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Calculate 2^(n) where 0<n<10000

So, this is my problem to solve:
I want to calculate 2^(n) where 0 < n< 10000
I am representing each element of array as a space where 4digit number should be "living" and if extra digit appears, I am replacing it to the next element of this array.
The principle I am using looks like this:
The code I am using is the following:
static string NotEfficient(int power)
{
if (power < 0)
throw new Exception("Power shouldn't be negative");
if (power == 0)
return "1";
if (power == 1)
return "2";
int[] A = new int[3750];
int current4Digit = 0;
//at first 2 is written in first element of array
A[current4Digit] = 2;
int currentPower = 1;
while (currentPower < power)
{
//multiply every 4digit by 2
for (int i = 0; i <= current4Digit; i++)
{
A[i] *= 2;
}
currentPower++;
//checking every 4digit if it
//contains 5 digit and if yes remove and
//put it in next 4digit
for (int i = 0; i <= current4Digit; i++)
{
if (A[i] / 10000 > 0)
{
int more = A[i] / 10000;
A[i] = A[i] % 10000;
A[i + 1] += more;
//if new digit should be opened
if (i + 1 > current4Digit)
{
current4Digit++;
}
}
}
}
//getting data from array to generate answer
string answer = "";
for (int i = current4Digit; i >= 0; i--)
{
answer += A[i].ToString() + ",";
}
return answer;
}
The problem I have is that it doesn't display correctly the number, which contains 0 in reality. for example 2 ^ (50) = 1 125 899 906 842 624 and with my algorithm I get 1 125 899 96 842 624 (0 is missing). This isn't only for 50...
This happens when I have the following situation for example:
How I can make this algorithm better?

Use BigInteger, which is already included in .Net Core or available in the System.Runtime.Numerics Nuget Package.
static string Efficient(int power)
{
var result = BigInteger.Pow(2, power);
return result.ToString(CultureInfo.InvariantCulture);
}
On my machine, NotEfficient takes roughly 80ms, where Efficient takes 0.3ms. You should be able to manipulate that string (if I'm understanding your problem statement correctly):
static string InsertCommas(string value)
{
var sb = new StringBuilder(value);
for (var i = value.Length - 4; i > 0; i -= 4)
{
sb.Insert(i, ',');
}
return sb.ToString();
}

One way to resolve this is to pad your 4-digit numbers with leading zeroes if they are less than four digits by using the PadLeft method:
answer += A[i].ToString().PadLeft(4, '0') + ",";
And then you can use the TrimStart method to remove any leading zeros from the final result:
return answer.TrimStart('0');

Efficient way to count the number of appearances of a digit in a number

I need to count the number of times a single digit (not 0) appears in a number (positive integer) of varying length.
The obvious solution is to convert the number to a string, the digit to a character and iterate over the string to count the number of times the character appears in the string.
static int CountDigitInString(string searchString, char digit)
{
int sum = 0;
for (int i = 0; i < searchString.Length; i++)
{
if (searchString[i] == digit)
sum++;
}
return sum;
}
The problem with this method, however, is that it is too slow for my purposes as I am running it many times.
public static void Run()
{
for (int i = 0; i < 1000000; i++)
{
CountDigitInString(i.ToString(), (char)j);
}
}
After I noted that the process took too much time, the CPU sampling profiler showed me that the problem was with the conversion to string.
So, how do I efficiently count the number of times a digit (single digit only, not a number) appears in a number (of any length)?

Here is more optimized version of #shaitibber solution. It replaces one division with multiplying and returns 1 for 0,0. It is about 20% faster.
static int CountDigitsInString2(int number, int digit)
{
int sum = 0;
do
{
int n2 = number / 10;
if (number - n2 * 10 == digit)
sum++;
number = n2;
} while (number != 0);
return sum;
}
And here is solution about three times faster than that (but does not work for 0 digit, which is not required). It precalculates results for numbers 0..9999.
private static int[][] cache = new int[10][];
private const int cacheSize = 10000;//or 100000
private static int[] initCache(int digit)
{
var ca = cache[digit] = new int[cacheSize];
for (int i = 0; i < ca.Length; ++i)
{
ca[i] = CountDigitsInString2(i, digit);
}
return ca;
}
static int CountDigitsInString3(int number, int digit)
{
var ca = cache[digit] ?? initCache(digit);
int sum = 0;
while (number != 0)
{
int n2 = number / cacheSize;
sum += ca[number - n2 * cacheSize];
number = n2;
};
return sum;
}

I found a way which turned out to be about 3 times as fast on average (checked using a Stopwatch):
static int CountDigitsInString(int number, int digit)
{
int sum = 0;
while (number != 0)
{
if (number % 10 == digit)
sum++;
number /= 10;
}
return sum;
}
EDIT:
I found a way which is over 4 times as fast as the one above. Before I start, note that this solution is valid only for cases in which you are counting appearances of a digit in consecutive numbers.
It occurred to me that if you counted the number of times the digit "d" appeared in a number "A", then you don't neccessarily have to recount the number of times "d" appears in "A + 1" to know what it is.
For example, if I know that the digit 3 appears 4 times in the number 35312336, I can know for a fact that it will still appear 4 times in the next consecutive number 35312337, without actually counting.
The reason I can do this is that the count would only change in one of three cases:
1) When the last digit of "A - 1" was a 9, "A" can change entirely due to numbers being carried over. This is the only case in which we actually have to count (although you could, theoretically, optimize this further by checking the numbers carried over to see if they affect the total but this strikes me as overly complicated).
2) When the last digit of "A - 1" was "d - 1", we know that the number of times "d" appears in "A" has increased by one.
3) When the last digit of "A - 1" was "d", we know that the number of times "d" appears in "A" has decreased by one.
This means that you only have to count the appearances of "d" in "A" using arithmetical operations in one out of 10 cases!
public static void Run()
{
int digit = 1;
int count = 0;
for (int i = 0; i < 100000; i++)
{
int previousLastDigit = (i - 1) % 10;
if (previousLastDigit == (digit - 1))
count++;
else if (previousLastDigit == 9)
count = CountDigitsInString(i, digit);
else if (previousLastDigit == digit)
count--;
Console.WriteLine(digit + " appears " + count + " times in the number " + i);
}
}
The CountDigitsInString function is the one above.

Here is a little snip with LINQ to give you another way to do it (didn't ran a stopwatch)
var number = 11334511;
var digit = 1;
var digitAsChar = Convert.ToChar(digit.ToString().ToLower());
// Occurence will be 4
var occurence = number.ToString().ToLower().Count(s => s == digitAsChar);

I suggest you use LINQ on string.
Source: https://msdn.microsoft.com/en-us/library/mt693025.aspx
static int CountDigitInString(string number, char digit)
{
int count = number.Count(ns => ns == digit);
return count;
}

Solving modulo equations programmatically

My goal is to implement a (simple) check digit alglorithm as described Here
My implemantion is the following but I am not sure if it is optimal:
private int CheckDigit(string SevenDecimal)
{
///Get UPC check digit of a 7-digit URI
///Add odd and multiply by 3 =Odds
///Add even =Evens
///Add Odds+Evens=sum
///Check digit is the number that makes Sum divisble by 10
int Odds = 0;
int Evens = 0;
int sum = 0;
int index = 0;
foreach (char digit in SevenDecimal)
{
index++;
int Digit = int.Parse(digit.ToString());
if (index % 2 == 0)
{
Evens +=Digit;
}
else
{
Odds +=Digit;
}
}
Odds = Odds * 3;
sum = Odds + Evens;
for (int i = 0; i < 10; i++) ///Brute force way check for better implementation
{
int Localsum;
Localsum = sum + i;
if (Localsum % 10 == 0)
{
return i;
}
}
return -1;//error;
}
My main concern is in the final for loop which as I describe is totallly brute.
Is there a better way to obtaining the check digit?
More precisely which is the best way to solve programmatically, the equation:
(sum+x)%10=0 //solve for x

To find "how much i you have to add to make the last digit of a number a 0", you can subtract from 10:
int checkDigit = (10 - (sum % 10)) % 10;
The second modulo is used for the special case when sum % 10 == 0, because 10 - 0 = 10

You are asking the wrong question. The expression is not one of equivalence thus x is not a value. The solution is that x is an infinite number of values each of which correctly solve the equation. As such you don't really want to solve for x but just check if x is in this solution space. You can check this simply with:
remainder = base - (sum % base)
You can then test if x sums up to the remainder with:
if (x % base === base - (sum % base))
{
// (sum + x) % base = 0 is true
}
Replace base with 10and you'll have it.

What number is a specified digit and how many of them are there in a number?

Ok, so at first, I'm very beginner in programming. It's my school homework and I cannot use conversion to string. Just if,else,for,while.
On input there is the number and the digit.
I know how to get information what number is a specified digit in a number but I have no idea how to find out how many of these numbers are there.
Let's say I have number 123 467 (it has to be less than 999 999) and I want the third number. I know it's bigger than 100 000, so I do the math - (int) 123 467 / 100 = 123 and then 123%10 = 3. Now I need to know if there are any more 3's in the number - but here is the point - I'm not sure what cycle should I use.
And I also have to create some code which determines how large is the number (bigger than 100/1000/10000/...).
I'm not asking for a full solution but little help would be appreciated. Even in a pseudolanguage.
Current code (almost nothing):
double digit, number;
try
{
digit = Convert.ToInt32(poledigit.Text);
number = Convert.ToInt32(polenumber.Text);
}
catch
{
MessageBox.Show("Zadejte číslo ve správném formátu");
return;
}
if (digit > 6 & number > 999999)
{
MessageBox.Show("Číslo musí být menší než 999 999 a digit musí být menší než 6.");
return;
}
while(number >= 100000)
{
number /= Math.Pow(10, digit);
number %= 10;
}

I would create an int array counting the number of digits
int[] digitCount = new int[10]; // Range: digitCount[0..9]
Then determine the digits one by one by eliminating the last one, until the number is zero. The loop would repeat the following code:
int digit = number % 10;
number /= 10;
digitCount[digit]++;
Now digitCount contains the count of each digit
int countOfDigit3 = digitCount[3];
If you cannot use arrays, count only the occurences of the desired digit
int digit = ...;
int digitCount = 0;
while (number != 0) {
int d = number % 10;
number /= 10;
if (d == digit) {
digitCount++;
}
}

You can iterate through the digits as follows:
int digitToSearch = 3;
int count = 0;
while (number != 0)
{
int digit = number % 10;
if (digit == digitToSearch)
count++;
number /= 10;
}

Get the seventh digit from an integer

I have a integer of 10 digits. I need to get the 7th digit of that integer.
I have found a mathematical solution to get the first digit of an integer.
var myDigit = 2345346792;
var firstDigit = Math.Abs(myDigit);
while (firstDigit >= 10)
{
firstDigit /= 10;
}
How can I get the seventh digit from myDigit? I am trying to avoid casting to string and doing a substring. I would like to see the mathemathical version of getting the seventh digit.
Anyone?

var seventh_digit = ( myDigit/1000000 ) % 10;

int getSeventhDigit(int number)
{
while(number >= 10000000)
number /= 10;
return number % 10;
}
This will take the last digit of numbers with 7 or less digits.
For numbers with 8 or more digits, it will divide by 10 until the number is 7 digits long, then take the last digit.

Mathematical solution without while loops:
int myDigit = 2345346792;
var seventh = (myDigit / 1000000) % 10;
//result should be 5, your seventh digit from the right

More generally, you can create a (zero-based) array from the digits:
uint myDigit = 2345346792;
int[] digits = new int[10];
for (int i = 9; i >= 0; i--)
{
digits[i] = (int)(myDigit % 10);
myDigit /= 10;
}
That should be useful for whatever manipulation you wish to do.

var nthDigit = (int)((number / Math.Pow(10, nth - 1)) % 10);
Where nth is n-th digit of the number.

Assuming that the "zeroth digit" is the least significant digit, this should do you:
public static int nthDigit( int value , int n )
{
if ( n < 0 ) throw new ArgumentException();
if ( value < 0 ) throw new ArgumentException() ;
while ( n-- > 0 )
{
value /= 10 ;
}
int digit = value % 10 ;
return digit ;
}

Something like this (C code, but should be readily portable):
if (n < 1000000)
return 0; // no 7th digit
while (n > 9999999)
n /= 10; // now in the range [1,000,000..9,999,999]
return n % 10;

This may seem outdated, but I wanted to get specific digits from a string of numbers and most of these solutions (and others I found) were lacking. So...I decided a workaround and converted the number to a string and then pulled the characters of the string, converting them back to an int. I know this isn't very efficient, but for small projects I don't concern myself with efficiency.
For my task, I was specifically working with phone numbers, so here is my code:
long number = 5559876543;
string s = "" + number;
int areaCode = int.Parse(s.Substring(0, 3));
int prefix = int.Parse(s.Substring(3, 3));
int suffix = int.Parse(s.Substring(6, 4));
I hope this helps anyone looking for a similar solution.

public static int GetNthDigit(this int value, int digits)
{
double mult = Math.Pow(10.0, digits);
if (value >= mult)
{
while(value >= mult)
value /= 10;
return value % 10;
}
else
{
throw new ArgumentOutOfRangeException("Digits greater than value");
}
}