd.NextDouble(),
Date = date.AddMinutes(15 * i)
};
maxSlidingWindow.Add(myObject);
var max = maxSlidingWindow.Max;
result.Add(new MyObject { Date = myObject.Date, Value = myObject.Value / max });
}
return result.ToArray();
}
查看下面的相对时间 - 上面的解决方案稍微快一些（超过 1000 万次运行），但几乎不引人注意：
Relative timings
一个有趣且具有挑战性的问题。我使用动态规划方法组合了一个解决方案（最早是在 78 年的 CS 算法 class 中学到的）。首先，构建一棵树，其中包含在递归定义的范围内预先计算的局部最大值。构造完成后，可以主要使用预先计算的值有效地计算任意范围的最大值。只有在范围的边缘，计算才会下降到元素级别。
它不如 julian bechtold 的 FlowThroughForward 方法快，但随机访问范围可能是一个优势。
要添加到 Main 的代码：
Console.WriteLine();
Stopwatch stopWatch3 = new Stopwatch();
stopWatch3.Start();
MyObject[] testresults3 = RangeTreeCalculation(ref testData, 10);
stopWatch3.Stop();
Console.WriteLine($"RangeTreeCalculation executed in {stopWatch3.ElapsedMilliseconds} ms");
... test comparison
Console.WriteLine($"Index: {index} brute: {testresults1[index].Value} flow: {testresults2[index].Value} rangeTree: {testresults3[index].Value}");
测试函数：
public static MyObject[] RangeTreeCalculation(ref MyObject[] testDataArray, int partitionThreshold)
{
// For this implementation, we need to convert the Array to an ArrayList, because we need a
// reference type object that can be shared.
List<MyObject> testDataList = testDataArray.ToList();
// Construct a tree containing recursive collections of pre-calculated values
var rangeTree = new RangeTree(testDataList, partitionThreshold);
MyObject[] result = new MyObject[testDataList.Count];
Parallel.ForEach(testDataList, (item, state, i) =>
{
var max = rangeTree.MaxForDateRange(item.Date.AddYears(-1), item.Date);
result[i] = new MyObject() { Date = item.Date, Value = item.Value / max };
});
return result;
}
支持class：
// Class used to divide and conquer using dynamic programming.
public class RangeTree
{
public List<MyObject> Data; // This reference is shared by all members of the tree
public int Start { get; } // Index of first element covered by this node.
public int Count { get; } // Number of elements covered by this node.
public DateTime FirstDateTime { get; }
public DateTime LastDateTime { get; }
public double MaxValue { get; } // Pre-calculated max for all elements covered by this node.
List<RangeTree> ChildRanges { get; }
// Top level node constructor
public RangeTree(List<MyObject> data, int partitionThreshold)
: this(data, 0, data.Count, partitionThreshold)
{
}
// Child node constructor, which covers an recursively decreasing range of element.
public RangeTree(List<MyObject> data, int start, int count, int partitionThreshold)
{
Data = data;
Start = start;
Count = count;
FirstDateTime = Data[Start].Date;
LastDateTime = Data[Start + Count - 1].Date;
if (count <= partitionThreshold)
{
// If the range is smaller than the threshold, just calculate the local max
// directly from the items. No child ranges are defined.
MaxValue = Enumerable.Range(Start, Count).Select(i => Data[i].Value).Max();
}
else
{
// We still have a significant range. Decide how to further divide them up into sub-ranges.
// (There may be room for improvement here to better balance the tree.)
int partitionSize = (count - 1) / partitionThreshold + 1;
int partitionCount = (count - 1) / partitionSize + 1;
if (count < partitionThreshold * partitionThreshold)
{
// When one away from leaf nodes, prefer fewer full leaf nodes over more
// less populated leaf nodes.
partitionCount = (count - 1) / partitionThreshold + 1;
partitionSize = (count - 1) / partitionCount + 1;
}
ChildRanges = Enumerable.Range(0, partitionCount)
.Select(partitionNum => new {
ChildStart = Start + partitionNum * partitionSize,
ChildCount = Math.Min(partitionSize, Count - partitionNum * partitionSize)
})
.Where(part => part.ChildCount > 0) // Defensive
.Select(part => new RangeTree(Data, part.ChildStart, part.ChildCount, partitionThreshold))
.ToList();
// Now is the dynamic programming part:
// Calculate the local max as the max of all child max values.
MaxValue = ChildRanges.Max(chile => chile.MaxValue);
}
}
// Get the max value for a given range of dates withing this rangeTree node.
// This used the precalculated values as much as possible.
// Only at the fringes of the date range to we calculate at the element level.
public double MaxForDateRange(DateTime fromDate, DateTime thruDate)
{
double calculatedMax = Double.MinValue;
if (fromDate > this.LastDateTime || thruDate < this.FirstDateTime)
{
// Entire range is excluded. Nothing of interest here folks.
calculatedMax = Double.MinValue;
}
else if (fromDate <= this.FirstDateTime && thruDate >= this.LastDateTime)
{
// Entire range is included. Use the already-calculated max.
calculatedMax = this.MaxValue;
}
else if (ChildRanges != null)
{
// We have child ranges. Recurse and accumulate.
// Possible optimization: Calculate max for middle ranges first, and only bother
// with extreme partial ranges if their local max values exceed the preliminary result.
for (int i = 0; i < ChildRanges.Count; ++i)
{
double childMax = ChildRanges[i].MaxForDateRange(fromDate, thruDate);
if (childMax > calculatedMax)
{
calculatedMax = childMax;
}
}
}
else
{
// Leaf range. Loop through just this limited range of notes, checking individually for
// date in range and accumulating the result.
for (int i = 0; i < this.Count; ++i)
{
var element = Data[this.Start + i];
if (fromDate <= element.Date && element.Date <= thruDate && element.Value > calculatedMax)
{
calculatedMax = element.Value;
}
}
}
return calculatedMax;
}
}
有很大的改进空间，例如参数化类型和泛化功能以支持不仅仅是 Max(Value)，但框架就在那里。
输入：
public class MyObject
{
public double Value { get; set; }
public DateTime Date { get; set; }
}
生成测试对象的方法：
public static MyObject[] GetTestObjects()
{
var rnd = new Random();
var date = new DateTime(2021, 1, 1, 0, 0, 0);
var result = new List<MyObject>();
for (int i = 0; i < 50000; i++)
{
//this is to simulate real data having gaps
if (rnd.Next(100) < 25)
{
continue;
}
var myObject = new MyObject()
{
Value = rnd.NextDouble(),
Date = date.AddMinutes(15 * i)
};
result.Add(myObject);
}
return result.ToArray();
}
鉴于此，我需要为每个 myObject 计算前 12 个月的最大值。我只能考虑 InParallel，但也许有优化的解决方案？
抱歉不清楚，这是我现在用来得到我想要的东西：
public MyObject[] BruteForceBackward(MyObject[] testData)
{
return testData.AsParallel().Select(point =>
{
var max = testData.Where(x => x.Date <= point.Date && x.Date >= point.Date.AddYears(-1)).Max(x => x.Value);
return new MyObject() { Date = point.Date, Value = point.Value / max };
}).OrderBy(r => r.Date).ToArray();
}
这可行，但它很慢并且会占用处理器资源（想象一下，你有 100k 个对象），我相信一定有更好的东西
假设您的意思是您需要从 result 开始的过去 12 个月中每个月的最大值 Value，那么您可以使用 LINQ：
var beginDateTime = DateTime.Now.AddMonths(-12);
var ans = result.Where(r => r.Date >= beginDateTime).GroupBy(r => r.Date.Month).Select(mg => mg.MaxBy(r => r.Value)).ToList();
运行 一些时间，我知道在 result 之后放置 AsParallel 将 运行 时间从大约 16 毫秒（第一个 运行）更改为大约 32 毫秒，所以它实际上更慢。 Where 之后和 GroupBy 之后大约 23 毫秒（并行处理 12 个组）大致相同。至少在我的 PC 上，没有足够的数据或复杂的并行操作，但 GroupBy 不是最有效的。
使用数组并测试每个元素，我在大约 1.2 毫秒内得到了结果：
var maxMOs = new MyObject[12];
foreach (var r in result.Where(r => r.Date >= beginDateTime)) {
var monthIndex = r.Date.Month-1;
if (maxMOs[monthIndex] == null || r.Value > maxMOs[monthIndex].Value)
maxMOs[monthIndex] = r;
}
请注意，结果不是按时间顺序排列的；如果需要，您可以将 monthIndex 偏移到今天的月份以对结果进行排序。
var maxMOs = new MyObject[12];
var offset = DateTime.Now.Month-11;
foreach (var r in result.Where(r => r.Date >= beginDateTime)) {
var monthIndex = r.Date.Month-offset;
if (maxMOs[monthIndex] == null || r.Value > maxMOs[monthIndex].Value)
maxMOs[monthIndex] = r;
}
微优化（主要用于重复 运行nings）是反转测试并使用空传播运算符：
if (!(r.Value <= maxMOs[monthIndex]?.Value))
这在第一个 运行 上节省了大约 0.2 毫秒，但在随后的 运行 上最多节省了 0.5 毫秒。
我有一个类似的项目，我必须根据大量传感器数据计算这些东西。
一般来说，您希望减少遍历所有数据的循环次数。充其量，您只想触摸每个元素一次。
进程数组（相当于BruteForceBackwards）
public static MyObject[] FlowThroughForward(ref MyObject[] testData)
{
// generate return array
MyObject[] returnData = new MyObject[testData.Length];
// keep track to minimize processing
double currentMaximum = 0;
List<MyObject> maximumValues = new List<MyObject>();
// go through the elements
for (int i = 0; i < testData.Length; i++)
{
// calculate the oldest date to keep in tracking list
DateTime targetDate = testData[i].Date.AddYears(-1);
// maximum logic
if (testData[i].Value >= currentMaximum)
{
// new maximum found, clear tracking list
// this is the best case scenario
maximumValues.Clear();
currentMaximum = testData[i].Value;
}
else
{
// unfortunately, no new maximum was found
// go backwards the maximum tracking list and check for smaller values
// clear the list of all smaller values. The list should therefore always
// be in descending order
for (int b = maximumValues.Count - 1; b >= 0; b--)
{
if (maximumValues[b].Value <= testData[i].Value)
{
// a lower value has been found. We have a newer, higher value
// clear this waste value from the tracking list
maximumValues.RemoveAt(b);
}
else
{
// there are no more lower values.
// stop looking for smaller values to save time
break;
}
}
}
// append new value to tracking list, no matter if higher or lower
// all future values might be lower
maximumValues.Add(testData[i]);
// check if the oldest value is too old to be kept in the tracking list
while (maximumValues[0].Date < targetDate)
{
// oldest value is to be removed
maximumValues.RemoveAt(0);
// update maximum
currentMaximum = maximumValues[0].Value;
}
// add object to result list
returnData[i] = new MyObject() { Date = testData[i].Date, Value = testData[i].Value / currentMaximum }; ;
}
return returnData;
}
实时数据或流数据
注意：如果列表非常大，则传递完整数组的方法可能会出现内存问题。在这种情况下：一次传递一个值，将它们从最旧的值传递到最新的值。一次存储一个值。
此功能也可用于实时数据。
测试方法包含在代码中。
static void Main(string[] args)
{
int length = 50000;
Stopwatch stopWatch1 = new Stopwatch();
stopWatch1.Start();
var myObject = new MyObject();
var result = new List<MyObject>();
var date = new DateTime(2021, 1, 1, 0, 0, 0);
for (int i = 0; i < length; i++)
{
//this is to simulate real data having gaps
if (rnd.Next(100) < 25)
{
continue;
}
myObject.Value = rnd.NextDouble();
myObject.Date = date.AddMinutes(15 * i);
result.Add(CalculateNextObject(ref myObject));
}
stopWatch1.Stop();
Console.WriteLine("test code executed in " + stopWatch1.ElapsedMilliseconds + " ms");
Thread.Sleep(1000000);
}
private static Random rnd = new Random();
private static double currentMaximum = 0;
private static List<MyObject> maximumValues = new List<MyObject>();
public static MyObject CalculateNextObject(ref MyObject input)
{
// calculate the oldest date to keep in tracking list
DateTime targetDate = input.Date.AddYears(-1);
// maximum logic
if (input.Value >= currentMaximum)
{
// new maximum found, clear tracking list
// this is the best case scenario
maximumValues.Clear();
currentMaximum = input.Value;
}
else
{
// unfortunately, no new maximum was found
// go backwards the maximum tracking list and check for smaller values
// clear the list of all smaller values. The list should therefore always
// be in descending order
for (int b = maximumValues.Count - 1; b >= 0; b--)
{
if (maximumValues[b].Value <= input.Value)
{
// a lower value has been found. We have a newer, higher value
// clear this waste value from the tracking list
maximumValues.RemoveAt(b);
}
else
{
// there are no more lower values.
// stop looking for smaller values to save time
break;
}
}
}
// append new value to tracking list, no matter if higher or lower
// all future values might be lower
maximumValues.Add(input);
// check if the oldest value is too old to be kept in the tracking list
while (maximumValues[0].Date < targetDate)
{
// oldest value is to be removed
maximumValues.RemoveAt(0);
// update maximum
currentMaximum = maximumValues[0].Value;
}
// add object to result list
MyObject returnData = new MyObject() { Date = input.Date, Value = input.Value / currentMaximum };
return returnData;
}
测试方法
static void Main(string[] args)
{
MyObject[] testData = GetTestObjects();
Stopwatch stopWatch1 = new Stopwatch();
Stopwatch stopWatch2 = new Stopwatch();
stopWatch1.Start();
MyObject[] testresults1 = BruteForceBackward(testData);
stopWatch1.Stop();
Console.WriteLine("BruteForceBackward executed in " + stopWatch1.ElapsedMilliseconds + " ms");
stopWatch2.Start();
MyObject[] testresults2 = FlowThroughForward(ref testData);
stopWatch2.Stop();
Console.WriteLine("FlowThroughForward executed in " + stopWatch2.ElapsedMilliseconds + " ms");
Console.WriteLine();
Console.WriteLine("Comparing some random test results: ");
var rnd = new Random();
for (int i = 0; i < 10; i++)
{
int index = rnd.Next(0, testData.Length);
Console.WriteLine("Index: " + index + " brute: " + testresults1[index].Value + " flow: " + testresults2[index].Value);
}
Thread.Sleep(1000000);
}
测试结果
测试是在 32 核的机器上进行的，所以理论上多线程方法应该有优势，但你会看到 ;)
| Function | Function Time | time % |
|---|---|---|
| BruteForceBackward | 5334 ms | 99.9% |
| FlowThroughForward | 5 ms | 0.094% |
性能提升系数：~time/1000
带数据验证的控制台输出：
BruteForceBackward executed in 5264 ms
FlowThroughForward executed in 5 ms
Comparing some random test results:
Index: 25291 brute: 0.989688139105413 flow: 0.989688139105413
Index: 11945 brute: 0.59670821976193 flow: 0.59670821976193
Index: 30282 brute: 0.413238225210297 flow: 0.413238225210297
Index: 33898 brute: 0.38258761939139 flow: 0.38258761939139
Index: 8824 brute: 0.833512217105447 flow: 0.833512217105447
Index: 22092 brute: 0.648052464067263 flow: 0.648052464067263
Index: 24633 brute: 0.35859417692481 flow: 0.35859417692481
Index: 24061 brute: 0.540642018793402 flow: 0.540642018793402
Index: 34219 brute: 0.498785766613022 flow: 0.498785766613022
Index: 2396 brute: 0.151471808392111 flow: 0.151471808392111
Cpu 由于并行化，Bruteforce 向后的使用率要高得多。
最坏的情况是价值长期下降。代码仍然可以大大优化，但我想这应该足够了。为了进一步优化，当 removing/adding 元素变为 maximumValues.
这是一个类似于 julian bechtold 的答案的解决方案。不同之处在于最大值（和所有相关变量）隐藏在远离主要实现的地方，在一个单独的 class 中，其目的只是为了跟踪过去一年的最大值。算法是一样的，我只是在这里和那里使用了一些 Linq 表达式。
我们跟踪以下最大值class：
public class MaxSlidingWindow
{
private readonly List<MyObject> _maximumValues;
private double _max;
public MaxSlidingWindow()
{
_maximumValues = new List<MyObject>();
_max = double.NegativeInfinity;
}
public double Max => _max;
public void Add(MyObject myObject)
{
if (myObject.Value >= _max)
{
_maximumValues.Clear();
_max = myObject.Value;
}
else
{
RemoveValuesSmallerThan(myObject.Value);
}
_maximumValues.Add(myObject);
RemoveObservationsBefore(myObject.Date.AddYears(-1));
_max = _maximumValues[0].Value;
}
private void RemoveObservationsBefore(DateTime targetDate)
{
var toRemoveFromFront = 0;
while (_maximumValues[toRemoveFromFront].Date < targetDate && toRemoveFromFront <= maximumValues3.Count -1)
{
toRemoveFromFront++;
}
_maximumValues.RemoveRange(0, toRemoveFromFront);
}
private void RemoveValuesSmallerThan(double targetValue)
{
var maxEntry = _maximumValues.Count - 1;
var toRemoveFromBack = 0;
while (toRemoveFromBack <= maxEntry && _maximumValues[maxEntry - toRemoveFromBack].Value <= targetValue)
{
toRemoveFromBack++;
}
_maximumValues.RemoveRange(maxEntry - toRemoveFromBack + 1, toRemoveFromBack);
}
}
可以这样使用：
public static MyObject[] GetTestObjects_MaxSlidingWindow()
{
var rnd = new Random();
var date = new DateTime(2021, 1, 1, 0, 0, 0);
var result = new List<MyObject>();
var maxSlidingWindow = new MaxSlidingWindow();
for (int i = 0; i < 50000; i++)
{
//this is to simulate real data having gaps
if (rnd.Next(100) < 25)
{
continue;
}
var myObject = new MyObject()
{
Value = rnd.NextDouble(),
Date = date.AddMinutes(15 * i)
};
maxSlidingWindow.Add(myObject);
var max = maxSlidingWindow.Max;
result.Add(new MyObject { Date = myObject.Date, Value = myObject.Value / max });
}
return result.ToArray();
}
查看下面的相对时间 - 上面的解决方案稍微快一些（超过 1000 万次运行），但几乎不引人注意：
Relative timings
一个有趣且具有挑战性的问题。我使用动态规划方法组合了一个解决方案（最早是在 78 年的 CS 算法 class 中学到的）。首先，构建一棵树，其中包含在递归定义的范围内预先计算的局部最大值。构造完成后，可以主要使用预先计算的值有效地计算任意范围的最大值。只有在范围的边缘，计算才会下降到元素级别。
它不如 julian bechtold 的 FlowThroughForward 方法快，但随机访问范围可能是一个优势。
要添加到 Main 的代码：
Console.WriteLine();
Stopwatch stopWatch3 = new Stopwatch();
stopWatch3.Start();
MyObject[] testresults3 = RangeTreeCalculation(ref testData, 10);
stopWatch3.Stop();
Console.WriteLine($"RangeTreeCalculation executed in {stopWatch3.ElapsedMilliseconds} ms");
... test comparison
Console.WriteLine($"Index: {index} brute: {testresults1[index].Value} flow: {testresults2[index].Value} rangeTree: {testresults3[index].Value}");
测试函数：
public static MyObject[] RangeTreeCalculation(ref MyObject[] testDataArray, int partitionThreshold)
{
// For this implementation, we need to convert the Array to an ArrayList, because we need a
// reference type object that can be shared.
List<MyObject> testDataList = testDataArray.ToList();
// Construct a tree containing recursive collections of pre-calculated values
var rangeTree = new RangeTree(testDataList, partitionThreshold);
MyObject[] result = new MyObject[testDataList.Count];
Parallel.ForEach(testDataList, (item, state, i) =>
{
var max = rangeTree.MaxForDateRange(item.Date.AddYears(-1), item.Date);
result[i] = new MyObject() { Date = item.Date, Value = item.Value / max };
});
return result;
}
支持class：
// Class used to divide and conquer using dynamic programming.
public class RangeTree
{
public List<MyObject> Data; // This reference is shared by all members of the tree
public int Start { get; } // Index of first element covered by this node.
public int Count { get; } // Number of elements covered by this node.
public DateTime FirstDateTime { get; }
public DateTime LastDateTime { get; }
public double MaxValue { get; } // Pre-calculated max for all elements covered by this node.
List<RangeTree> ChildRanges { get; }
// Top level node constructor
public RangeTree(List<MyObject> data, int partitionThreshold)
: this(data, 0, data.Count, partitionThreshold)
{
}
// Child node constructor, which covers an recursively decreasing range of element.
public RangeTree(List<MyObject> data, int start, int count, int partitionThreshold)
{
Data = data;
Start = start;
Count = count;
FirstDateTime = Data[Start].Date;
LastDateTime = Data[Start + Count - 1].Date;
if (count <= partitionThreshold)
{
// If the range is smaller than the threshold, just calculate the local max
// directly from the items. No child ranges are defined.
MaxValue = Enumerable.Range(Start, Count).Select(i => Data[i].Value).Max();
}
else
{
// We still have a significant range. Decide how to further divide them up into sub-ranges.
// (There may be room for improvement here to better balance the tree.)
int partitionSize = (count - 1) / partitionThreshold + 1;
int partitionCount = (count - 1) / partitionSize + 1;
if (count < partitionThreshold * partitionThreshold)
{
// When one away from leaf nodes, prefer fewer full leaf nodes over more
// less populated leaf nodes.
partitionCount = (count - 1) / partitionThreshold + 1;
partitionSize = (count - 1) / partitionCount + 1;
}
ChildRanges = Enumerable.Range(0, partitionCount)
.Select(partitionNum => new {
ChildStart = Start + partitionNum * partitionSize,
ChildCount = Math.Min(partitionSize, Count - partitionNum * partitionSize)
})
.Where(part => part.ChildCount > 0) // Defensive
.Select(part => new RangeTree(Data, part.ChildStart, part.ChildCount, partitionThreshold))
.ToList();
// Now is the dynamic programming part:
// Calculate the local max as the max of all child max values.
MaxValue = ChildRanges.Max(chile => chile.MaxValue);
}
}
// Get the max value for a given range of dates withing this rangeTree node.
// This used the precalculated values as much as possible.
// Only at the fringes of the date range to we calculate at the element level.
public double MaxForDateRange(DateTime fromDate, DateTime thruDate)
{
double calculatedMax = Double.MinValue;
if (fromDate > this.LastDateTime || thruDate < this.FirstDateTime)
{
// Entire range is excluded. Nothing of interest here folks.
calculatedMax = Double.MinValue;
}
else if (fromDate <= this.FirstDateTime && thruDate >= this.LastDateTime)
{
// Entire range is included. Use the already-calculated max.
calculatedMax = this.MaxValue;
}
else if (ChildRanges != null)
{
// We have child ranges. Recurse and accumulate.
// Possible optimization: Calculate max for middle ranges first, and only bother
// with extreme partial ranges if their local max values exceed the preliminary result.
for (int i = 0; i < ChildRanges.Count; ++i)
{
double childMax = ChildRanges[i].MaxForDateRange(fromDate, thruDate);
if (childMax > calculatedMax)
{
calculatedMax = childMax;
}
}
}
else
{
// Leaf range. Loop through just this limited range of notes, checking individually for
// date in range and accumulating the result.
for (int i = 0; i < this.Count; ++i)
{
var element = Data[this.Start + i];
if (fromDate <= element.Date && element.Date <= thruDate && element.Value > calculatedMax)
{
calculatedMax = element.Value;
}
}
}
return calculatedMax;
}
}
有很大的改进空间，例如参数化类型和泛化功能以支持不仅仅是 Max(Value)，但框架就在那里。