老赵在反对北大青鸟的随笔中提到了数组反转。这的确是一道非常基础的算法题，然而也是一道很不平常的算法题（也许所有的算法深究下去都会很不平常）。因为我写着写着，就写出来8种方法……现在我们以字符串的反转为例，来介绍这几种方法并对它们的性能进行比较。
使用Array.Reverse方法
对于字符串反转，我们可以使用.NET类库自带的Array.Reverse方法
public static string ReverseByArray(this string original)
{
char[] c = original.ToCharArray();
Array.Reverse(c);
return new string(c);
}
使用字符缓存
在面试或笔试中，往往要求不用任何类库方法，那么有朋友大概会使用类似下面这样的循环方法
public static string ReverseByCharBuffer(this string original)
{
char[] c = original.ToCharArray();
int l = original.Length;
char[] o = new char[l];
for (int i = 0; i < l ; i++)
{
o[i] = c[l - i - 1];
}
return new string(o);
}
当然，聪明的同学们一定会发现不必对这个字符数组进行完全遍历，通常情况下我们会只遍历一半
public static string ReverseByCharBuffer2(this string original)
{
char[] c = original.ToCharArray();
int l = original.Length;
for (int i = 0; i < l / 2; i++)
{
char t = c[i];
c[i] = c[l - i - 1];
c[l - i - 1] = t;
}
return new string(c);
}
ReverseByCharBuffer使用了一个新的数组，而且遍历了字符数组的所有元素，因此时间和空间的开销都要大于ReverseByCharBuffer2。
在Array.Reverse内部，调用了非托管方法TrySZReverse，如果TrySZReverse不成功，实际上也是调用了类似ReverseByCharBuffer2的方法。
if (!TrySZReverse(array, index, length))
{
int num = index;
int num2 = (index + length) - 1;
object[] objArray = array as object[];
if (objArray == null)
{
while (num < num2)
{
object obj3 = array.GetValue(num);
array.SetValue(array.GetValue(num2), num);
array.SetValue(obj3, num2);
num++;
num2--;
}
}
else
{
while (num < num2)
{
object obj2 = objArray[num];
objArray[num] = objArray[num2];
objArray[num2] = obj2;
num++;
num2--;
}
}
}
大致上我能想到的算法就是这么多了，但是我无意间发现了StackOverflow上的一篇帖子，才发现这么一个看似简单的反转算法实现起来真可谓花样繁多。
使用StringBuilder
使用StringBuilder方法大致和ReverseByCharBuffer一样，只不过不使用字符数组做缓存，而是使用StringBuilder。
public static string ReverseByStringBuilder(this string original)
{
StringBuilder sb = new StringBuilder(original.Length);
for (int i = original.Length - 1; i >= 0; i--)
{
sb.Append(original[i]);
}
return sb.ToString();
}
当然，你可以预见，这种算法的效率不会比ReverseByCharBuffer要高。
我们可以像使用字符缓存那样，对使用StringBuilder方法进行优化，使其遍历过程也减少一半
public static string ReverseByStringBuilder2(this string original)
{
StringBuilder sb = new StringBuilder(original);
for (int i = 0, j = original.Length - 1; i <= j; i++, j--)
{
sb[i] = original[j];
sb[j] = original[i];
}
return sb.ToString();
}
以上这几种方法按算法角度来说，其实可以归结为一类。然而下面的几种算法就完全不是同一类型的了。
使用栈
栈是一个很神奇的数据结构。我们可以使用它后进先出的特性来对数组进行反转。先将数组所有元素压入栈，然后再取出，顺序很自然地就与原先相反了。
public static string ReverseByStack(this string original)
{
Stack<char> stack = new Stack<char>();
foreach (char ch in original)
{
stack.Push(ch);
}
char[] c = new char[original.Length];
for (int i = 0; i < original.Length; i++)
{
c[i] = stack.Pop();
}
return new string(c);
}
两次循环和栈的开销无疑使这种方法成为目前为止开销最大的方法。但使用栈这个数据结构的想法还是非常有价值的。
使用XOR
使用逻辑异或也可以进行反转
public static string ReverseByXor(this string original)
{
char[] charArray = original.ToCharArray();
int l = original.Length - 1;
for (int i = 0; i < l; i++, l--)
{
charArray[i] ^= charArray[l];
charArray[l] ^= charArray[i];
charArray[i] ^= charArray[l];
}
return new string(charArray);
}
在C#中，x ^= y相当于x = x ^ y。通过3次异或操作，可以将两个字符为止互换。对于算法具体的解释可以参考这篇文章。
使用指针
使用指针可以达到最快的速度，但是unsafe代码不是微软所推荐的，在这里我们就不多做讨论了
public static unsafe string ReverseByPointer(this string original)
{
fixed (char* pText = original)
{
char* pStart = pText;
char* pEnd = pText + original.Length - 1;
for (int i = original.Length / 2; i >= 0; i--)
{
char temp = *pStart;
*pStart++ = *pEnd;
*pEnd-- = temp;
}
return original;
}
}
使用递归
对于反转这类算法，都可以使用递归方法
public static string ReverseByRecursive(this string original)
{
if (original.Length == 1)
return original;
else
return original.Substring(1).ReverseByRecursive() + original[0];
}
使用委托，还可以使代码变得更加简洁
public static string ReverseByRecursive2(this string original)
{
Func<string, string> f = null;
f = s => s.Length > 0 ? f(s.Substring(1)) + s[0] : string.Empty;
return f(original);
}
但是委托开销大的弊病在这里一点也没有减少，以至于我做性能测试的时候导致系统假死甚至内存益处。
使用LINQ
System.Enumerable里提供了默认的Reverse扩展方法，我们可以基于该方法来对String类型进行扩展
public static string ReverseByLinq(this string original)
{
return new string(original.Reverse().ToArray());
}
性能比较
接下来让我们来对以上8种方法的11个扩展方法来进行性能比较。
影响字符串反转算法性能的因素主要就是字符串的长度。让我们分别取1、10、15、25、50、75、100、1000、10000作为字符串长度来进行测试。用下面的方法来随机生成不同长度的字符串
static string GenerateStringByLength(int length)
{
Random random = new Random();
StringBuilder sb = new StringBuilder();
for (int i = 0; i < length; i++)
{
sb.Append(Convert.ToChar(Convert.ToInt32(
Math.Floor(26 * random.NextDouble() + 65))));
}
return sb.ToString();
}
用下面的方法来计算时间
static void Benchmark(string description, Func<string> func, int times)
{
Stopwatch sw = new Stopwatch();
sw.Start();
for (int j = 0; j < times; j++)
{
func();
}
sw.Stop();
Debug.WriteLine("{0} Ticks {1} : called {2} times.",
sw.ElapsedTicks, description, times);
}
测试的主方法如下
static void Main(string[] args)
{
// 预热
"abcde".ReverseByArray();
"abcde".ReverseByCharBuffer();
"abcde".ReverseByCharBuffer2();
"abcde".ReverseByLinq();
"abcde".ReverseByPointer();
"abcde".ReverseByRecursive();
"abcde".ReverseByRecursive2();
"abcde".ReverseByStack();
"abcde".ReverseByStringBuilder();
"abcde".ReverseByStringBuilder2();
"abcde".ReverseByXor();
int[] lengths = new int[] { 1, 10, 15, 25, 50, 75, 100, 1000, 100000 };
foreach (int l in lengths)
{
int iterations = 100;
string text = GenerateStringByLength(l);
Benchmark(String.Format("ReverseByArray (Length: {0})", l),
text.ReverseByArray, iterations);
Benchmark(String.Format("ReverseByCharBuffer (Length: {0})", l),
text.ReverseByCharBuffer, iterations);
Benchmark(String.Format("ReverseByCharBuffer2 (Length: {0})", l),
text.ReverseByCharBuffer2, iterations);
Benchmark(String.Format("ReverseByStringBuilder (Length: {0})", l),
text.ReverseByStringBuilder, iterations);
Benchmark(String.Format("ReverseByStringBuilder2 (Length: {0})", l),
text.ReverseByStringBuilder2, iterations);
Benchmark(String.Format("ReverseByStack (Length: {0})", l),
text.ReverseByStack, iterations);
Benchmark(String.Format("ReverseByXor (Length: {0})", l),
text.ReverseByXor, iterations);
Benchmark(String.Format("ReverseByPointer (Length: {0})", l),
text.ReverseByPointer, iterations);
Benchmark(String.Format("ReverseByRecursive (Length: {0})", l),
text.ReverseByRecursive, iterations);
Benchmark(String.Format("ReverseByRecursive2 (Length: {0})", l),
text.ReverseByRecursive2, iterations);
Benchmark(String.Format("ReverseByLinq (Length: {0})", l),
text.ReverseByLinq, iterations);
Debug.WriteLine(Environment.NewLine);
}
}
好了，来看看结果吧。（由于递归算法与其他算法的开销不在一个数量级上，因此忽略了对该算法的比较）
197602 Ticks ReverseByArray (Length: 1) : called 100 times.
75773 Ticks ReverseByCharBuffer (Length: 1) : called 100 times.
111833 Ticks ReverseByCharBuffer2 (Length: 1) : called 100 times.
134535 Ticks ReverseByStringBuilder (Length: 1) : called 100 times.
148598 Ticks ReverseByStringBuilder2 (Length: 1) : called 100 times.
192435 Ticks ReverseByStack (Length: 1) : called 100 times.
63098 Ticks ReverseByXor (Length: 1) : called 100 times.
51945 Ticks ReverseByPointer (Length: 1) : called 100 times.
587865 Ticks ReverseByLinq (Length: 1) : called 100 times.
185325 Ticks ReverseByArray (Length: 10) : called 100 times.
189712 Ticks ReverseByCharBuffer (Length: 10) : called 100 times.
100155 Ticks ReverseByCharBuffer2 (Length: 10) : called 100 times.
216232 Ticks ReverseByStringBuilder (Length: 10) : called 100 times.
209497 Ticks ReverseByStringBuilder2 (Length: 10) : called 100 times.
669832 Ticks ReverseByStack (Length: 10) : called 100 times.
163237 Ticks ReverseByXor (Length: 10) : called 100 times.
74303 Ticks ReverseByPointer (Length: 10) : called 100 times.
1058348 Ticks ReverseByLinq (Length: 10) : called 100 times.
215437 Ticks ReverseByArray (Length: 15) : called 100 times.
206610 Ticks ReverseByCharBuffer (Length: 15) : called 100 times.
168180 Ticks ReverseByCharBuffer2 (Length: 15) : called 100 times.
260542 Ticks ReverseByStringBuilder (Length: 15) : called 100 times.
296153 Ticks ReverseByStringBuilder2 (Length: 15) : called 100 times.
785857 Ticks ReverseByStack (Length: 15) : called 100 times.
177915 Ticks ReverseByXor (Length: 15) : called 100 times.
84802 Ticks ReverseByPointer (Length: 15) : called 100 times.
1113262 Ticks ReverseByLinq (Length: 15) : called 100 times.
266167 Ticks ReverseByArray (Length: 25) : called 100 times.
260820 Ticks ReverseByCharBuffer (Length: 25) : called 100 times.
236025 Ticks ReverseByCharBuffer2 (Length: 25) : called 100 times.
380408 Ticks ReverseByStringBuilder (Length: 25) : called 100 times.
440430 Ticks ReverseByStringBuilder2 (Length: 25) : called 100 times.
1197593 Ticks ReverseByStack (Length: 25) : called 100 times.
262388 Ticks ReverseByXor (Length: 25) : called 100 times.
110453 Ticks ReverseByPointer (Length: 25) : called 100 times.
1611900 Ticks ReverseByLinq (Length: 25) : called 100 times.
258435 Ticks ReverseByArray (Length: 50) : called 100 times.
474135 Ticks ReverseByCharBuffer (Length: 50) : called 100 times.
341655 Ticks ReverseByCharBuffer2 (Length: 50) : called 100 times.
662242 Ticks ReverseByStringBuilder (Length: 50) : called 100 times.
587078 Ticks ReverseByStringBuilder2 (Length: 50) : called 100 times.
2116350 Ticks ReverseByStack (Length: 50) : called 100 times.
417375 Ticks ReverseByXor (Length: 50) : called 100 times.
177847 Ticks ReverseByPointer (Length: 50) : called 100 times.
9114592 Ticks ReverseByLinq (Length: 50) : called 100 times.
270022 Ticks ReverseByArray (Length: 75) : called 100 times.
488647 Ticks ReverseByCharBuffer (Length: 75) : called 100 times.
378225 Ticks ReverseByCharBuffer2 (Length: 75) : called 100 times.
1096148 Ticks ReverseByStringBuilder (Length: 75) : called 100 times.
772312 Ticks ReverseByStringBuilder2 (Length: 75) : called 100 times.
3069427 Ticks ReverseByStack (Length: 75) : called 100 times.
479092 Ticks ReverseByXor (Length: 75) : called 100 times.
234195 Ticks ReverseByPointer (Length: 75) : called 100 times.
3330945 Ticks ReverseByLinq (Length: 75) : called 100 times.
319717 Ticks ReverseByArray (Length: 100) : called 100 times.
584857 Ticks ReverseByCharBuffer (Length: 100) : called 100 times.
505470 Ticks ReverseByCharBuffer2 (Length: 100) : called 100 times.
1076715 Ticks ReverseByStringBuilder (Length: 100) : called 100 times.
942375 Ticks ReverseByStringBuilder2 (Length: 100) : called 100 times.
4390493 Ticks ReverseByStack (Length: 100) : called 100 times.
649725 Ticks ReverseByXor (Length: 100) : called 100 times.
293025 Ticks ReverseByPointer (Length: 100) : called 100 times.
6405082 Ticks ReverseByLinq (Length: 100) : called 100 times.
3262087 Ticks ReverseByArray (Length: 1000) : called 100 times.
5511607 Ticks ReverseByCharBuffer (Length: 1000) : called 100 times.
9097485 Ticks ReverseByCharBuffer2 (Length: 1000) : called 100 times.
10325760 Ticks ReverseByStringBuilder (Length: 1000) : called 100 times.
18120420 Ticks ReverseByStringBuilder2 (Length: 1000) : called 100 times.
40247490 Ticks ReverseByStack (Length: 1000) : called 100 times.
6837915 Ticks ReverseByXor (Length: 1000) : called 100 times.
2654011 Ticks ReverseByPointer (Length: 1000) : called 100 times.
84809355 Ticks ReverseByLinq (Length: 1000) : called 100 times.
368229982 Ticks ReverseByArray (Length: 100000) : called 100 times.
609454380 Ticks ReverseByCharBuffer (Length: 100000) : called 100 times.
507932685 Ticks ReverseByCharBuffer2 (Length: 100000) : called 100 times.
748738972 Ticks ReverseByStringBuilder (Length: 100000) : called 100 times.
732820133 Ticks ReverseByStringBuilder2 (Length: 100000) : called 100 times.
2249140177 Ticks ReverseByStack (Length: 100000) : called 100 times.
508241490 Ticks ReverseByXor (Length: 100000) : called 100 times.
192039592 Ticks ReverseByPointer (Length: 100000) : called 100 times.
2346782325 Ticks ReverseByLinq (Length: 100000) : called 100 times.
整理成表格如下
绘制成更直观的折线图（由于数量级差别太大，故舍去1000和10000长度的情况）
是的，LINQ方法处理长度为50的数组时，效率比长度为75的数组还要低。我测试了很多次，都是这样的结果，感兴趣的朋友可以深入研究一下。
将耗时明显偏高的LINQ方法和Stack方法去掉，剩下各种算法在时间上的优劣就一目了然了。
可见，直接使用指针的效率是最高的。而类库自带的Array.Reverse尽管在面对长度较小的数组时没有明显优势，但面对大数组其算法效率却十分稳定。XOR方法在小数组面前效率很高，但面对大数组就败下阵来。遍历了数组一半元素的CharBuffer2表现优异，无论面对大数组还是小数组，排名都很靠前。
指针方法尽管高效，但其带来的问题也许会很严重，而且面对大数组时Array.Reverse也同样优秀，因此一般情况下还是推荐使用Array.Reverse。当然如果面试官希望你拿出一套不使用类库的高效方案，CharBuffer2将是最佳选择。
当然，你也可以去找一个数组长度的临界点，在临界点以下使用CharBuffer2，在临界点以上使用Array.Reverse。如
public static string Reverse(this string original)
{
if (original.Length <= 25)
return original.ReverseByCharBuffer2();
else
return original.ReverseByArray();
}
希望本文对你有所帮助。