Author Archives: MantasCode

C#: How to get correlation coefficient of two arrays Correl()

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This simple example shows you how to get the correlation coefficient of two arrays.  Microsoft Excel and OpenOffice Calc has a function for this called CORREL() :

//Two arrays
double[] array1 = { 3, 2, 4, 5, 6 };
double[] array2 = { 9, 7, 12, 15, 17 };
 
double[] array_xy = new double[array1.Length];
double[] array_xp2 = new double[array1.Length];
double[] array_yp2 = new double[array1.Length];
for (int i = 0; i < array1.Length; i++)
    array_xy[i] = array1[i] * array2[i];
for (int i = 0; i < array1.Length; i++)
    array_xp2[i] = Math.Pow(array1[i], 2.0);
for (int i = 0; i < array1.Length; i++)
    array_yp2[i] = Math.Pow(array2[i], 2.0);
double sum_x = 0;
double sum_y = 0;
foreach (double n in array1)
    sum_x += n;
foreach (double n in array2)
    sum_y += n;
double sum_xy = 0;
foreach (double n in array_xy)
    sum_xy += n;
double sum_xpow2 = 0;
foreach (double n in array_xp2)
    sum_xpow2 += n;
double sum_ypow2 = 0;
foreach (double n in array_yp2)
    sum_ypow2 += n;
double Ex2 = Math.Pow(sum_x, 2.00);
double Ey2 = Math.Pow(sum_y, 2.00);
 
double Correl = 
(array1.Length * sum_xy - sum_x * sum_y) /
Math.Sqrt((array1.Length * sum_xpow2 - Ex2) * (array1.Length * sum_ypow2 - Ey2));
 
Console.WriteLine("CORREL : "+ Correl);

C#: Project Euler Solution to Problem 27

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http://projecteuler.net/problem=27

Considering quadratics of the form:

n² + an + b, where |a| < 1000 and |b| < 1000 where |n| is the modulus/absolute value of n e.g. |11| = 11 and |-4| = 4 Find the product of the coefficients, a and b, for the quadratic expression that produces the maximum number of primes for consecutive values of n, starting with n = 0. 

static void Main(string[] args)
{
    //n² + an + b
    int maxprimes = 0;
    int maxproduct = 0;
    for (int a = 0; a < 1000; a++)
    {
        for (int b = 0; b < 1000; b++)
        {
            int prime = countPrime(a, b);
            if (maxprimes < prime)
            {
                maxprimes = prime;
                maxproduct= (-a*b );
            }
        }
    }
    Console.WriteLine(maxproduct);
}
 
public static int countPrime(int a, int b)
{
    int count = 0;
    int n = 0;
    while (true)
    {
        double result = Math.Pow(n, 2.00) - (a * n) + b;
        if (isPrime((int)result) && result >= 0)
            count++;
        else
            return count;
        n++;
    }
}
 
public static bool isPrime(int n)
{
    if (n == 1)
        return false;
    if (n == 2)
        return true;
    for (int i = 2; i < n; ++i)
    {
        if ((n % i) == 0)
            return false;
    }
    return true;
}

C#: Project Euler Solution to Problem 32

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http://projecteuler.net/problem=32

We shall say that an n-digit number is pandigital if it makes use of all the digits 1 to n exactly once; for example, the 5-digit number, 15234, is 1 through 5 pandigital.

The product 7254 is unusual, as the identity, 39 x 186 = 7254, containing multiplicand, multiplier, and product is 1 through 9 pandigital.

Find the sum of all products whose multiplicand/multiplier/product identity can be written as a 1 through 9 pandigital. 

public static LinkedList<string> onetonine = new LinkedList<string>();
static void Main(string[] args)
{
    LinkedList<int> distinct_product = new LinkedList<int>();
    int product = 0;
    for (int a = 1; a < 2000; a++)
    {
        for (int b = 1; b < 2000; b++)
        {
            product = a * b;
 
            if (isDigits(a + "" + b + "" + product))
            {
                if (!distinct_product.Contains(product) )
                    distinct_product.AddLast(product);
            }
        }
    }
    int sum = 0;
    foreach (int prod in distinct_product)
        sum += prod;
    Console.WriteLine("sum : "+sum);
}
 
public static bool isDigits(string s)
{
    onetonine.Clear();
    onetonine.AddLast("1");
    onetonine.AddLast("2");
    onetonine.AddLast("3");
    onetonine.AddLast("4");
    onetonine.AddLast("5");
    onetonine.AddLast("6");
    onetonine.AddLast("7");
    onetonine.AddLast("8");
    onetonine.AddLast("9");
    if (s.Length != 9)
        return false;
    for (int i = 0; i < s.Length; i++)
    {
        if (onetonine.Contains("" + s[i]))
            onetonine.Remove("" + s[i]);
        else
            return false;
    }
    return true;
}

C#: Project Euler Solution to Problem 39

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http://projecteuler.net/problem=39

If p is the perimeter of a right angle triangle with integral length sides, {a,b,c}, there are exactly three solutions for p = 120.

{20,48,52}, {24,45,51}, {30,40,50}

For which value of p <= 1000, is the number of solutions maximised? 

int Max_P = 0;
int P_position = 0;
for (int p = 1; p < 1000; p++)
{
    int count_p = 0;
    for (int a = 1; a < 500; a++)
    {
        for (int b = 1; b < 500; b++)
        {
            for (int c = 1; c < 500; c++)
            {
                if (  (a + b + c == p) &&
                (Math.Pow(a, 2.00) + Math.Pow(b, 2.00) == Math.Pow(c, 2.00)) )
                    count_p++;
            }
        }
    }
    if (Max_P < count_p)
    {
        Max_P = count_p;
        P_position = p;
    }
}
Console.WriteLine("p = "+P_position);

C#: Project Euler Solution to Problem 47

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http://projecteuler.net/problem=47

The first two consecutive numbers to have two distinct prime factors are:

14 = 2 x 7
15 = 3 x 5

Find the first four consecutive integers to have four distinct primes factors. What is the first of these numbers? 

static void Main(string[] args)
{
    LinkedList<int> threefactors = new LinkedList<int>();
    int n = 0;
    while (true)
    {
        n++;
        int factcount = 0;
        for (int i = 1; i <= n; i++)
        {
            if (n % i == 0 && isPrime(i))
                factcount++;
        }
        if (factcount == 4)
        {
            threefactors.AddLast(n);
            int lastn = (n - 1);
            int lastn2 = (n - 2);
            int lastn3 = (n - 3);
            if (threefactors.Contains(lastn)  && threefactors.Contains(lastn2) && threefactors.Contains(lastn3))
            {
                Console.WriteLine(n);
                Console.WriteLine(lastn);
                Console.WriteLine(lastn2);
                Console.WriteLine(lastn3);
                break;
            }
        }
    }
}
public static bool isPrime(int n)
{
    if (n == 1)
        return false;
    if (n == 2)
        return true;
    for (int i = 2; i < n; ++i)
    {
        if ((n % i) == 0)
            return false;
    }
    return true;
}

C#: Project Euler Solutions to Problems 9, 13, and 38

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For solving ten consecutive problems (1-10).

http://projecteuler.net/problem=9

a2 + b2 = c2

There exists exactly one Pythagorean triplet for which a + b + c = 1000.
Find the product abc. 

for (int a = 1; a < 1000; a++)
{
    for (int b = 1; b < 1000; b++)
    {
        double a_pow2 = Math.Pow(a, 2);
        double b_pow2 = Math.Pow(b, 2);
        double c_root = Math.Sqrt(a_pow2 + b_pow2);
        if ((a + b + c_root) == 1000.00)
        {
            Console.WriteLine("a "+a+" b "+b+" c "+c_root+" product : "+(a * b * c_root));
            break;
        }
    }
}

http://projecteuler.net/problem=13

Work out the first ten digits of the sum of the following one-hundred 50-digit numbers. 

string[] linerows = totalstring.Split('\n');
long sum = 0;
foreach (string row in linerows)
{
    // Console.WriteLine(row);
    string longnum = row;
    string num11 = longnum.Substring(0, 11);
    long num = long.Parse(num11);
    sum += num;
}
Console.WriteLine(sum.ToString().Substring(0, 10));

http://projecteuler.net/problem=38

What is the largest 1 to 9 pandigital 9-digit number that can be formed as the concatenated product of an integer with (1,2, … , n) where n 1? 

static void Main(string[] args)
{
    int number = 0;
    int numberofappend = 2;
    int max = 0;
    while (true)
    {
        number++;
        string catstring = appendmore(number, numberofappend);
        if (catstring.Length > 9)
        {
            number = 0;
            numberofappend++;
        }
        else if  (catstring.Length == 9 && Order(catstring))
        {
            int catint = int.Parse(catstring);
            if (max < catint)
            {
                max = catint;
                Console.WriteLine("max so far : "+ max);
            }
        }
    }
}
public static string appendmore(int num, int howmany)
{
    string cat = "";
    for (int i = 1; i <= howmany; i++)
        cat += "" + num * i;
    return cat;
}
public static bool Order(string n)
{
    string mynum = "" + n;
    int[] int_array = new int[mynum.Length];
    for (int i = 0; i < mynum.Length; i++)
    {
        int_array[i] = int.Parse(mynum[i].ToString());
    }
    Array.Sort(int_array);
    if (int_array[0] == 1)
    {
        int count = 2;
        for (int j = 1; j < int_array.Length; j++)
        {
            if (count == int_array[j])
                count++;
            else
                return false;
        }
    }
    else
        return false;
    return true;
}

C#: Project Euler Solutions to Problems 12 and 41

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I have completed 25 Project Euler Questions without cheating. I was awarded a badge that looks like this.

http://projecteuler.net/problem=12

What is the value of the first triangle number to have over five hundred divisors? 

int max = 0;
int n = 1;
while(true)
{
    double value = (.5 * n) * (n + 1);
    int devisor_count = 0;
    for (int i = 1; i <= value; i++)
    {
        if (value % i == 0)
            devisor_count++;
    }
    if (max < devisor_count)
    {
        max = devisor_count;
        Console.WriteLine(n + " value  " + value + " devisor Count :" + devisor_count);
    }
    if (devisor_count > 500)
    {
        Console.WriteLine(n + " value  " + value + " FINAL  devisor Count :" + devisor_count);
        break;
    }
    n++;
}

http://projecteuler.net/problem=41

We shall say that an n-digit number is pandigital if it makes use of all the digits 1 to n exactly once. For example, 2143 is a 4-digit pandigital and is also prime.

What is the largest n-digit pandigital prime that exists? 

static void Main(string[] args)
{
    int n = 1;
    while (true)
    {
        if (isPrime(n))
        {
            if (Order(n))
                Console.WriteLine(n);
        }
        n++;
    }
}
 
public static bool Order(int n)
{
    string mynum = ""+n;
    int [] int_array = new int[mynum.Length];
    for (int i = 0; i < mynum.Length; i++)
        int_array[i] = int.Parse(mynum[i].ToString());
    Array.Sort(int_array);
    if (int_array[0] == 1)
    {
        int count = 2;
        for (int j = 1; j < int_array.Length; j++)
        {
            if (count == int_array[j])
                count++;
            else 
                return false; 
        }
    }
    else
        return false;
    return true;
}
 
public static bool isPrime(int n)
{
    if (n == 1)
        return false;
    if (n == 2)
        return true;
    for (int i = 2; i < n; ++i)
    {
        if ((n % i) == 0)
            return false;
    }
    return true;
}

C#: Project Euler Solution to Problem 42

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http://projecteuler.net/problem=42

The nth term of the sequence of triangle numbers is given by, tn = ½n(n+1); so the first ten triangle numbers are:

1, 3, 6, 10, 15, 21, 28, 36, 45, 55, …

Using words.txt, a 16K text file containing nearly two-thousand common English words, how many are triangle words? 

//get a list of 100 triangle numbers
LinkedList<double> tri_nums = new LinkedList<double>();
for( int n = 1; n<101 ; n++)
{
    double value = (.5 * n) * (n + 1);
    tri_nums.AddLast(value);
}
//evaluate word values and compare
StreamReader nameStream;
string fullBook = "";
nameStream = File.OpenText("C:\\Euler\\words.txt");
fullBook = nameStream.ReadToEnd();
nameStream.Close();
string[] names = fullBook.Split(',');
int tri_count = 0;
for (int i = 0; i < names.Length; i++)
{
    int namePosition = (i + 1);
    string name1 = names[i].Replace('"', ' ').Trim();
    int letter_sum = 0;
    for (int j = 0; j < name1.Length; j++)
        letter_sum += (int)(name1[j] - 64);
    if (tri_nums.Contains(letter_sum))
    {
        Console.WriteLine("triangle Word : " +  name1 );
        tri_count++;
    }
}
Console.WriteLine();
Console.WriteLine("Triangle word count : " + tri_count);

C#: Project Euler Solutions to Problems 21 and 52

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http://projecteuler.net/problem=21

Evaluate the sum of all the amicable numbers under 10000. 

int totalsum = 0;
for (int num = 1; num < 10000; num++)
{
    int tempsum = 0;
    for (int i = 1; i < num; i++)
    {
        if (num % i == 0)
            tempsum += i;
    }
    int secondtempsum = 0;
    for (int i = 1; i < tempsum; i++)
    {
        if (tempsum % i == 0)
            secondtempsum += i;
    }
    if (secondtempsum == num && num !=tempsum)
    {
        Console.WriteLine("amicable pair  " + num + " , " + tempsum );
        totalsum += num;
    }
}
Console.WriteLine(" Final sum : "+totalsum);

http://projecteuler.net/problem=52

It can be seen that the number, 125874, and its double, 251748, contain exactly the same digits, but in a different order.

Find the smallest positive integer, x, such that 2x, 3x, 4x, 5x, and 6x, contain the same digits. 

static void Main(string[] args)
{
    long count = 1;
    while (true)
    {
        long initnum = count;
        long t2 = initnum * 2;
        long t3 = initnum * 3;
        long t4 = initnum * 4;
        long t5 = initnum * 5;
        long t6 = initnum * 6;
        if (compareNums(initnum, t2) && 
            compareNums(initnum, t3) && 
            compareNums(initnum, t4) && 
            compareNums(initnum, t5) && 
            compareNums(initnum, t6))
        {
            Console.WriteLine(initnum);
            break;
        }
        count++;
    }
}
 
public static bool compareNums(long a, long b)
{
    string initstring = "" + a;
    string doublestring = "" + b;
    bool found = false;
    foreach (char digit in doublestring)
    {
        foreach (char innerchar in initstring)
        {
            if (innerchar == digit)
                found = true;
        }
        if (!found)
            return false;
        found = false;
    }
    return true;
}