Develop Reference

How do I insert an int into a sorted array quickly?

I'd like to insert an int into a sorted array. This operation is going to be performed very often, so it needs to be as fast as possible.
It is possible and even preferred to use a List or any other class instead of an array
All values are in the 1 to 34 range
The array typically contains exactly 14 values
I was thinking of many different approaches, including binary search and simple insert-on-copy, but found it hard to decide. Also, I felt like I missed an idea. Do you have experiences on this topic or any new ideas to consider?

I will use an int array whose length is 35(because you said range 1-34) to record the status of the numbers.
int[] status = Enumerable.Repeat(0, 35).ToArray();
//an array contains 35 zeros
//which means currently there is no elements in the array
status[10] = 1; // now the array have only one number: 10
status[11] ++; // a new number 11 is added to the list
So if you want to add a number i to the list:
status[i]++; // O(1) to add a number
To remove an i from the list:
status[i]--; // O(1) to remove a number
Want to know all the numebrs in the list?
for (int i = 0; i < status.Length; i++)
{
if (status[i] > 0)
{
for (int j = 0; j < status[i]; j++)
Console.WriteLine(i);
}
}
//or more easier using LINQ
var result = status.SelectMany((i, index) => Enumerable.Repeat(index, i));
The following example may help you understand my code better:
the real number array: 1 12 12 15 9 34 // i don't care if it's sorted
the status array: status[1]=1,status[12]=2,status[15]=1,status[9]=1,status[34]=1
all others are 0

At 14 values this is a pretty small array, I don't think switching to a smarter data structure such as a list will win you much, especially if you fast good random access. Even binary search may actually be slower than linear search at this scale. Are you sure that, say, insert-on-copy does not satisfy your performance requirements?

This operation is going to be performed very often, so it needs to be as fast as possible.
The things that you notice happen "very often" are frequently not the bottlenecks in the program - it's often surprising what the actual bottlenecks are. You should code something simple and measure the actual performance of your program before performing any optimizations.
I was thinking of many different approaches, including binary search and simple insert-on-copy, but found it hard to decide.
Assuming that this is the bottleneck, the big-O performance of the different methods is not going to be relevant here because of the small size of your array. It is easier to just try a few different approaches, measure the results, see which performs best and choose that method. If you have followed the advice from the first paragraph you already have a profiler setup that you can use for this step too.

For inserting into the middle, a LinkedList<int> would be the fastest option - anything else involves copying data. At 14 elements, don't stress over binary search etc - just walk forwards to the item you want:
using System;
using System.Collections.Generic;
static class Program
{
static void Main()
{
LinkedList<int> data = new LinkedList<int>();
Random rand = new Random(12345);
for (int i = 0; i < 20; i++)
{
data.InsertSortedValue(rand.Next(300));
}
foreach (int i in data) Console.WriteLine(i);
}
}
static class LinkedListExtensions {
public static void InsertSortedValue(this LinkedList<int> list, int value)
{
LinkedListNode<int> node = list.First, next;
if (node == null || node.Value > value)
{
list.AddFirst(value);
}
else
{
while ((next = node.Next) != null && next.Value < value)
node = next;
list.AddAfter(node, value);
}
}
}

Doing the brute-force approach is the best decision here because 14 isn't a number :). However, this is not a scalable decision, since should 14 become 14000 one day that will cause problems

What is the most common operation with your array?
Insert? Read?
Heap data structure will give you O(log(14)) for both of them. SortedDictionary may hit your performance.
Using a simple array will give you O(1) for reading and O(14) for insert.
By the way, have you tried System.Collections.Generic.SortedDictionary ot System.Collections.Generic.SortedList?

If you're on .Net 4 you should take a look at the SortedSet<T>. Otherwise take a look at SortedDictionary<TKey, TValue> where you make TValue as object and just put null into it, cause you're just interested into the keys.

If there is no repeated value on the array and the possible values won´t change maybe a fixed size array where the value is equal to the index is a good choice
Both insert and read are O(1)

You have a range of possible values from 1-34 which is rather narrow. So the fastest way would likely be using an array with 34 slots. To insert a number n just do array[n-1]++ and to remove it do array[n.1]-- (if n>0).
To check if a value exists in your collection you do array[n-1]>0.
edit: Damn...Danny was faster. :)

Write a method takes an array of integers and sorts them in place using Bubble Sort. The method is not allowed to create any additional arrays. Bubble Sort is a simple sorting algorithm that works by looping through the array to be sorted, comparing each pair of adjacent elements and swapping them if they are in the wrong order.

C++ ">>" and "<<" IO in C#?

Is there a C# library that provides the functionality of ">>" and "<<" for IO in C++? It was really convenient for console apps. Granted not a lot of console apps are in C#, but some of us use it for them.
I know about Console.Read[Line]|Write[Line] and Streams|FileStream|StreamReader|StreamWriter thats not part of the question.
I dont think im specific enough
int a,b;
cin >> a >> b;
IS AMAZING!!
string input = Console.ReadLine();
string[] data = input.split( ' ' );
a = Convert.ToInt32( data[0] );
b = Convert.ToInt32( data[1] );
... long winded enough? Plus there are other reasons why the C# solution is worse. I must get the entire line or make my own buffer for it. If the line im working on is IDK say the 1000 line of Bells Triangle, I waste so much time reading everything at one time.
EDIT:
GAR!!!
OK THE PROBLEM!!!
Using IntX to do HUGE number like the .net 4.0 BigInteger to produce the bell triangle. If you know the bell triangle it gets freaking huge very very quickly. The whole point of this question is that I need to deal with each number individually. If you read an entire line, you could easily hit Gigs of data. This is kinda the same as digits of Pi. For Example 42pow1048576 is 1.6 MB! I don't have time nor memory to read all the numbers as one string then pick the one I want

No, and I wouldn't. C# != C++
You should try your best to stick with the language convention of whatever language you are working in.

I think I get what you are after: simple, default formatted input. I think the reason there is no TextReader.ReadXXX() is that this is parsing, and parsing is hard: for example: should ReadFloat():
ignore leading whitespace
require decimal point
require trailing whitespace (123abc)
handle exponentials (12.3a3 parses differently to 12.4e5?)
Not to mention what the heck does ReadString() do? From C++, you would expect "read to the next whitespace", but the name doesn't say that.
Now all of these have good sensible answers, and I agree C# (or rather, the BCL) should provide them, but I can certainly understand why they would choose to not provide fragile, nearly impossible to use correctly, functions right there on a central class.
EDIT:
For the buffering problem, an ugly solution is:
static class TextReaderEx {
static public string ReadWord(this TextReader reader) {
int c;
// Skip leading whitespace
while (-1 != (c = reader.Peek()) && char.IsWhiteSpace((char)c)) reader.Read();
// Read to next whitespace
var result = new StringBuilder();
while (-1 != (c = reader.Peek()) && !char.IsWhiteSpace((char)c)) {
reader.Read();
result.Append((char)c);
}
return result.ToString();
}
}
...
int.Parse(Console.In.ReadWord())

Nope. You're stuck with Console.WriteLine. You could create a wrapper that offered this functionality, though.

You can Use Console.WriteLine , Console.ReadLine ..For the purpose.Both are in System NameSpace.

You have System.IO.Stream(Reader|Writer)
And for console: Console.Write, Console.Read

Not that I know of. If you are interested of the chaining outputs you can use System.Text.StringBuilder.
http://msdn.microsoft.com/en-us/library/system.text.stringbuilder(VS.71).aspx
StringBuilder builder = new StringBuilder();
builder.Append("hello").Append(" world!");
Console.WriteLine(builder.ToString());
Perhaps not as pretty as C++, but as another poster states, C# != C++.

This is not even possible in C#, no matter how hard you try:
The left hand side and right hand side of operators is always passed by value; this rules out the possibility of cin.
The right hand side of << and >> must be an integer; this rules out cout.
The first point is to make sure operator overloading is a little less messy than in C++ (debatable, but it surely makes things a lot simpler), and the second point was specifically chosen to rule out C++'s cin and cout way of dealing with IO, IIRC.

Designing a custom Random class

I know C# has the Random class and probably a few classes in LINQ to do this, but if I was to write my own code to randomly select an item from a collection without using any built in .NET objects, how would this be done?
I can't seem to nail the logic required for this - how would I tell the system when to stop an iteration and select the current value - at random?
EDIT: This is a hypothetical question. This is not related to a production coding matter. I am just curious.

Selecting a random element from a collection can be done as follows.
Random r = new Random();
int randomIndex = r.Next(0, myCollection.Size -1);
var randomCollectionItem = myCollection[randomIndex];
Unless you have a VERY good reason, writing your own random generator is not necessary.

My advice to you is DON'T DO IT. Whatever reason you think you may have for not wanting to use the built-in library, I am pretty sure you misunderstood something. Please go back to the drawing board.
All of the advice above is technically accurate, but is kind of like giving a chemistry textbook to someone who wants to refine his own oil to use in his car.

There are many pseudo-random number generators. They aren't truly random, but they come at different quality, distinguished by their statistical and sequential properties and what purpose they are applicable for.
It very much depends on "how random you need it". If it just needs to "look random to a human", simple generators look like that:
rnd = seed; // some starting value
rnd = (a * rnd + b) % c; // next value
...
For well chosen values of a, b, and cthese generators are ok for simple statistical tests. A detailed discussion and common values for these you find here.
One interesting approach is to collect as much "external" data as possible - like time between keypresses, mouse movements, duration of disk reads etc. -, and use an algorithm that accumulates randomness while discarding dependency. That is mathematically tricky though (IIRC not long ago a critical attack surfaced based on one of these not being as random as thought).
Only a very few special applications use a truly random external hardware source - anything between a open-imput amplifier and radioactive decay.

You need to use a seed, something semi random provided by the computer itself.
Maybe use very fine resolution time and use the last couple microseconds when the method is called. That should be random enough to generate anything from 00 to 99, you can then go from there.

It sounds like your problem isn't in calculating a random number, but in how to use that random number to select an item from a list. Assuming you can create a random number somehow, all you need to do is use it as the argument to the list's indexer.
int index = customRandomGenerator.Next();
var selection = items[index];
Assuming that your presupposition about having to iterate through the list is correct (or the collection doesn't have an indexer) then you could do:
int index = customRandomGenerator.Next();
Item selection = null;
for (int i = 0; i < items.Length; i++)
{
if (i == index)
{
selection = items[i];
break;
}
}

The only true "cryptographically strong" random number generator in the .Net Framework is in System.Cryptography.RandomNumberGenerator - run this through Reflector to see what is does? Looking at your problem you would need a to know the Count of the collection otherwise you may never retrieve an item - you would need to specify a start and end value to draw random numbers from - the Random class would work best - pop it through Reflector.

Well, I never thought about implementing that myself as it seems like reinventing the wheel but you may have a look on this wikipedia article, hope it helps you do what you want
Random Number Generator

Optimizing a Recursive Function for Very Large Lists .Net

I have built an application that is used to simulate the number of products that a company can produce in different "modes" per month. This simulation is used to aid in finding the optimal series of modes to run in for a month to best meet the projected sales forecast for the month. This application has been working well, until recently when the plant was modified to run in additional modes. It is now possible to run in 16 modes. For a month with 22 work days this yields 9,364,199,760 possible combinations. This is up from 8 modes in the past that would have yielded a mere 1,560,780 possible combinations. The PC that runs this application is on the old side and cannot handle the number of calculations before an out of memory exception is thrown. In fact the entire application cannot support more than 15 modes because it uses integers to track the number of modes and it exceeds the upper limit for an integer. Baring that issue, I need to do what I can to reduce the memory utilization of the application and optimize this to run as efficiently as possible even if it cannot achieve the stated goal of 16 modes. I was considering writing the data to disk rather than storing the list in memory, but before I take on that overhead, I would like to get people’s opinion on the method to see if there is any room for optimization there.
EDIT
Based on a suggestion by few to consider something more academic then merely calculating every possible answer, listed below is a brief explanation of how the optimal run (combination of modes) is chosen.
Currently the computer determines every possible way that the plant can run for the number of work days that month. For example 3 Modes for a max of 2 work days would result in the combinations (where the number represents the mode chosen) of (1,1), (1,2), (1,3), (2,2), (2,3), (3,3) For each mode a product produces at a different rate of production, for example in mode 1, product x may produce at 50 units per hour where product y produces at 30 units per hour and product z produces at 0 units per hour. Each combination is then multiplied by work hours and production rates. The run that produces numbers that most closely match the forecasted value for each product for the month is chosen. However, because some months the plant does not meet the forecasted value for a product, the algorithm increases the priority of a product for the next month to ensure that at the end of the year the product has met the forecasted value. Since warehouse space is tight, it is important that products not overproduce too much either.
Thank you
private List<List<int>> _modeIterations = new List<List<int>>();
private void CalculateCombinations(int modes, int workDays, string combinationValues)
{
List<int> _tempList = new List<int>();
if (modes == 1)
{
combinationValues += Convert.ToString(workDays);
string[] _combinations = combinationValues.Split(',');
foreach (string _number in _combinations)
{
_tempList.Add(Convert.ToInt32(_number));
}
_modeIterations.Add(_tempList);
}
else
{
for (int i = workDays + 1; --i >= 0; )
{
CalculateCombinations(modes - 1, workDays - i, combinationValues + i + ",");
}
}
}

This kind of optimization problem is difficult but extremely well-studied. You should probably read up in the literature on it rather than trying to re-invent the wheel. The keywords you want to look for are "operations research" and "combinatorial optimization problem".
It is well-known in the study of optimization problems that finding the optimal solution to a problem is almost always computationally infeasible as the problem grows large, as you have discovered for yourself. However, it is frequently the case that finding a solution guaranteed to be within a certain percentage of the optimal solution is feasible. You should probably concentrate on finding approximate solutions. After all, your sales targets are already just educated guesses, therefore finding the optimal solution is already going to be impossible; you haven't got complete information.)
What I would do is start by reading the wikipedia page on the Knapsack Problem:
http://en.wikipedia.org/wiki/Knapsack_problem
This is the problem of "I've got a whole bunch of items of different values and different weights, I can carry 50 pounds in my knapsack, what is the largest possible value I can carry while meeting my weight goal?"
This isn't exactly your problem, but clearly it is related -- you've got a certain amount of "value" to maximize, and a limited number of slots to pack that value into. If you can start to understand how people find near-optimal solutions to the knapsack problem, you can apply that to your specific problem.

You could process the permutation as soon as you have generated it, instead of collecting them all in a list first:
public delegate void Processor(List<int> args);
private void CalculateCombinations(int modes, int workDays, string combinationValues, Processor processor)
{
if (modes == 1)
{
List<int> _tempList = new List<int>();
combinationValues += Convert.ToString(workDays);
string[] _combinations = combinationValues.Split(',');
foreach (string _number in _combinations)
{
_tempList.Add(Convert.ToInt32(_number));
}
processor.Invoke(_tempList);
}
else
{
for (int i = workDays + 1; --i >= 0; )
{
CalculateCombinations(modes - 1, workDays - i, combinationValues + i + ",", processor);
}
}
}
I am assuming here, that your current pattern of work is something along the lines
CalculateCombinations(initial_value_1, initial_value_2, initial_value_3);
foreach( List<int> list in _modeIterations ) {
... process the list ...
}
With the direct-process-approach, this would be
private void ProcessPermutation(List<int> args)
{
... process ...
}
... somewhere else ...
CalculateCombinations(initial_value_1, initial_value_2, initial_value_3, ProcessPermutation);
I would also suggest, that you try to prune the search tree as early as possible; if you can already tell, that certain combinations of the arguments will never yield something, which can be processed, you should catch those already during generation, and avoid the recursion alltogether, if this is possible.
In new versions of C#, generation of the combinations using an iterator (?) function might be usable to retain the original structure of your code. I haven't really used this feature (yield) as of yet, so I cannot comment on it.

The problem lies more in the Brute Force approach that in the code itself. It's possible that brute force might be the only way to approach the problem but I doubt it. Chess, for example, is unresolvable by Brute Force but computers play at it quite well using heuristics to discard the less promising approaches and focusing on good ones. Maybe you should take a similar approach.
On the other hand we need to know how each "mode" is evaluated in order to suggest any heuristics. In your code you're only computing all possible combinations which, anyway, will not scale if the modes go up to 32... even if you store it on disk.

if (modes == 1)
{
List<int> _tempList = new List<int>();
combinationValues += Convert.ToString(workDays);
string[] _combinations = combinationValues.Split(',');
foreach (string _number in _combinations)
{
_tempList.Add(Convert.ToInt32(_number));
}
processor.Invoke(_tempList);
}
Everything in this block of code is executed over and over again, so no line in that code should make use of memory without freeing it. The most obvious place to avoid memory craziness is to write out combinationValues to disk as it is processed (i.e. use a FileStream, not a string). I think that in general, doing string concatenation the way you are doing here is bad, since every concatenation results in memory sadness. At least use a stringbuilder (See back to basics , which discusses the same issue in terms of C). There may be other places with issues, though. The simplest way to figure out why you are getting an out of memory error may be to use a memory profiler (Download Link from download.microsoft.com).
By the way, my tendency with code like this is to have a global List object that is Clear()ed rather than having a temporary one that is created over and over again.

I would replace the List objects with my own class that uses preallocated arrays to hold the ints. I'm not really sure about this right now, but I believe that each integer in a List is boxed, which means much more memory is used than with a simple array of ints.
Edit: On the other hand it seems I am mistaken: Which one is more efficient : List<int> or int[]

How to find what numbers in a set add up to another given number?

Here's a problem that I seem to be running into working with an accounting system.
I have a set of transactions, but their sum does not equal the amount that the accounting department thinks that it should. They are not questioning the math, just the transactions being included :p
Is there an algorithm that would help me determine which transactions in the set should not be included in order for the sum to match a given amount.
Given Set:
2
4
5
7
Given Sum Amount:
13
Result Set:
2
4
7
Edit:
There's less than 100 transactions in the set. Does anyone have a C# example as there is not one on the Solving the NP-complete problem in XKCD question?
Man, I should have gotten a CS degree.

This is the Subset Sum problem, which is NP-Complete. But that doesn't mean there isn't an algorithm for finding a subset sum.

This is the Knapsack Problem and it's NP-Complete. You won't easily solve it exactly with anything except small input sets. For any decent-sized problem set, it's one of those lifetime-of-the-universe-to-solve problems.
That said, there are genetic-algorithm knapsack solvers out there.

As the above members have said, this is the Subset Sum problem (or knapsack problem).
However, to say it cannot be done efficiently is not very precise. It can be done, just not
in polynomial time. THe solution is actually quite simple using dynamic programming
and recursion (and in pseudo-polynomial time).
Given integers [a_1, ... ,a_n] and a number T,
Define the array S[i,k] to denote if there is a subset of elements between
a_1, ... a_i which add up to k. (This is a binary matrix).
We can then define a recursive relationship as follows:
S[i,k] = S[i-1,k] or S[i-1,k-a_j]
In words, this means we either use element a_i or we do not.
The answer will be located at S[n,T].
What is the work load to construct matrix S?
Well, S has n*T elements. To compute each element,
we must do O(1) work. So the complete running
time is O(n*T).
Now at this point, it seems that I have proven P=NP, as this
seems to be a polynomial time algorithm. However, remember
that we measure input size in binary, so T = 2^p for some
p.
I don't think anyone would say that the above solution, when
implemented properly is unreasonable. IN fact, for many
reasonable problem sizes, it will perform admirably.
Also, there are some heuristics for solving this problem, but I am
not an expert in that area.

This is a version of the knapsack problem. It's NP complete, so you're not going to get a good general answer. How big are your sets of transactions? Is it 5 like you showed, or is it more like 500?

OK. Lots of people have given the name of the problem and mentioned how NP hard it is . And in general, they are correct. However, you have a very specific case you need to solve. The first question to ask is whether or not you think your 100 transactions are close to being the right ones. You have some total ("your" total). They have some total. ("real" total). Some of your transactions are therefore bogus. If you suspect that there are only a few bogus transactions in there, then this isn't so bad. For example, let's consider the case where there is only one bogus transaction. In that case, we'd only have to check 100 different numbers. If there are 2 bogus trans, then you're looking at 100*99 checks, and things will get crazy at 4 bogus trans, with almost 100,000,000 steps. though if all you're doing is adding some int's that's not too terrible.
Another possible shortcut is to examine the nature of your data (incidentally, is it possible to post the 100 "numbers" and the expected sum?). How much is your sum over the real sum? Are there any values so big that eliminating them would make your sum suddenly lower than the real sum? If so, you know those values cannot be the bogus ones. For example, in your example, 7 is absolutely required.

bool bBreak = false;
int iEnd = 13;
ArrayList ar1 = new ArrayList();
ar1.Add(2);
ar1.Add(4);
ar1.Add(5);
ar1.Add(7);
String s1 = " ";
foreach (int i in ar1)
{
if (i == iEnd)
{
s1 = "Result = " + i;
bBreak = true;
}
if (bBreak) break;
ArrayList ar2 = new ArrayList();
ar2.AddRange(ar1);
ar2.Remove(i);
foreach (int j in ar2)
{
if ((i + j) == iEnd)
{
s1 = "Results = " + i + ", " + j;
bBreak = true;
}
if (bBreak) break;
ArrayList ar3 = new ArrayList();
ar3.AddRange(ar2);
ar3.Remove(j);
foreach (int k in ar3)
{
if (bBreak) break;
if ((i + j + k) == iEnd)
{
s1 = "Results = " + i + ", " + j + ", " + k;
bBreak = true;
}
}
}
}
Console.WriteLine(s1);

Yes this is possible. Not sure if this post is still opened. But you would want to do the Excel Solver add-in. Post all numbers, with 1s on the adjacent cell. Then put the desired output number.. then all the used numbers, will keep their adjacent "1", while the unused ones will turn to "0". Then do a filter formula that lists only those that have a "1" beside it.