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Convert byte array of zeros and ones (0,1) to string of zeros and ones [duplicate]

What's the most efficient way to concatenate strings?

Rico Mariani, the .NET Performance guru, had an article on this very subject. It's not as simple as one might suspect. The basic advice is this:
If your pattern looks like:
x = f1(...) + f2(...) + f3(...) + f4(...)
that's one concat and it's zippy, StringBuilder probably won't help.
If your pattern looks like:
if (...) x += f1(...)
if (...) x += f2(...)
if (...) x += f3(...)
if (...) x += f4(...)
then you probably want StringBuilder.
Yet another article to support this claim comes from Eric Lippert where he describes the optimizations performed on one line + concatenations in a detailed manner.

The StringBuilder.Append() method is much better than using the + operator. But I've found that, when executing 1000 concatenations or less, String.Join() is even more efficient than StringBuilder.
StringBuilder sb = new StringBuilder();
sb.Append(someString);
The only problem with String.Join is that you have to concatenate the strings with a common delimiter.
Edit: as #ryanversaw pointed out, you can make the delimiter string.Empty.
string key = String.Join("_", new String[]
{ "Customers_Contacts", customerID, database, SessionID });

There are 6 types of string concatenations:
Using the plus (+) symbol.
Using string.Concat().
Using string.Join().
Using string.Format().
Using string.Append().
Using StringBuilder.
In an experiment, it has been proved that string.Concat() is the best way to approach if the words are less than 1000(approximately) and if the words are more than 1000 then StringBuilder should be used.
For more information, check this site.
string.Join() vs string.Concat()
The string.Concat method here is equivalent to the string.Join method invocation with an empty separator. Appending an empty string is fast, but not doing so is even faster, so the string.Concat method would be superior here.

From Chinh Do - StringBuilder is not always faster:
Rules of Thumb
When concatenating three dynamic string values or less, use traditional string concatenation.
When concatenating more than three dynamic string values, use StringBuilder.
When building a big string from several string literals, use either the # string literal or the inline + operator.
Most of the time StringBuilder is your best bet, but there are cases as shown in that post that you should at least think about each situation.

If you're operating in a loop, StringBuilder is probably the way to go; it saves you the overhead of creating new strings regularly. In code that'll only run once, though, String.Concat is probably fine.
However, Rico Mariani (.NET optimization guru) made up a quiz in which he stated at the end that, in most cases, he recommends String.Format.

Here is the fastest method I've evolved over a decade for my large-scale NLP app. I have variations for IEnumerable<T> and other input types, with and without separators of different types (Char, String), but here I show the simple case of concatenating all strings in an array into a single string, with no separator. Latest version here is developed and unit-tested on C# 7 and .NET 4.7.
There are two keys to higher performance; the first is to pre-compute the exact total size required. This step is trivial when the input is an array as shown here. For handling IEnumerable<T> instead, it is worth first gathering the strings into a temporary array for computing that total (The array is required to avoid calling ToString() more than once per element since technically, given the possibility of side-effects, doing so could change the expected semantics of a 'string join' operation).
Next, given the total allocation size of the final string, the biggest boost in performance is gained by building the result string in-place. Doing this requires the (perhaps controversial) technique of temporarily suspending the immutability of a new String which is initially allocated full of zeros. Any such controversy aside, however...
...note that this is the only bulk-concatenation solution on this page which entirely avoids an extra round of allocation and copying by the String constructor.
Complete code:
/// <summary>
/// Concatenate the strings in 'rg', none of which may be null, into a single String.
/// </summary>
public static unsafe String StringJoin(this String[] rg)
{
int i;
if (rg == null || (i = rg.Length) == 0)
return String.Empty;
if (i == 1)
return rg[0];
String s, t;
int cch = 0;
do
cch += rg[--i].Length;
while (i > 0);
if (cch == 0)
return String.Empty;
i = rg.Length;
fixed (Char* _p = (s = new String(default(Char), cch)))
{
Char* pDst = _p + cch;
do
if ((t = rg[--i]).Length > 0)
fixed (Char* pSrc = t)
memcpy(pDst -= t.Length, pSrc, (UIntPtr)(t.Length << 1));
while (pDst > _p);
}
return s;
}
[DllImport("MSVCR120_CLR0400", CallingConvention = CallingConvention.Cdecl)]
static extern unsafe void* memcpy(void* dest, void* src, UIntPtr cb);
I should mention that this code has a slight modification from what I use myself. In the original, I call the cpblk IL instruction from C# to do the actual copying. For simplicity and portability in the code here, I replaced that with P/Invoke memcpy instead, as you can see. For highest performance on x64 (but maybe not x86) you may want to use the cpblk method instead.

From this MSDN article:
There is some overhead associated with
creating a StringBuilder object, both
in time and memory. On a machine with
fast memory, a StringBuilder becomes
worthwhile if you're doing about five
operations. As a rule of thumb, I
would say 10 or more string operations
is a justification for the overhead on
any machine, even a slower one.
So if you trust MSDN go with StringBuilder if you have to do more than 10 strings operations/concatenations - otherwise simple string concat with '+' is fine.

Try this 2 pieces of code and you will find the solution.
static void Main(string[] args)
{
StringBuilder s = new StringBuilder();
for (int i = 0; i < 10000000; i++)
{
s.Append( i.ToString());
}
Console.Write("End");
Console.Read();
}
Vs
static void Main(string[] args)
{
string s = "";
for (int i = 0; i < 10000000; i++)
{
s += i.ToString();
}
Console.Write("End");
Console.Read();
}
You will find that 1st code will end really quick and the memory will be in a good amount.
The second code maybe the memory will be ok, but it will take longer... much longer.
So if you have an application for a lot of users and you need speed, use the 1st. If you have an app for a short term one user app, maybe you can use both or the 2nd will be more "natural" for developers.
Cheers.

It's also important to point it out that you should use the + operator if you are concatenating string literals.
When you concatenate string literals or string constants by using the + operator, the compiler creates a single string. No run time concatenation occurs.
How to: Concatenate Multiple Strings (C# Programming Guide)

Adding to the other answers, please keep in mind that StringBuilder can be told an initial amount of memory to allocate.
The capacity parameter defines the maximum number of characters that can be stored in the memory allocated by the current instance. Its value is assigned to the Capacity property. If the number of characters to be stored in the current instance exceeds this capacity value, the StringBuilder object allocates additional memory to store them.
If capacity is zero, the implementation-specific default capacity is used.
Repeatedly appending to a StringBuilder that hasn't been pre-allocated can result in a lot of unnecessary allocations just like repeatedly concatenating regular strings.
If you know how long the final string will be, can trivially calculate it, or can make an educated guess about the common case (allocating too much isn't necessarily a bad thing), you should be providing this information to the constructor or the Capacity property. Especially when running performance tests to compare StringBuilder with other methods like String.Concat, which do the same thing internally. Any test you see online which doesn't include StringBuilder pre-allocation in its comparisons is wrong.
If you can't make any kind of guess about the size, you're probably writing a utility function which should have its own optional argument for controlling pre-allocation.

Following may be one more alternate solution to concatenate multiple strings.
String str1 = "sometext";
string str2 = "some other text";
string afterConcate = $"{str1}{str2}";
string interpolation

Another solution:
inside the loop, use List instead of string.
List<string> lst= new List<string>();
for(int i=0; i<100000; i++){
...........
lst.Add(...);
}
return String.Join("", lst.ToArray());;
it is very very fast.

The most efficient is to use StringBuilder, like so:
StringBuilder sb = new StringBuilder();
sb.Append("string1");
sb.Append("string2");
...etc...
String strResult = sb.ToString();
#jonezy: String.Concat is fine if you have a couple of small things. But if you're concatenating megabytes of data, your program will likely tank.

System.String is immutable. When we modify the value of a string variable then a new memory is allocated to the new value and the previous memory allocation released. System.StringBuilder was designed to have concept of a mutable string where a variety of operations can be performed without allocation separate memory location for the modified string.

I've tested all the methods in this page and at the end I've developed my solution that is the fastest and less memory expensive.
Note: tested in Framework 4.8
[MemoryDiagnoser]
public class StringConcatSimple
{
private string
title = "Mr.", firstName = "David", middleName = "Patrick", lastName = "Callan";
[Benchmark]
public string FastConcat()
{
return FastConcat(
title, " ",
firstName, " ",
middleName, " ",
lastName);
}
[Benchmark]
public string StringBuilder()
{
var stringBuilder =
new StringBuilder();
return stringBuilder
.Append(title).Append(' ')
.Append(firstName).Append(' ')
.Append(middleName).Append(' ')
.Append(lastName).ToString();
}
[Benchmark]
public string StringBuilderExact24()
{
var stringBuilder =
new StringBuilder(24);
return stringBuilder
.Append(title).Append(' ')
.Append(firstName).Append(' ')
.Append(middleName).Append(' ')
.Append(lastName).ToString();
}
[Benchmark]
public string StringBuilderEstimate100()
{
var stringBuilder =
new StringBuilder(100);
return stringBuilder
.Append(title).Append(' ')
.Append(firstName).Append(' ')
.Append(middleName).Append(' ')
.Append(lastName).ToString();
}
[Benchmark]
public string StringPlus()
{
return title + ' ' + firstName + ' ' +
middleName + ' ' + lastName;
}
[Benchmark]
public string StringFormat()
{
return string.Format("{0} {1} {2} {3}",
title, firstName, middleName, lastName);
}
[Benchmark]
public string StringInterpolation()
{
return
$"{title} {firstName} {middleName} {lastName}";
}
[Benchmark]
public string StringJoin()
{
return string.Join(" ", title, firstName,
middleName, lastName);
}
[Benchmark]
public string StringConcat()
{
return string.
Concat(new String[]
{ title, " ", firstName, " ",
middleName, " ", lastName });
}
}
Yes, it use unsafe
public static unsafe string FastConcat(string str1, string str2, string str3, string str4, string str5, string str6, string str7)
{
var capacity = 0;
var str1Length = 0;
var str2Length = 0;
var str3Length = 0;
var str4Length = 0;
var str5Length = 0;
var str6Length = 0;
var str7Length = 0;
if (str1 != null)
{
str1Length = str1.Length;
capacity = str1Length;
}
if (str2 != null)
{
str2Length = str2.Length;
capacity += str2Length;
}
if (str3 != null)
{
str3Length = str3.Length;
capacity += str3Length;
}
if (str4 != null)
{
str4Length = str4.Length;
capacity += str4Length;
}
if (str5 != null)
{
str5Length = str5.Length;
capacity += str5Length;
}
if (str6 != null)
{
str6Length = str6.Length;
capacity += str6Length;
}
if (str7 != null)
{
str7Length = str7.Length;
capacity += str7Length;
}
string result = new string(' ', capacity);
fixed (char* dest = result)
{
var x = dest;
if (str1Length > 0)
{
fixed (char* src = str1)
{
Unsafe.CopyBlock(x, src, (uint)str1Length * 2);
x += str1Length;
}
}
if (str2Length > 0)
{
fixed (char* src = str2)
{
Unsafe.CopyBlock(x, src, (uint)str2Length * 2);
x += str2Length;
}
}
if (str3Length > 0)
{
fixed (char* src = str3)
{
Unsafe.CopyBlock(x, src, (uint)str3Length * 2);
x += str3Length;
}
}
if (str4Length > 0)
{
fixed (char* src = str4)
{
Unsafe.CopyBlock(x, src, (uint)str4Length * 2);
x += str4Length;
}
}
if (str5Length > 0)
{
fixed (char* src = str5)
{
Unsafe.CopyBlock(x, src, (uint)str5Length * 2);
x += str5Length;
}
}
if (str6Length > 0)
{
fixed (char* src = str6)
{
Unsafe.CopyBlock(x, src, (uint)str6Length * 2);
x += str6Length;
}
}
if (str7Length > 0)
{
fixed (char* src = str7)
{
Unsafe.CopyBlock(x, src, (uint)str7Length * 2);
}
}
}
return result;
}
You can edit the method and adapt it to your case. For example you can make it something like
public static unsafe string FastConcat(string str1, string str2, string str3 = null, string str4 = null, string str5 = null, string str6 = null, string str7 = null)

For just two strings, you definitely do not want to use StringBuilder. There is some threshold above which the StringBuilder overhead is less than the overhead of allocating multiple strings.
So, for more that 2-3 strings, use DannySmurf's code. Otherwise, just use the + operator.

It really depends on your usage pattern.
A detailed benchmark between string.Join, string,Concat and string.Format can be found here: String.Format Isn't Suitable for Intensive Logging
(This is actually the same answer I gave to this question)

It would depend on the code.
StringBuilder is more efficient generally, but if you're only concatenating a few strings and doing it all in one line, code optimizations will likely take care of it for you. It's important to think about how the code looks too: for larger sets StringBuilder will make it easier to read, for small ones StringBuilder will just add needless clutter.

Performance char vs string

Just out of curiousity (not really expecting a measurable result) which of the following codes are better in case of performance?
private void ReplaceChar(ref string replaceMe) {
if (replaceMe.Contains('a')) {
replaceMe=replaceMe.Replace('a', 'b');
}
}
private void ReplaceString(ref string replaceMe) {
if (replaceMe.Contains("a")) {
replaceMe=replaceMe.Replace("a", "b");
}
}
In the first example I use char, while in the second using strings in Contains() and Replace()
Would the first one have better performance because of the less memory-consuming "char" or does the second perform better, because the compiler does not have to cast in this operation?
(Or is this all nonsense, cause the CLR generates the same code in both variations?)

If you have two horses and want to know which is faster...
String replaceMe = new String('a', 10000000) +
new String('b', 10000000) +
new String('a', 10000000);
Stopwatch sw = new Stopwatch();
sw.Start();
// String replacement
if (replaceMe.Contains("a")) {
replaceMe = replaceMe.Replace("a", "b");
}
// Char replacement
//if (replaceMe.Contains('a')) {
// replaceMe = replaceMe.Replace('a', 'b');
//}
sw.Stop();
Console.Write(sw.ElapsedMilliseconds);
I've got 60 ms for Char replacement and 500 ms for String one (Core i5 3.2GHz, 64-bit, .Net 4.6). So
replaceMe = replaceMe.Replace('a', 'b')
is about 9 times faster

We can't know for sure without testing the code since most of the replacing is done inside the CLR and it heavily optimized.
What we can say is this: replacing a char has some performance benefits since the code is simpler and the outcome is more predictable: replacing a char will always yield the same number of characters as the original for example.
In the performance of the replacing itself doesn't matter too much. In a tight loop, the allocation and garbage collection of the 'old' string will have a bigger impact than the replacement itself.

Reducing time complexity of the code

I have the following code but it takes 20sec to process the 52957 inputs of type BigInteger. This is the question that i want to solve https://www.hackerearth.com/problem/algorithm/girlfriends-demands/
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Numerics;
namespace girldfriends_demands
{
class Program
{
private static string inputString = String.Empty;
private static int testCases=0;
private static BigInteger[,] indexArray;
static void Main(string[] args)
{
initialize();
printDemand();
Console.ReadLine();
}
private static void initialize()
{
inputString = Console.ReadLine();
testCases = int.Parse(Console.ReadLine());
indexArray = new BigInteger[testCases, 2];
for (int i = 0; i < testCases; i++)
{
string[] tokens = Console.ReadLine().Split();
indexArray[i, 0] = BigInteger.Parse(tokens[0]);
indexArray[i, 1] = BigInteger.Parse(tokens[1]);
}
}
private static void printDemand()
{
char[] convertedString = inputString.ToCharArray();
for (int i = 0; i < testCases; i++)
{
BigInteger length=inputString.Length;
BigInteger startf, endf; ;
BigInteger.DivRem(indexArray[i, 0] - 1,length,out startf);
BigInteger.DivRem(indexArray[i, 1]-1,length,out endf);
char c=convertedString[((int)startf)];
char e=convertedString[((int)endf)];
if(c==e)
{
Console.WriteLine("Yes");
}
else
{
Console.WriteLine("No");
}
}
}
}
}
Please specify how to reduce the time complexity of the code.This program gets the letters at the specified position in a string and prints true if they are same else false. Also computing the range at prior to the loop isn't helping

Why you use BigInteger ?
In any case string.length is typeof int.
It mean that if your string exceed 2147483647 (2^31 -1) your program will be broken.
I think changing BigInteger to int will help.

Console.ReadLine().Split()
is the biggest of your problems. For every single line in the file, you create an array of strings, one letter per string. This is a huge performance drain, and almost certainly not what you intended - in particular, it would be wholy unnecessary to use BigInteger to store a single-digit number...
I assume that you actually want to split the line in two based on some delimiter. For example, if your numbers are separated by a comma, you can use
Console.ReadLine().Split(',')
Even then, there is little reason to use BigInteger at all. The operation you're trying to perform is distinctly string-based, and very easy to do with strings. However, I can't really help you more specifically, because your problem description is incredibly ambiguous for such a simple task, and the code is so obviously wrong it's entirely useless to guess at what exactly you're trying to do.
EDIT:
Okay, your link confirmed my assumptions - you are massively overcomplicating this. For example, code like this will do:
var word = Console.ReadLine();
var items = int.Parse(Console.ReadLine());
for (var _ = 0; _ < items; _++)
{
var indices =
Console.ReadLine()
.Split(' ')
.Select(i => (int)((long.Parse(i) - 1) % word.Length))
.ToArray();
Console.WriteLine(word[indices[0]] == word[indices[1]] ? "Yes" : "No");
}
First, note that the numbers will always fit in a long, which allows you to avoid using BigIntever. Second, you need to use Split properly - in this case, the delimiter is a space. Third, there's no reason not to do the whole processing in a single stream - waiting for the whole input, collecting it in memory and then outputting everything at once is a waste of memory. Fourth, note how easy it was to avoid most of the complex checks while incorporating the whole necessary mechanism in simple arithmetic operations.
This runs under 2 seconds on each of the input data, only using ~80kiB of memory.
I think that ideologically, this fits the site perfectly - it's very simple and straightforward and works for all the expected inputs - the perfect hack. Of course, you'd want extra checks if this was for an end-user application, but the HackerEarth site name implies hacks are what's expected, really.

In my experience, frequent Console.WriteLine calls can lead to huge execution times.
Instead of calling that function whenever you want to add some output, I think you should use a StringBuilder object, and append all your output to it. Then, after the for-loop, call Console.WriteLine once to print the StringBuilder's contents.
This might not be your program's biggest problem, but it will help quite a bit.

Myabe by removing casts in these line and using string.compare you cand decrease execution time
if(string.Compare(startf.ToString(), endf.ToString()))
{
Console.WriteLine("Yes");
continue;
}
Console.WriteLine("No");

Which is faster in a loop: calling a property twice, or storing the property once?

This is more of an academic question about performance than a realistic 'what should I use' but I'm curious as I don't dabble much in IL at all to see what's constructed and I don't have a large dataset on hand to profile against.
So which is faster:
List<myObject> objs = SomeHowGetList();
List<string> strings = new List<string>();
foreach (MyObject o in objs)
{
if (o.Field == "something")
strings.Add(o.Field);
}
or:
List<myObject> objs = SomeHowGetList();
List<string> strings = new List<string>();
string s;
foreach (MyObject o in objs)
{
s = o.Field;
if (s == "something")
strings.Add(s);
}
Keep in mind that I don't really want to know the performance impact of the string.Add(s) (as whatever operation needs to be done can't really be changed), just the performance difference between setting s each iteration (let's say that s can be any primitive type or string) verses calling the getter on the object each iteration.

Your first option is noticeably faster in my tests. I'm such flip flopper! Seriously though, some comments were made about the code in my original test. Here's the updated code that shows option 2 being faster.
class Foo
{
public string Bar { get; set; }
public static List<Foo> FooMeUp()
{
var foos = new List<Foo>();
for (int i = 0; i < 10000000; i++)
{
foos.Add(new Foo() { Bar = (i % 2 == 0) ? "something" : i.ToString() });
}
return foos;
}
}
static void Main(string[] args)
{
var foos = Foo.FooMeUp();
var strings = new List<string>();
Stopwatch sw = Stopwatch.StartNew();
foreach (Foo o in foos)
{
if (o.Bar == "something")
{
strings.Add(o.Bar);
}
}
sw.Stop();
Console.WriteLine("It took {0}", sw.ElapsedMilliseconds);
strings.Clear();
sw = Stopwatch.StartNew();
foreach (Foo o in foos)
{
var s = o.Bar;
if (s == "something")
{
strings.Add(s);
}
}
sw.Stop();
Console.WriteLine("It took {0}", sw.ElapsedMilliseconds);
Console.ReadLine();
}

Most of the time, your second code snippet should be at least as fast as the first snippet.
These two code snippets are not functionally equivalent. Properties are not guaranteed to return the same result across individual accesses. As a consequence, the JIT optimizer is not able to cache the result (except for trivial cases) and it will be faster if you cache the result of a long running property. Look at this example: why foreach is faster than for loop while reading richtextbox lines.
However, for some specific cases like:
for (int i = 0; i < myArray.Length; ++i)
where myArray is an array object, the compiler is able to detect the pattern and optimize the code and omit the bound checks. It might be slower if you cache the result of Length property like:
int len = myArray.Length;
for (int i = 0; i < myArray.Length; ++i)

It really depends on the implementation. In most cases, it is assumed (as a matter of common practice / courtesy) that a property is inexpensive. However, it could that each "get" does a non-cached search over some remote resource. For standard, simple properties, you'll never notice a real difference between the two. For the worst-case, fetch-once, store and re-use will be much faster.
I'd be tempted to use get twice until I know there is a problem... "premature optimisation", etc... But; if I was using it in a tight loop, then I might store it in a variable. Except for Length on an array, which has special JIT treatment ;-p

Generally the second one is faster, as the first one recalculates the property on each iteration.
Here is an example of something that could take significant amount of time:
var d = new DriveInfo("C:");
d.VolumeLabel; // will fetch drive label on each call

Storing the value in a field is the faster option.
Although a method call doesn't impose a huge overhead, it far outweighs storing the value once to a local variable on the stack and then retrieving it.
I for one do it consistently.

Is String.Format as efficient as StringBuilder

Suppose I have a stringbuilder in C# that does this:
StringBuilder sb = new StringBuilder();
string cat = "cat";
sb.Append("the ").Append(cat).(" in the hat");
string s = sb.ToString();
would that be as efficient or any more efficient as having:
string cat = "cat";
string s = String.Format("The {0} in the hat", cat);
If so, why?
EDIT
After some interesting answers, I realised I probably should have been a little clearer in what I was asking. I wasn't so much asking for which was quicker at concatenating a string, but which is quicker at injecting one string into another.
In both cases above I want to inject one or more strings into the middle of a predefined template string.
Sorry for the confusion

NOTE: This answer was written when .NET 2.0 was the current version. This may no longer apply to later versions.
String.Format uses a StringBuilder internally:
public static string Format(IFormatProvider provider, string format, params object[] args)
{
if ((format == null) || (args == null))
{
throw new ArgumentNullException((format == null) ? "format" : "args");
}
StringBuilder builder = new StringBuilder(format.Length + (args.Length * 8));
builder.AppendFormat(provider, format, args);
return builder.ToString();
}
The above code is a snippet from mscorlib, so the question becomes "is StringBuilder.Append() faster than StringBuilder.AppendFormat()"?
Without benchmarking I'd probably say that the code sample above would run more quickly using .Append(). But it's a guess, try benchmarking and/or profiling the two to get a proper comparison.
This chap, Jerry Dixon, did some benchmarking:
http://jdixon.dotnetdevelopersjournal.com/string_concatenation_stringbuilder_and_stringformat.htm
Updated:
Sadly the link above has since died. However there's still a copy on the Way Back Machine:
http://web.archive.org/web/20090417100252/http://jdixon.dotnetdevelopersjournal.com/string_concatenation_stringbuilder_and_stringformat.htm
At the end of the day it depends whether your string formatting is going to be called repetitively, i.e. you're doing some serious text processing over 100's of megabytes of text, or whether it's being called when a user clicks a button now and again. Unless you're doing some huge batch processing job I'd stick with String.Format, it aids code readability. If you suspect a perf bottleneck then stick a profiler on your code and see where it really is.

From the MSDN documentation:
The performance of a concatenation operation for a String or StringBuilder object depends on how often a memory allocation occurs. A String concatenation operation always allocates memory, whereas a StringBuilder concatenation operation only allocates memory if the StringBuilder object buffer is too small to accommodate the new data. Consequently, the String class is preferable for a concatenation operation if a fixed number of String objects are concatenated. In that case, the individual concatenation operations might even be combined into a single operation by the compiler. A StringBuilder object is preferable for a concatenation operation if an arbitrary number of strings are concatenated; for example, if a loop concatenates a random number of strings of user input.

I ran some quick performance benchmarks, and for 100,000 operations averaged over 10 runs, the first method (String Builder) takes almost half the time of the second (String Format).
So, if this is infrequent, it doesn't matter. But if it is a common operation, then you may want to use the first method.

I would expect String.Format to be slower - it has to parse the string and then concatenate it.
Couple of notes:
Format is the way to go for user-visible strings in professional applications; this avoids localization bugs
If you know the length of the resultant string beforehand, use the StringBuilder(Int32) constructor to predefine the capacity

I think in most cases like this clarity, and not efficiency, should be your biggest concern. Unless you're crushing together tons of strings, or building something for a lower powered mobile device, this probably won't make much of a dent in your run speed.
I've found that, in cases where I'm building strings in a fairly linear fashion, either doing straight concatenations or using StringBuilder is your best option. I suggest this in cases where the majority of the string that you're building is dynamic. Since very little of the text is static, the most important thing is that it's clear where each piece of dynamic text is being put in case it needs updated in the future.
On the other hand, if you're talking about a big chunk of static text with two or three variables in it, even if it's a little less efficient, I think the clarity you gain from string.Format makes it worth it. I used this earlier this week when having to place one bit of dynamic text in the center of a 4 page document. It'll be easier to update that big chunk of text if its in one piece than having to update three pieces that you concatenate together.

If only because string.Format doesn't exactly do what you might think, here is a rerun of the tests 6 years later on Net45.
Concat is still fastest but really it's less than 30% difference. StringBuilder and Format differ by barely 5-10%. I got variations of 20% running the tests a few times.
Milliseconds, a million iterations:
Concatenation: 367
New stringBuilder for each key: 452
Cached StringBuilder: 419
string.Format: 475
The lesson I take away is that the performance difference is trivial and so it shouldn't stop you writing the simplest readable code you can. Which for my money is often but not always a + b + c.
const int iterations=1000000;
var keyprefix= this.GetType().FullName;
var maxkeylength=keyprefix + 1 + 1+ Math.Log10(iterations);
Console.WriteLine("KeyPrefix \"{0}\", Max Key Length {1}",keyprefix, maxkeylength);
var concatkeys= new string[iterations];
var stringbuilderkeys= new string[iterations];
var cachedsbkeys= new string[iterations];
var formatkeys= new string[iterations];
var stopwatch= new System.Diagnostics.Stopwatch();
Console.WriteLine("Concatenation:");
stopwatch.Start();
for(int i=0; i<iterations; i++){
var key1= keyprefix+":" + i.ToString();
concatkeys[i]=key1;
}
Console.WriteLine(stopwatch.ElapsedMilliseconds);
Console.WriteLine("New stringBuilder for each key:");
stopwatch.Restart();
for(int i=0; i<iterations; i++){
var key2= new StringBuilder(keyprefix).Append(":").Append(i.ToString()).ToString();
stringbuilderkeys[i]= key2;
}
Console.WriteLine(stopwatch.ElapsedMilliseconds);
Console.WriteLine("Cached StringBuilder:");
var cachedSB= new StringBuilder(maxkeylength);
stopwatch.Restart();
for(int i=0; i<iterations; i++){
var key2b= cachedSB.Clear().Append(keyprefix).Append(":").Append(i.ToString()).ToString();
cachedsbkeys[i]= key2b;
}
Console.WriteLine(stopwatch.ElapsedMilliseconds);
Console.WriteLine("string.Format");
stopwatch.Restart();
for(int i=0; i<iterations; i++){
var key3= string.Format("{0}:{1}", keyprefix,i.ToString());
formatkeys[i]= key3;
}
Console.WriteLine(stopwatch.ElapsedMilliseconds);
var referToTheComputedValuesSoCompilerCantOptimiseTheLoopsAway= concatkeys.Union(stringbuilderkeys).Union(cachedsbkeys).Union(formatkeys).LastOrDefault(x=>x[1]=='-');
Console.WriteLine(referToTheComputedValuesSoCompilerCantOptimiseTheLoopsAway);

String.Format uses StringBuilder internally, so logically that leads to the idea that it would be a little less performant due to more overhead. However, a simple string concatenation is the fastest method of injecting one string between two others, by a significant degree. This evidence was demonstrated by Rico Mariani in his very first Performance Quiz, years ago. Simple fact is that concatenations, when the number of string parts is known (without limitation — you could concatenate a thousand parts, as long as you know it's always 1000 parts), are always faster than StringBuilder or String.Format. They can be performed with a single memory allocation and a series of memory copies. Here is the proof.
And here is the actual code for some String.Concat methods, which ultimately call FillStringChecked, which uses pointers to copy memory (extracted via Reflector):
public static string Concat(params string[] values)
{
int totalLength = 0;
if (values == null)
{
throw new ArgumentNullException("values");
}
string[] strArray = new string[values.Length];
for (int i = 0; i < values.Length; i++)
{
string str = values[i];
strArray[i] = (str == null) ? Empty : str;
totalLength += strArray[i].Length;
if (totalLength < 0)
{
throw new OutOfMemoryException();
}
}
return ConcatArray(strArray, totalLength);
}
public static string Concat(string str0, string str1, string str2, string str3)
{
if (((str0 == null) && (str1 == null)) && ((str2 == null) && (str3 == null)))
{
return Empty;
}
if (str0 == null)
{
str0 = Empty;
}
if (str1 == null)
{
str1 = Empty;
}
if (str2 == null)
{
str2 = Empty;
}
if (str3 == null)
{
str3 = Empty;
}
int length = ((str0.Length + str1.Length) + str2.Length) + str3.Length;
string dest = FastAllocateString(length);
FillStringChecked(dest, 0, str0);
FillStringChecked(dest, str0.Length, str1);
FillStringChecked(dest, str0.Length + str1.Length, str2);
FillStringChecked(dest, (str0.Length + str1.Length) + str2.Length, str3);
return dest;
}
private static string ConcatArray(string[] values, int totalLength)
{
string dest = FastAllocateString(totalLength);
int destPos = 0;
for (int i = 0; i < values.Length; i++)
{
FillStringChecked(dest, destPos, values[i]);
destPos += values[i].Length;
}
return dest;
}
private static unsafe void FillStringChecked(string dest, int destPos, string src)
{
int length = src.Length;
if (length > (dest.Length - destPos))
{
throw new IndexOutOfRangeException();
}
fixed (char* chRef = &dest.m_firstChar)
{
fixed (char* chRef2 = &src.m_firstChar)
{
wstrcpy(chRef + destPos, chRef2, length);
}
}
}
So, then:
string what = "cat";
string inthehat = "The " + what + " in the hat!";
Enjoy!

Oh also, the fastest would be:
string cat = "cat";
string s = "The " + cat + " in the hat";

It really depends. For small strings with few concatenations, it's actually faster just to append the strings.
String s = "String A" + "String B";
But for larger string (very very large strings), it's then more efficient to use StringBuilder.

In both cases above I want to inject one or more strings into the middle of a predefined template string.
In which case, I would suggest String.Format is the quickest because it is design for that exact purpose.

It really depends on your usage pattern.
A detailed benchmark between string.Join, string,Concat and string.Format can be found here: String.Format Isn't Suitable for Intensive Logging

I would suggest not, since String.Format was not designed for concatenation, it was design for formatting the output of various inputs such as a date.
String s = String.Format("Today is {0:dd-MMM-yyyy}.", DateTime.Today);