Mg.*_*Mg. 9 c# sorting algorithm
我有一个可以轻松比较的元素列表Equals().我必须洗牌,但洗牌必须满足一个条件:
第i个元素shuffledList[i]必须不等于元素i +/- 1和元素i +/- 2.该清单应视为循环; 也就是说,列表中的最后一个元素后跟第一个元素,反之亦然.
另外,如果可能的话,我想检查一下是否可以进行随机播放.
我正在使用c#4.0.
根据一些回复,我将再解释一下:
该列表不会有超过200个元素,因此不需要良好的性能.如果计算它需要2秒钟,那不是最好的事情,但它也不是世界末日.将保存随机列表,除非真实列表发生更改,否则将使用随机列表.
是的,它是一个"受控"的随机性,但我希望在这个方法上运行的几个会返回不同的洗牌列表.
在我尝试下面的一些回复之后,我将进行进一步的编辑.
样本1:
`List<int> list1 = new List<int>{0,1,1,1,2,2,2,3,3,3,4,4,4,5,5,6,6,6,7,7,7,7,8,8,8,8,9,9,9,9,9,10};`
可能的方法:
List<int> shuffledList1 = new List<int>
{9,3,1,4,7,9,2,6,8,1,4,9,2,0,6,5,7,8,4,3,10,9,6,7,8,5,3,9,1,2,7,8}
样本2:
`List<int> list2 = new List<int> {0,1,1,2,2,2,3,3,4,4,4,4,5,5,5,6,6,6,7,7,7,7,8,8,8,8,8,9,9,9,9,10};`
验证:我正在使用这种方法,它不是我制作的最有效和最优雅的代码,但它确实有效:
public bool TestShuffle<T>(IEnumerable<T> input)
{
bool satisfied = true;
int prev1 = 0; int prev2 = 0;
int next1 = 0; int next2 = 0;
int i = 0;
while (i < input.Count() && satisfied)
{
prev1 = i - 1; prev2 = i - 2; next1 = i + 1; next2 = i + 2;
if (i == 0)
{
prev1 = input.Count() - 1;
prev2 = prev1 - 1;
}
else if (i == 1)
prev2 = input.Count() - 1;
if (i == (input.Count() - 1))
{
next1 = 0;
next2 = 1;
}
if (i == (input.Count() - 2))
next2 = 0;
satisfied =
(!input.ElementAt(i).Equals(input.ElementAt(prev1)))
&& (!input.ElementAt(i).Equals(input.ElementAt(prev2)))
&& (!input.ElementAt(i).Equals(input.ElementAt(next1)))
&& (!input.ElementAt(i).Equals(input.ElementAt(next2)))
;
if (satisfied == false)
Console.WriteLine("TestShuffle fails at " + i);
i++;
}
return satisfied;
}
有时失败的另一个测试输入:
List<int> list3 = new List<int>(){0,1,1,2,2,3,3,3,4,4,4,5,5,5,5,6,6,6,6,7,7,7,8,8,8,8,9,9,9,9,10,10};
令我失望的是，我的优化函数的运行速度仅比 LINQ“直接”版本快 7 倍。未优化的 LINQ 1m43s优化的14.7s。
-optimize+，TESTITERATIONSVERBOSE不#define-d优化了什么：
GroupBy（使用ValueRun结构）ValueRun结构放在数组中而不是枚举（列表）中；就地排序/随机播放unsafe块和指针（没有明显的区别......）MAGICLinq 代码ValueRun，这似乎很容易做到；然而，转置索引（循环约束所需）使事情变得复杂。无论如何，通过更大的输入和许多唯一值以及一些高度重复的值，以某种方式应用此优化的收益将会更大。这是优化版本的代码。_可以通过移除 RNG 的种子来获得额外的速度增益；这些只是为了能够对输出进行回归测试。
[... old code removed as well ...]
如果我的理解是对的，那么您正在尝试设计一种洗牌方法，以防止重复项在输出中连续出现（最小交错为 2 个元素）。
这在一般情况下是无法解决的。想象一下只有相同元素的输入:)
正如我在笔记中提到的，我认为我一直没有走在正确的轨道上。要么我应该调用图论（有人吗？），要么使用简单的“暴力”算法，这是埃里克的长建议。
无论如何，这样你就可以看到我一直在做什么，以及问题是什么（使随机样本能够快速看到问题）：
#define OUTPUT // to display the testcase results
#define VERIFY // to selfcheck internals and verify results
#define SIMPLERANDOM
// #define DEBUG // to really traces the internals
using System;
using System.Linq;
using System.Collections.Generic;
public static class Q5899274
{
// TEST DRIVER CODE
private const int TESTITERATIONS = 100000;
public static int Main(string[] args)
{
var testcases = new [] {
new [] {0,1,1,2,2,2,3,3,4,4,4,4,5,5,5,6,6,6,7,7,7,7,8,8,8,8,8,9,9,9,9,10},
new [] {0,1,1,1,2,2,2,3,3,3,4,4,4,5,5,6,6,6,7,7,7,7,8,8,8,8,9,9,9,9,9,10},
new [] { 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41, 42, 42, 42, },
new [] {1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4},
}.AsEnumerable();
// // creating some very random testcases
// testcases = Enumerable.Range(0, 10000).Select(nr => Enumerable.Range(GROUPWIDTH, _seeder.Next(GROUPWIDTH, 400)).Select(el => _seeder.Next(-40, 40)).ToArray());
foreach (var testcase in testcases)
{
// _seeder = new Random(45); for (int i=0; i<TESTITERATIONS; i++) // for benchmarking/regression
{
try
{
var output = TestOptimized(testcase);
#if OUTPUT
Console.WriteLine("spread\t{0}", string.Join(", ", output));
#endif
#if VERIFY
AssertValidOutput(output);
#endif
} catch(Exception e)
{
Console.Error.WriteLine("Exception for input {0}:", string.Join(", ", testcase));
Console.Error.WriteLine("Sequence length {0}: {1} groups and remainder {2}", testcase.Count(), (testcase.Count()+GROUPWIDTH-1)/GROUPWIDTH, testcase.Count() % GROUPWIDTH);
Console.Error.WriteLine("Analysis: \n\t{0}", string.Join("\n\t", InternalAnalyzeInputRuns(testcase)));
Console.Error.WriteLine(e);
}
}
}
return 0;
}
#region Algorithm Core
const int GROUPWIDTH = 3; /* implying a minimum distance of 2
(GROUPWIDTH-1) values in between duplicates
must be guaranteed*/
public static T[] TestOptimized<T>(T[] input, bool doShuffle = false)
where T: IComparable<T>
{
if (input.Length==0)
return input;
var runs = InternalAnalyzeInputRuns(input);
#if VERIFY
CanBeSatisfied(input.Length, runs); // throws NoValidOrderingExists if not
#endif
var transpositions = CreateTranspositionIndex(input.Length, runs);
int pos = 0;
for (int run=0; run<runs.Length; run++)
for (int i=0; i<runs[run].runlength; i++)
input[transpositions[pos++]] = runs[run].value;
return input;
}
private static ValueRun<T>[] InternalAnalyzeInputRuns<T>(T[] input)
{
var listOfRuns = new List<ValueRun<T>>();
Array.Sort(input);
ValueRun<T> current = new ValueRun<T> { value = input[0], runlength = 1 };
for (int i=1; i<=input.Length; i++)
{
if (i<input.Length && input[i].Equals(current.value))
current.runlength++;
else
{
listOfRuns.Add(current);
if (i<input.Length)
current = new ValueRun<T> { value = input[i], runlength = 1 };
}
}
#if SIMPLERANDOM
var rng = new Random(_seeder.Next());
listOfRuns.ForEach(run => run.tag = rng.Next()); // this shuffles them
#endif
var runs = listOfRuns.ToArray();
Array.Sort(runs);
return runs;
}
// NOTE: suboptimal performance
// * some steps can be done inline with CreateTranspositionIndex for
// efficiency
private class NoValidOrderingExists : Exception { public NoValidOrderingExists(string message) : base(message) { } }
private static bool CanBeSatisfied<T>(int length, ValueRun<T>[] runs)
{
int groups = (length+GROUPWIDTH-1)/GROUPWIDTH;
int remainder = length % GROUPWIDTH;
// elementary checks
if (length<GROUPWIDTH)
throw new NoValidOrderingExists(string.Format("Input sequence shorter ({0}) than single group of {1})", length, GROUPWIDTH));
if (runs.Length<GROUPWIDTH)
throw new NoValidOrderingExists(string.Format("Insufficient distinct values ({0}) in input sequence to fill a single group of {1})", runs.Length, GROUPWIDTH));
int effectivewidth = Math.Min(GROUPWIDTH, length);
// check for a direct exhaustion by repeating a single value more than the available number of groups (for the relevant groupmember if there is a remainder group)
for (int groupmember=0; groupmember<effectivewidth; groupmember++)
{
int capacity = remainder==0? groups : groups -1;
if (capacity < runs[groupmember].runlength)
throw new NoValidOrderingExists(string.Format("Capacity exceeded on groupmember index {0} with capacity of {1} elements, (runlength {2} in run of '{3}'))",
groupmember, capacity, runs[groupmember].runlength, runs[groupmember].value));
}
// with the above, no single ValueRun should be a problem; however, due
// to space exhaustion duplicates could end up being squeezed into the
// 'remainder' group, which could be an incomplete group;
// In particular, if the smallest ValueRun (tail) has a runlength>1
// _and_ there is an imcomplete remainder group, there is a problem
if (runs.Last().runlength>1 && (0!=remainder))
throw new NoValidOrderingExists("Smallest ValueRun would spill into trailing incomplete group");
return true;
}
// will also verify solvability of input sequence
private static int[] CreateTranspositionIndex<T>(int length, ValueRun<T>[] runs)
where T: IComparable<T>
{
int remainder = length % GROUPWIDTH;
int effectivewidth = Math.Min(GROUPWIDTH, length);
var transpositions = new int[length];
{
int outit = 0;
for (int groupmember=0; groupmember<effectivewidth; groupmember++)
for (int pos=groupmember; outit<length && pos<(length-remainder) /* avoid the remainder */; pos+=GROUPWIDTH)
transpositions[outit++] = pos;
while (outit<length)
{
transpositions[outit] = outit;
outit += 1;
}
#if DEBUG
int groups = (length+GROUPWIDTH-1)/GROUPWIDTH;
Console.WriteLine("Natural transpositions ({1} elements in {0} groups, remainder {2}): ", groups, length, remainder);
Console.WriteLine("\t{0}", string.Join(" ", transpositions));
var sum1 = string.Join(":", Enumerable.Range(0, length));
var sum2 = string.Join(":", transpositions.OrderBy(i=>i));
if (sum1!=sum2)
throw new ArgumentException("transpositions do not cover range\n\tsum1 = " + sum1 + "\n\tsum2 = " + sum2);
#endif
}
return transpositions;
}
#endregion // Algorithm Core
#region Utilities
private struct ValueRun<T> : IComparable<ValueRun<T>>
{
public T value;
public int runlength;
public int tag; // set to random for shuffling
public int CompareTo(ValueRun<T> other) { var res = other.runlength.CompareTo(runlength); return 0==res? tag.CompareTo(other.tag) : res; }
public override string ToString() { return string.Format("[{0}x {1}]", runlength, value); }
}
private static /*readonly*/ Random _seeder = new Random(45);
#endregion // Utilities
#region Error detection/verification
public static void AssertValidOutput<T>(IEnumerable<T> output)
where T:IComparable<T>
{
var repl = output.Concat(output.Take(GROUPWIDTH)).ToArray();
for (int i=1; i<repl.Length; i++)
for (int j=Math.Max(0, i-(GROUPWIDTH-1)); j<i; j++)
if (repl[i].Equals(repl[j]))
throw new ArgumentException(String.Format("Improper duplicate distance found: (#{0};#{1}) out of {2}: value is '{3}'", j, i, output.Count(), repl[j]));
}
#endregion
}