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How to dynamically add indexes values of an array in C#?

I have an array where the first two smallest values have to be added, and consequently the result has to be added to next smallest and so on until it reaches the end of the array to give a final total.
However, how can I dynamically modify the method/function so if the values changes and I have 6 vehicles and 6 specs values in the array, the return of the method/function total is not restricted to just 4 indexes.
The array values are unsorted, so in order to add the first smallest, it has to be sorted. Once that's done it adds the values of the new array.
Here's what I've tried:
public static int vehicles = 4;
public static int[] specs = new int[] { 40, 8, 16, 6 };
public static int time(int vehicles, int[] specs)
{
int newValue = 0;
for (int i = 1; i < vehicles; i++)
{
newValue = specs[i];
int j = i;
while (j > 0 && specs[j - 1] > newValue)
{
specs[j] = specs[j - 1];
j--;
}
specs[j] = newValue;
}
// How can I dynamically change this below:
int result1 = specs[0] + specs[1];
int result2 = result1 + specs[2];
int result3 = result2 + specs[3];
int total = result1 + result2 + result3;
return total; // Returns 114
}
Here's the idea of how it works:
4, [40, 8, 16, 6] = 14 --> [40, 14, 16] = 30 --> [40, 30] = 70 ==>> 14 + 30 + 70 = 114
6, [62, 14, 2, 6, 28, 41 ] = 8 --> [62, 14, 8, 28, 41 ] --> 22 [62, 22, 28, 41 ] --> 50
[62, 50, 41 ] --> 91 [62, 91 ] --> 153 ==> 8 + 22 + 50 + 91 + 153 = 324

First off, if you are not restricted to arrays for some weird reason use List<int> and your life will be easier.
List<int> integers = { 14, 6, 12, 8 };
integers.Sort();
integers.Reverse();
while( integers.Count > 1 )
{
int i = integers[integers.Count - 1];
int j = integers[integers.Count - 2];
integers[integers.Count - 2] = i + j;
integers.RemoveAt(integers.Count - 1);
}
var result = integers[0];
P.S.: This can be easily modified to operate on the array version, you can't RemoveAt() from an array but can separately maintain a lastValidIndex.

I would go with the simplest version of a one line solution using LINQ:
Array.Sort(specs);
int total = specs.Select((n, i) => specs.Take(i + 1).Sum()).Sum() - (specs.Length > 1 ? specs[0] : 0);

I would use Linq.
Enumerable.Range(2, specs.Length - 1)
.Select(i => specs
.Take(i)
.Sum())
.Sum();
Explanation:
We take a range starting from 2 ending with specs.Length.
We sum the first i values of specs where i is the current value in the range.
After we have all those sums, we sum them up as well.
To learn more about linq, start here.
This code only works if the values have been sorted already.
If you want to sort the values using linq, you should use this:
IEnumerable<int> sorted = specs.OrderBy(x => x);
Enumerable.Range(2, sorted.Count() - 1)
.Select(i => sorted
.Take(i)
.Sum())
.Sum();
The OrderBy function needs to know how to get the value it should use to compare the array values. Because the array values are the values we want to compare we can just select them using x => x. This lamba takes the value and returns it again.

See comments in code for explanation.
using System;
using System.Linq;
class Program
{
static void Main()
{
//var inputs = new [] { 40, 8, 16, 6 }; // total = 114
var inputs = new[] { 62, 14, 2, 6, 28, 41 }; // total = 324
var total = 0;
var query = inputs.AsEnumerable();
while (query.Count() > 1)
{
// sort the numbers
var sorted = query.OrderBy(x => x).ToList();
// get sum of the first two smallest numbers
var sumTwoSmallest = sorted.Take(2).Sum();
// count total
total += sumTwoSmallest;
// remove the first two smallest numbers
query = sorted.Skip(2);
// add the sum of the two smallest numbers into the numbers
query = query.Append(sumTwoSmallest);
}
Console.WriteLine($"Total = {total}");
Console.WriteLine("Press any key...");
Console.ReadKey(true);
}
}
I benchmark my code and the result was bad when dealing with large dataset. I suspect it was because of the sorting in the loop. The sorting is needed because I need to find the 2 smallest numbers in each iteration. So I think I need a better way to solve this. I use a PriorityQueue (from visualstudiomagazine.com) because the elements are dequeued based on priority, smaller numbers have higher priority in this case.
long total = 0;
while (pq.Count() > 0)
{
// get two smallest numbers when the priority queue is not empty
int sum = (pq.Count() > 0 ? pq.Dequeue() : 0) + (pq.Count() > 0 ? pq.Dequeue() : 0);
total += sum;
// put the sum of two smallest numbers in the priority queue if the queue is not empty
if (pq.Count() > 0) pq.Enqueue(sum);
}
Here's some benchmark results of the new (priority queue) code and the old code in release build. Results are in milliseconds. I didn't test the 1 million data with the old code because it's too slow.
+---------+----------+-------------+
| Data | New | Old |
+---------+----------+-------------+
| 10000 | 3.9158 | 5125.9231 |
| 50000 | 16.8375 | 147219.4267 |
| 1000000 | 406.8693 | |
+---------+----------+-------------+
Full code:
using System;
using System.Diagnostics;
using System.IO;
using System.Linq;
class Program
{
static void Main()
{
const string fileName = #"numbers.txt";
using (var writer = new StreamWriter(fileName))
{
var random = new Random();
for (var i = 0; i < 10000; i++)
writer.WriteLine(random.Next(100));
writer.Close();
}
var sw = new Stopwatch();
var pq = new PriorityQueue<int>();
var numbers = File.ReadAllLines(fileName);
foreach (var number in numbers)
pq.Enqueue(Convert.ToInt32(number));
long total = 0;
sw.Start();
while (pq.Count() > 0)
{
// get two smallest numbers when the priority queue is not empty
int sum = (pq.Count() > 0 ? pq.Dequeue() : 0) + (pq.Count() > 0 ? pq.Dequeue() : 0);
total += sum;
// put the sum of two smallest numbers in the priority queue if the queue is not empty
if (pq.Count() > 0) pq.Enqueue(sum);
}
sw.Stop();
Console.WriteLine($"Total = {total}");
Console.WriteLine($"Time = {sw.Elapsed.TotalMilliseconds}");
total = 0;
var query = File.ReadAllLines(fileName).Select(x => Convert.ToInt32(x));
sw.Restart();
while (query.Count() > 0)
{
// sort the numbers
var sorted = query.OrderBy(x => x).ToList();
// get sum of the first two smallest numbers
var sumTwoSmallest = sorted.Take(2).Sum();
// count total
total += sumTwoSmallest;
// remove the first two smallest numbers
query = sorted.Skip(2);
// add the sum of the two smallest numbers into the numbers
if (query.Count() > 0)
query = query.Append(sumTwoSmallest);
}
sw.Stop();
Console.WriteLine($"Total = {total}");
Console.WriteLine($"Time = {sw.Elapsed.TotalMilliseconds}");
Console.WriteLine("Press any key...");
Console.ReadKey(true);
}
}
PriorityQueue code:
using System;
using System.Collections.Generic;
// From http://visualstudiomagazine.com/articles/2012/11/01/priority-queues-with-c.aspx
public class PriorityQueue<T> where T : IComparable<T>
{
private List<T> data;
public PriorityQueue()
{
this.data = new List<T>();
}
public void Enqueue(T item)
{
data.Add(item);
int ci = data.Count - 1; // child index; start at end
while (ci > 0)
{
int pi = (ci - 1) / 2; // parent index
if (data[ci].CompareTo(data[pi]) >= 0)
break; // child item is larger than (or equal) parent so we're done
T tmp = data[ci];
data[ci] = data[pi];
data[pi] = tmp;
ci = pi;
}
}
public T Dequeue()
{
// assumes pq is not empty; up to calling code
int li = data.Count - 1; // last index (before removal)
T frontItem = data[0]; // fetch the front
data[0] = data[li];
data.RemoveAt(li);
--li; // last index (after removal)
int pi = 0; // parent index. start at front of pq
while (true)
{
int ci = pi * 2 + 1; // left child index of parent
if (ci > li)
break; // no children so done
int rc = ci + 1; // right child
if (rc <= li && data[rc].CompareTo(data[ci]) < 0) // if there is a rc (ci + 1), and it is smaller than left child, use the rc instead
ci = rc;
if (data[pi].CompareTo(data[ci]) <= 0)
break; // parent is smaller than (or equal to) smallest child so done
T tmp = data[pi];
data[pi] = data[ci];
data[ci] = tmp; // swap parent and child
pi = ci;
}
return frontItem;
}
public T Peek()
{
T frontItem = data[0];
return frontItem;
}
public int Count()
{
return data.Count;
}
public override string ToString()
{
string s = "";
for (int i = 0; i < data.Count; ++i)
s += data[i].ToString() + " ";
s += "count = " + data.Count;
return s;
}
public bool IsConsistent()
{
// is the heap property true for all data?
if (data.Count == 0)
return true;
int li = data.Count - 1; // last index
for (int pi = 0; pi < data.Count; ++pi)
{ // each parent index
int lci = 2 * pi + 1; // left child index
int rci = 2 * pi + 2; // right child index
if (lci <= li && data[pi].CompareTo(data[lci]) > 0)
return false; // if lc exists and it's greater than parent then bad.
if (rci <= li && data[pi].CompareTo(data[rci]) > 0)
return false; // check the right child too.
}
return true; // passed all checks
}
// IsConsistent
}
// PriorityQueue
Reference:
https://visualstudiomagazine.com/articles/2012/11/01/priority-queues-with-c.aspx
https://en.wikipedia.org/wiki/Priority_queue

You can simply sort it using Array.Sort(), then get the sums in a new array which starts with the smallest value and add each next value to the most recent sum, the total will be the value of the last sum.
public static int time(int vehicles, int[] specs)
{
int i, total;
int[] sums = new int[vehicles];
Array.Sort(spec);
sums[0] = specs[0];
for (i = 1; i < vehicles; i++)
sums[i] = sums[i - 1] + spec[i];
total = sums[spec - 1];
}

How to distribute items evenly, without random numbers

I have a situation where I need to evenly distribute N items across M slots. Each item has its own distribution %. For discussion purposes say there are three items (a,b,c) with respective percentages of (50,25,25) to be distributed evenly across 20 slots. Hence 10 X a,5 X b & 5 X c need to be distributed. The outcome would be as follows:
1. a
2. a
3. c
4. b
5. a
6. a
7. c
8. b
9. a
10. a
11. c
12. b
13. a
14. a
15. c
16. b
17. a
18. a
19. c
20. b
The part that I am struggling with is that the number of slots, number of items and percentages can all vary, of course the percentage would always total up to 100%. The code that I wrote resulted in following output, which is always back weighted in favour of item with highest percentage. Any ideas would be great.
1. a
2. b
3. c
4. a
5. b
6. c
7. a
8. b
9. c
10. a
11. c
12. b
13. a
14. b
15. c
16. a
17. a
18. a
19. a
20. a
Edit
This is what my code currently looks like. Results in back weighted distribution as I mentioned earlier. For a little context, I am trying to evenly assign commercials across programs. Hence every run with same inputs has to result in exactly the same output. This is what rules out the use of random numbers.
foreach (ListRecord spl in lstRecords){
string key = spl.AdvertiserName + spl.ContractNumber + spl.AgencyAssignmentCode;
if (!dictCodesheets.ContainsKey(key)){
int maxAssignmentForCurrentContract = weeklyList.Count(c => (c.AdvertiserName == spl.AdvertiserName) && (c.AgencyAssignmentCode == spl.AgencyAssignmentCode)
&& (c.ContractNumber == spl.ContractNumber) && (c.WeekOf == spl.WeekOf));
int tmpAssignmentCount = 0;
for (int i = 0; i < tmpLstGridData.Count; i++)
{
GridData gData = tmpLstGridData[i];
RotationCalculation commIDRotationCalc = new RotationCalculation();
commIDRotationCalc.commercialID = gData.commercialID;
commIDRotationCalc.maxAllowed = (int)Math.Round(((double)(maxAssignmentForCurrentContract * gData.rotationPercentage) / 100), MidpointRounding.AwayFromZero);
tmpAssignmentCount += commIDRotationCalc.maxAllowed;
if (tmpAssignmentCount > maxAssignmentForCurrentContract)
{
commIDRotationCalc.maxAllowed -= 1;
}
if (i == 0)
{
commIDRotationCalc.maxAllowed -= 1;
gridData = gData;
}
commIDRotationCalc.frequency = (int)Math.Round((double)(100/gData.rotationPercentage));
if (i == 1)
{
commIDRotationCalc.isNextToBeAssigned = true;
}
lstCommIDRotCalc.Add(commIDRotationCalc);
}
dictCodesheets.Add(key, lstCommIDRotCalc);
}else{
List<RotationCalculation> lstRotCalc = dictCodesheets[key];
for (int i = 0; i < lstRotCalc.Count; i++)
{
if (lstRotCalc[i].isNextToBeAssigned)
{
gridData = tmpLstGridData.Where(c => c.commercialID == lstRotCalc[i].commercialID).FirstOrDefault();
lstRotCalc[i].maxAllowed -= 1;
if (lstRotCalc.Count != 1)
{
if (i == lstRotCalc.Count - 1 && lstRotCalc[0].maxAllowed > 0)
{
//Debug.Print("In IF");
lstRotCalc[0].isNextToBeAssigned = true;
lstRotCalc[i].isNextToBeAssigned = false;
if (lstRotCalc[i].maxAllowed == 0)
{
lstRotCalc.RemoveAt(i);
}
break;
}
else
{
if (lstRotCalc[i + 1].maxAllowed > 0)
{
//Debug.Print("In ELSE");
lstRotCalc[i + 1].isNextToBeAssigned = true;
lstRotCalc[i].isNextToBeAssigned = false;
if (lstRotCalc[i].maxAllowed == 0)
{
lstRotCalc.RemoveAt(i);
}
break;
}
}
}
}
}
}
}
Edit 2
Trying to clear up my requirement here. Currently, because item 'a' is to be assigned 10 times which is the highest among all three items, towards the end of distribution, items 16 - 20 all have been assigned only 'a'. As has been asked in comments, I am trying to achieve a distribution that "looks" more even.

One way to look at this problem is as a multi-dimensional line drawing problem. So I used Bresenham's line algorithm to create the distribution:
public static IEnumerable<T> GetDistribution<T>( IEnumerable<Tuple<T, int>> itemCounts )
{
var groupCounts = itemCounts.GroupBy( pair => pair.Item1 )
.Select( g => new { Item = g.Key, Count = g.Sum( pair => pair.Item2 ) } )
.OrderByDescending( g => g.Count )
.ToList();
int maxCount = groupCounts[0].Count;
var errorValues = new int[groupCounts.Count];
for( int i = 1; i < errorValues.Length; ++i )
{
var item = groupCounts[i];
errorValues[i] = 2 * groupCounts[i].Count - maxCount;
}
for( int i = 0; i < maxCount; ++i )
{
yield return groupCounts[0].Item;
for( int j = 1; j < errorValues.Length; ++j )
{
if( errorValues[j] > 0 )
{
yield return groupCounts[j].Item;
errorValues[j] -= 2 * maxCount;
}
errorValues[j] += 2 * groupCounts[j].Count;
}
}
}
The input is the actual number of each item you want. This has a couple advantages. First it can use integer arithmetic, which avoids any rounding issues. Also it gets rid of any ambiguity if you ask for 10 items and want 3 items evenly distributed (which is basically just the rounding issue again).

Here's one with no random number that gives the required output.
using System;
using System.Collections.Generic;
public class Program
{
public static void Main()
{
// name, percentage
Dictionary<string, double> distribution = new Dictionary<string,double>();
// name, amount if one more were to be distributed
Dictionary<string, int> dishedOut = new Dictionary<string, int>();
//Initialize
int numToGive = 20;
distribution.Add("a", 0.50);
distribution.Add("b", 0.25);
distribution.Add("c", 0.25);
foreach (string name in distribution.Keys)
dishedOut.Add(name, 1);
for (int i = 0; i < numToGive; i++)
{
//find the type with the lowest weighted distribution
string nextUp = null;
double lowestRatio = double.MaxValue;
foreach (string name in distribution.Keys)
if (dishedOut[name] / distribution[name] < lowestRatio)
{
lowestRatio = dishedOut[name] / distribution[name];
nextUp = name;
}
//distribute it
dishedOut[nextUp] += 1;
Console.WriteLine(nextUp);
}
Console.ReadLine();
}
}

Instead of a truly random number generator, use a fixed seed, so that the program has the same output every time you run it (for the same input). In the code below, the '0' is the seed, which means the 'random' numbers generated will always be the same each time the program is run.
Random r = new Random(0);

//AABC AABC…
int totalA = 10
int totalB = 5
int totalC = 5
int totalItems = 20 //A+B+C
double frequencyA = totalA / totalItems; //0.5
double frequencyB = totalB / totalItems; //0.25
double frequencyC = totalC / totalItems; //0.25
double filledA = frequencyA;
double filledB = frequencyB;
double filledC = frequencyC;
string output = String.Empty;
while(output.Length < totalItems)
{
filledA += frequencyA;
filledB += frequencyB;
filledC += frequencyC;
if(filledA >= 1)
{
filledA -= 1;
output += "A";
if(output.Length == totalItems){break;}
}
if(filledB >= 1)
{
filledB -= 1
output += "B";
if(output.Length == totalItems){break;}
}
if(filledC >= 1)
{
filledC -= 1
output += "C";
if(output.Length == totalItems){break;}
}
}

This answer was mostly stolen and lightly adapted for your use from here
My idea is that you distribute your items in the simplest way possible without care of order, then shuffle the list.
public static void ShuffleTheSameWay<T>(this IList<T> list)
{
Random rng = new Random(0);
int n = list.Count;
while (n > 1) {
n--;
int k = rng.Next(n + 1);
T value = list[k];
list[k] = list[n];
list[n] = value;
}
}
Fiddle here

I have a list with 13 numbers and i want to multiply them together

I have a string numbers which contains 13 digits, e.g.:
string numbers = "01234567890123456781";
and I have to multiply them:
0 * 1 * 2 * 3 * ... * 7 * 8 * 1
I've a got a solution for adding the digits together:
0 + 1 + 2 + 3 + ... + 7 + 8 + 1
I convert number string to List<int> numb and then sum items of the list with a help of Linq Sum() method:
string numbers = "01234567890123456781";
List<int> numb = new List<int>();
for (int i = 0; i < numbers.Length; i++)
{
int num = int.Parse(numbers[i].ToString());
numb.Add(num);
}
for (int b = 0; b <numb.Count()-12; b++)
{
var x = numb.Skip(b).Take(13);
int a = x.Sum(); // <- it's easy to sum, but what shall I do to multiply?
Console.WriteLine(a);
}
However, Linq doesn't have any Mult() or alike method, so what can I do to multiply the items together?

Providing that the numbers contains digits [0..9] only, a simple Linq will do:
// since 0 * anything == 0, I've removed all 0's to obtain non-zero result:
// 1 * 2 * 3 * ... * 7 * 8 * 1
string numbers = "123456789123456781";
// long: int is not large enough
long result = numbers
.Select(c => (long) (c - '0'))
.Aggregate((s, a) => s * a);
Outcome:
// 14631321600
Console.Write(result);
Aggregate (custom aggregation) will do if you want to change IEnumerable<T>.Sum() from summation (as in your current code) to multiplication:
...
var x = numb.Skip(b).Take(13); //TODO: get rid of magic number 13
// instead of summation
// int a = x.Sum();
// let's use multiplication as a custom aggregation:
// please, mind overflow: int is not enough when multiplying items
long a = x
.Select(item => (long) item)
.Aggregate((s, item) => s * item);

Pick a varying number of item combinations from a List

Assume I have a list of integers of any length, for an example I have the list of 1,3,5 and 7.
I would like an algorithm to pick a combination of X elements from the list.
For example, X = 1 would return:
1
3
5
7
x = 2 would return:
1 + 1
1 + 3
1 + 5
1 + 7
3 + 3
3 + 5
3 + 7
5 + 5
5 + 7
7 + 7
var listOfInts = new List<int> { 1, 3, 5, 7 };
var combinedInts = new List<int>();
// x = 1 solution
// This is only picking one item from the list.
for (int i = 0; i < listOfInts.Count(); i++)
{
combinedInts.Add(listOfInts[i]);
}
// x = 2 solution
// This is how to pick two. I wrap it around another for loop.
for (int i = 0; i < listOfInts.Count(); i++)
{
for (int j = i; j < listOfInts.Count(); j++)
{
combinedInts.Add(listOfInts[i] + listOfInts[j]);
}
}
// x = 3 solution
// If I go up another level I have to wrap it around another for loop. This solution won't scale.
for (int i = 0; i < listOfInts.Count(); i++)
{
for (int j = i; j < listOfInts.Count(); j++)
{
for (int k = j; k < listOfInts.Count(); k++)
{
combinedInts.Add(listOfInts[i] + listOfInts[j] + listOfInts[k]);
}
}
}
This solution doesn't scale as I have to continually wrap around another for loop for each number of element I'm picking. For example X = 7 would need 7-nested for loops. Is there a better way to write this method that doesn't involve nesting for loops?

You can use the following to get combinations of the sequences:
public static class LinqHelper
{
public static IEnumerable<IEnumerable<T>> Combinations<T>(this IEnumerable<T> elements, int? k = null)
{
if (!k.HasValue)
k = elements.Count();
return k == 0 ? new[] { new T[0] } :
elements.SelectMany((e, i) => elements.Skip(i).Combinations(k - 1).Select(c => (new[] { e }).Concat(c)));
}
}
var list = new List<int> { 1, 3, 5, 7 };
int x = 2; //Change to 3, 4, 5, etc
var result = list.Combinations(x);
Yields:
1 1
1 3
1 5
1 7
3 3
3 5
3 7
5 7
7 7
To get the sum of each one, you'd aggregate the result:
var result = list.Combinations(x).Select(g => g.Aggregate((left, right) => left + right));
Which produces:
2
4
6
8
6
8
10
10
12
14

There is also a purely iterative way to do this. It requires a great deal more thought and complexity, but can be made very efficient. The basic idea is to simulate the same nested loops, but track the iterations of each nested loop as an array of loop counters, which are iterated forward in the same manner as the original nested loop code. Here is a fully working example:
var listOfInts = new List<int> { 1, 3, 5, 7 };
var combinedInts = new List<int>();
var numInts = listOfInts.Count;
var numElements = 5; // number of "nested loops", or ints selected in each combination
var loopCounters = new int[numElements]; // make one loop counter for each "nested loop"
var lastCounter = numElements - 1; // iterate the right-most counter by default
// maintain current sum in a variable for efficiency, since most of the time
// it is changing only by the value of one loop counter change.
var tempSum = listOfInts[0] * numElements;
// we are finished when the left/outer-most counter has looped past number of ints
while (loopCounters[0] < numInts) {
// you can use this to verify the output is iterating correctly:
// Console.WriteLine(string.Join(",", loopCounters.Select(x => listOfInts[x])) + ": " + loopCounters.Select(x => listOfInts[x]).Sum() + "; " + tempSum);
combinedInts.Add(tempSum);
tempSum -= listOfInts[loopCounters[lastCounter]];
loopCounters[lastCounter]++;
if (loopCounters[lastCounter] < numInts) tempSum += listOfInts[loopCounters[lastCounter]];
// if last element reached in inner-most counter, increment previous counter(s).
while (lastCounter > 0 && loopCounters[lastCounter] == numInts) {
lastCounter--;
tempSum -= listOfInts[loopCounters[lastCounter]];
loopCounters[lastCounter]++;
if (loopCounters[lastCounter] < numInts) tempSum += listOfInts[loopCounters[lastCounter]];
}
// if a previous counter was advanced, reset all future counters to same
// starting number to start iteration forward again.
while (lastCounter < numElements - 1) {
lastCounter++;
if (loopCounters[lastCounter] < numInts) tempSum -= listOfInts[loopCounters[lastCounter]];
loopCounters[lastCounter] = loopCounters[lastCounter - 1];
if (loopCounters[lastCounter] < numInts) tempSum += listOfInts[loopCounters[lastCounter]];
}
}
At the end of the iteration, combinedInts should contains a list of all sum combinations, similar to the original code or the other recursive solutions. If you are working with small sets, and small combinations, then this level of efficiency is unnecessary and you should prefer a recursive solution which is easier to reason about correctness. I present this as an alternative way to think about the problem. Cheers!

This works for me:
Func<IEnumerable<int>, int, IEnumerable<IEnumerable<int>>> generate = null;
generate = (xs, n) =>
(xs == null || !xs.Any())
? Enumerable.Empty<IEnumerable<int>>()
: n == 1
? xs.Select(x => new [] { x })
: xs.SelectMany(x => generate(xs, n - 1).Select(ys => ys.Concat(new [] { x })));
int[] array = { 1, 3, 5, 7, };
var results =
generate(array, 3)
.Select(xs => String.Join("+", xs));
With this call I get:
1+1+1, 3+1+1, 5+1+1, 7+1+1, 1+3+1, 3+3+1, 5+3+1, 7+3+1, 1+5+1, 3+5+1, 5+5+1, 7+5+1, 1+7+1, 3+7+1, 5+7+1, 7+7+1, 1+1+3, 3+1+3, 5+1+3, 7+1+3, 1+3+3, 3+3+3, 5+3+3, 7+3+3, 1+5+3, 3+5+3, 5+5+3, 7+5+3, 1+7+3, 3+7+3, 5+7+3, 7+7+3, 1+1+5, 3+1+5, 5+1+5, 7+1+5, 1+3+5, 3+3+5, 5+3+5, 7+3+5, 1+5+5, 3+5+5, 5+5+5, 7+5+5, 1+7+5, 3+7+5, 5+7+5, 7+7+5, 1+1+7, 3+1+7, 5+1+7, 7+1+7, 1+3+7, 3+3+7, 5+3+7, 7+3+7, 1+5+7, 3+5+7, 5+5+7, 7+5+7, 1+7+7, 3+7+7, 5+7+7,7+7+7

Create a list of sequential numbers excluding one number

Requirements:
Create a list of n sequential numbers starting at a.
Exclude number x.
This is the best I have right now, the problem being that it creates n + 1 numbers if x is not within the range.
var numbers = Enumerable
.Range(a, numberOfDataRowsToAdd + 1)
.Where(i => i != TechnicalHeaderRowIndex);
Example 1 should produce 0,1,2,3,4,5,6,7,8,9.
var a = 0;
var n = 10;
var x = 11;
Example 2 should produce 0,1,2,3,4,5,7,8,9,10.
var a = 0;
var n = 10;
var x = 6;
Here is a Fiddle that demonstrates Mark's answer.

How about
Enumerable.Range(a, n + 1)
.Where(i => i != x)
.Take(n);

My example, how it can be done without LINQ and extra loop iterations:
public static IEnumerable<int> GenerateNumbers(int a, int n, int x)
{
for (var i = 0; i < n; i++)
{
if (a == x)
{
i--;
a++;
continue;
}
yield return a++;
}
}
But if you don't want create new method for this purpose, Mark Sowul or Jakub Lortz answers are better.

The problem can be described as
Get n + 1 sequential numbers starting from a
If x is in the range, remove x, otherwise remove the maximum number from the list
Translated to C#
int numberToExclude = Math.Min(n + a, x);
var numbers = Enumerable.Range(a, n + 1).Where(i => i != numberToExclude);

It makes sense to generate only necessary values instead of generating n + 1 values and then remove x:
Enumerable.Range(a, n).Select(i => i < x ? i : i + 1);
Example 1: 0,1,2,3,4,5,6,7,8,9.
Example 2: 0,1,2,3,4,5,7,8,9,10.

You can drop the last if your enumerable count is bigger than numberOfDataRowsToAdd
Extension method:
public static IEnumerable<T> DropLast<T>(this IEnumerable<T> enumerable)
{
return enumerable.Take(enumerable.Count()-1);
}
Usage:
var numbers = Enumerable
.Range(a, numberOfDataRowsToAdd + 1)
.Where(i => i != TechnicalHeaderRowIndex);
if(numbers.Count() > numberOfDataRowsToAdd)
numbers = numbers.DropLast();

I don't see what really is the challenge - Linq shortest or fastest or just working. How about the natural (which should also be the fastest Linq based)
var numbers = a <= x && x < a + n ?
Enumerable.Range(a, x - a).Concat(Enumerable.Range(x + 1, a - x + n)) :
Enumarble.Range(a, n);