XP Service Pack 3, where is my console login!?!?!

I recently upgraded to XP Service Pack 3 today and found that I could not remote into my Windows 2003 Console login with my normal command line.  A quick google search led me to this blog post that describes the change.  Could it have been so hard to support both switches?

In short:

mstsc /console is now mstsc /admin

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Project Euler – Problem 10

Calculate the sum of all the primes below two million.

Problem:
The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.

Find the sum of all the primes below two million.

My Solution:
Uses my IsPrime function from other problems

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace Euler
{
    class Problem10 : IProblemBase
    {

        //he sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.

        //Find the sum of all the primes below two million.

        //Note: result is long, if you use int, you will get the wrong result
        //ask me how I know...lol

        public Problem10()
        {
        }   

        public string GetAnswer()
        {
            long result = 0;
            long limit = 2000000;

            for (int i = 2; i < limit; i++)//two is the first prime
            {
                if (Util.isPrime(i))
                {
                    result = result + i;

                }

            }

            return result.ToString();

        }
    }
}

Project Euler – Problem 3

Find the largest prime factor of a composite number.

Problem:
The prime factors of 13195 are 5, 7, 13 and 29.

What is the largest prime factor of the number 600851475143 ?

My Solution:
This one was a pain in the ass.  I had to do a lot of reading on this one.

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace Euler
{
    class Problem3 : IProblemBase
    {
        //The prime factors of 13195 are 5, 7, 13 and 29.

        //What is the largest prime factor of the number 600851475143 ?

        public Problem3()
        {         

        }

        public string GetAnswer()
        {
            long result = 0;
            long limit = 600851475143;
            long lastResult = limit;

            int divisor = 2;//default smallest prime

            do
            {
                if (lastResult % divisor == 0)
                {
                    //keep dividing it out
                    lastResult = lastResult / divisor;
                    result = lastResult;
                }
                else
                {
                    //find next prime
                    for (int i = divisor + 1; i < limit;i++ )
                    {
                        if (isPrime(i))
                        {
                            divisor = i;
                            break;
                        }
                    }
                }

            } while (divisor < lastResult / divisor);

            return result.ToString();
        }

        private bool isPrime(int n)
        {
            if (n == 1)
            {
                return false;
            }
            else if (n < 4)
            {
                return true; //2 and 3 are prime
            }
            else if (n % 2 == 0)
            {
                return false;
            }
            else if (n < 9)
            {
                return true; //we have already excluded 4,6 and 8.
            }
            else if (n % 3 == 0)
            {
                return false;
            }
            else
            {
                int r = (int)(Math.Floor(Math.Sqrt((double)n))); // n rounded to the greatest integer r so that r*r<=n
                int f = 5;
                while (f <= r)
                {
                    if (n % f == 0) { return false; } //(and step out of the function)
                    if (n % (f + 2) == 0) { return false; } //(and step out of the function)
                    f = f + 6;
                }
                return true; //(in all other cases)
            }

        }

    }
}

Solving Project Euler with C#3.0 and functional programming…sigh

Samuel Jack has been tackling Project Euler over on his blog http://blog.functionalfun.net.

The problems he has solved so far and the source code to the solutions can be found here.

FYI, I know nothing about functinal programming, just thought others might find the solutions interesting.

Project Euler – Problem 8

Discover the largest product of five consecutive digits in the 1000-digit number.

Problem:
Find the greatest product of five consecutive digits in the 1000-digit number.

73167176531330624919225119674426574742355349194934
96983520312774506326239578318016984801869478851843
85861560789112949495459501737958331952853208805511
12540698747158523863050715693290963295227443043557
66896648950445244523161731856403098711121722383113
62229893423380308135336276614282806444486645238749
30358907296290491560440772390713810515859307960866
70172427121883998797908792274921901699720888093776
65727333001053367881220235421809751254540594752243
52584907711670556013604839586446706324415722155397
53697817977846174064955149290862569321978468622482
83972241375657056057490261407972968652414535100474
82166370484403199890008895243450658541227588666881
16427171479924442928230863465674813919123162824586
17866458359124566529476545682848912883142607690042
24219022671055626321111109370544217506941658960408
07198403850962455444362981230987879927244284909188
84580156166097919133875499200524063689912560717606
05886116467109405077541002256983155200055935729725
71636269561882670428252483600823257530420752963450

My Solution:

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace Euler
{
    class Problem8 : IProblemBase
    {

        //Find the greatest product of five consecutive digits in the 1000-digit number.

        //73167176531330624919225119674426574742355349194934
        //96983520312774506326239578318016984801869478851843
        //85861560789112949495459501737958331952853208805511
        //12540698747158523863050715693290963295227443043557
        //66896648950445244523161731856403098711121722383113
        //62229893423380308135336276614282806444486645238749
        //30358907296290491560440772390713810515859307960866
        //70172427121883998797908792274921901699720888093776
        //65727333001053367881220235421809751254540594752243
        //52584907711670556013604839586446706324415722155397
        //53697817977846174064955149290862569321978468622482
        //83972241375657056057490261407972968652414535100474
        //82166370484403199890008895243450658541227588666881
        //16427171479924442928230863465674813919123162824586
        //17866458359124566529476545682848912883142607690042
        //24219022671055626321111109370544217506941658960408
        //07198403850962455444362981230987879927244284909188
        //84580156166097919133875499200524063689912560717606
        //05886116467109405077541002256983155200055935729725
        //71636269561882670428252483600823257530420752963450

        public Problem8()
        {
        }

        string s = "7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450";

        public string GetAnswer()
        {
            int result = 0;

            char[] c = s.ToCharArray();

            for (int i = 0; i < c.Length-5;i++ )
            {
                char[] c2= new char[5];

                char[] one = new char[1];
                one[0] = c[i];
                int ione = Int32.Parse(new string(one));

                char[] two = new char[1];
                two[0] = c[i+1];
                int itwo = Int32.Parse(new string(two));

                char[] three = new char[1];
                three[0] = c[i+2];
                int ithree = Int32.Parse(new string(three));

                char[] four = new char[1];
                four[0] = c[i+3];
                int ifour = Int32.Parse(new string(four));

                char[] five = new char[1];
                five[0] = c[i+4];
                int ifive = Int32.Parse(new string(five));

                int tempResult = (ione * itwo * ithree * ifour * ifive);
                if (result < tempResult)
                {
                    result = tempResult;
                }
            }

            return result.ToString(); ;

        }

    }
}

Project Euler – Problem 7

Find the 10001st prime.

Problem:
By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6^(th) prime is 13.

What is the 10001^(st) prime number?

My Original Brut Force Solution knowing nothing about primes SLOW:

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace Euler
{
    class Problem7 : IProblemBase
    {

        //By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13,
        //we can see that the 6^(th) prime is 13.

        //What is the 10001^(st) prime number?

       //The algorithm

       //1. Create a contiguous list of numbers from two to some highest number n.
       //2. Strike out from the list all multiples of two (4, 6, 8 etc.).
       //3. The list's next number that has not been struck out is a prime number.
       //4. Strike out from the list all multiples of the number you identified in the previous step.
       //5. Repeat steps 3 and 4 until you reach a number that is greater than the square root of n (the highest number in the list).
       //6. All the remaining numbers in the list are prime.

        public Problem7()
        {
        }

        public string GetAnswer()
        {

            int primeCount = 0;
            int result = 0;

            for(int i=2;i>0;i++) //loop forever starting at 1
            {
                int matchCount = 0;
                for (int j = i; j > 0; j--)//loop down from current number to find prime
                {
                    if(i % j == 0)
                    {
                        matchCount++;
                    }

                }
                if (matchCount == 2)//prime
                {
                    primeCount++;
                    result = i;
                    if (primeCount == 10001)
                    {
                        break;
                    }
                }

            }                

            return result.ToString(); ;
        }

    }
}

My Solution after learning about primes and using Sieve of Eratosthenes:

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace Euler
{
    class Problem7 : IProblemBase
    {

        //By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13,
        //we can see that the 6^(th) prime is 13.

        //What is the 10001^(st) prime number?

       //The algorithm

       //1. Create a contiguous list of numbers from two to some highest number n.
       //2. Strike out from the list all multiples of two (4, 6, 8 etc.).
       //3. The list's next number that has not been struck out is a prime number.
       //4. Strike out from the list all multiples of the number you identified in the previous step.
       //5. Repeat steps 3 and 4 until you reach a number that is greater than the square root of n (the highest number in the list).
       //6. All the remaining numbers in the list are prime.

        public Problem7()
        {
        }

        private bool isPrime(int n)
        {
            if (n==1)
            {
                return false;
            }
            else if (n < 4)
            {
                return true; //2 and 3 are prime
            }
            else if (n % 2 == 0)
            {
                return false;
            }
            else if (n<9)
            {
                return true; //we have already excluded 4,6 and 8.
            }
            else if (n % 3 == 0)
            {
                return false;
            }
            else
            {
                int r= (int)(Math.Floor(Math.Sqrt((double)n))); // n rounded to the greatest integer r so that r*r<=n
                int f=5;
                while (f<=r)
                {
                    if (n % f==0){return false;} //(and step out of the function)
                    if (n %(f+2)==0){return false;} //(and step out of the function)
                    f=f+6;
                }
                return true; //(in all other cases)
            }

        }

        public string GetAnswer()
        {
            int limit = 10001;
            int count=1; //we know that 2 is prime
            int candidate=1;
            do{
                candidate=candidate+2;
                if (isPrime(candidate)) { count +=1; }
            } while(count<limit);

            return candidate.ToString();

        }

    }
}

Project Euler – Problem 6

What is the difference between the sum of the squares and the square of the sums?

Problem:
The sum of the squares of the first ten natural numbers is,
1^(2) + 2^(2) + … + 10^(2) = 385

The square of the sum of the first ten natural numbers is,
(1 + 2 + … + 10)^(2) = 55^(2) = 3025

Hence the difference between the sum of the squares of the first ten natural numbers and the square of the sum is 3025 − 385 = 2640.

Find the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum.

My Solution:

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace Euler
{
    class Problem6 : IProblemBase
    {

        //The sum of the squares of the first ten natural numbers is,
        //1^(2) + 2^(2) + ... + 10^(2) = 385

        //The square of the sum of the first ten natural numbers is,
        //(1 + 2 + ... + 10)^(2) = 55^(2) = 3025

        //Hence the difference between the sum of the squares of the first ten natural numbers
        //and the square of the sum is 3025 − 385 = 2640.

        //Find the difference between the sum of the squares of the first one hundred natural numbers
        //and the square of the sum.

        public Problem6()
        {
        }

        public string GetAnswer()
        {
            int limit = 100;
            return (SquareOfTheSum(limit) - SumOfSquares(limit)).ToString();
        }

        private int SquareOfTheSum(int p)
        {
            int result = 0;
            for (int i = 0; i <= p; i++)
            {
                result += i;
            }
            return (result * result);
        }

        private int SumOfSquares(int p)
        {
            int result = 0;
            for (int i = 0; i <= p; i++)
            {
                result += (i * i);
            }
            return result;
        }
    }
}