public static void Problem9(ProblemArguments arguments)
{
int a = 1, b = 1, c = 1;
int sum = Convert.ToInt32(arguments.Number);
bool found = false;
do
{
b = a + 1;
do
{
c = sum - a - b;
if (c < b)
{
break;
}
if (Math.Pow(a, 2) + Math.Pow(b, 2) == Math.Pow(c, 2))
{
found = true;
}
else
{
b++;
a++;
}
} while (b < sum - a && !found);
} while (a < sum && !found);
Console.WriteLine("The product of the special pithagorean triplet {0}x{1}x{2} is {3}.", a, b, c, a * b * c);
}
public static void Problem11(ProblemArguments arguments)
{
string sequence = arguments.Sequence;
int adjacent = Convert.ToInt32(arguments.Number);
int maxProduct = int.MinValue, product = 0;
CellList VisitedCellBlocks = new CellList(); //so we don't calculate on repeated blocks of adjcent cells
//initialize grid from string sequence
string[][] grid = sequence.Split(':').Select(row => row.Split(',')).ToArray();
int size = grid.Length;
//get highest adajacent product of adjacents to every grid cell
for (int i = 0; i < size; i++)
{
for (int j = 0; j < size; j++)
{
product = GetAdjacentMaxproduct(i, j, adjacent, size, grid, VisitedCellBlocks);
if (product > maxProduct)
{
maxProduct = product;
}
}
}
Console.WriteLine("The greatest product of {0} adjacent numbers in the same direction (up, down, left, right, or diagonally) in the {1}×{1} grid is {2}.", adjacent, size, maxProduct);
}
public static void Problem2(ProblemArguments arguments)
{
long target = arguments.Number;
long[] fibonacci = new long[] { 1, 2 };
long sum = 0;
long iteration = 1;
while (fibonacci[0] < target)
{
//only add even fibonacci numbers
if (fibonacci[0] % 2 == 0)
{
sum += fibonacci[0];
}
if (fibonacci[1] % 2 == 0)
{
sum += fibonacci[1];
}
fibonacci[0] = fibonacci[0] + fibonacci[1];
fibonacci[1] = fibonacci[0] + fibonacci[1];
iteration++;
}
Console.WriteLine("Sum of all even fibonnaci numbers less than {0} is {1}", target, sum);
}
static void Problem5(ProblemArguments arguments)
{
long maximum = arguments.Number;
int[] multiples = new int[maximum];
bool found = false;
long number = 0;
for (int i = 1; i <= maximum; i++)
{
multiples[i - 1] = i;
}
while (!found && number < long.MaxValue)
{
if (!found)
{
number += maximum;
}
found = UtilityMath.IsMultiple(multiples, number);
}
if (found)
{
Console.WriteLine("{0} is the smallest positive number that is evenly divisible by {1}", number, string.Join(",", multiples));
}
else
{
Console.WriteLine("No evenly positive multiple number found.");
}
}
static void ProblemTree(ProblemArguments arguments)
{
Tree <long> tree = new Tree <long>(arguments.Numbers);
long max = (long)tree.Max();
Console.WriteLine("Tree [{0}] size {1} maximum {2}", tree.ToString(), tree.Size, max);
}
static void Problem4_1(ProblemArguments arguments)
{
long number = 993 * 913;
if (UtilityMath.IsPalindrome(number))
{
Console.WriteLine("x. {0} is palipndrome", number);
}
}
public static void ProblemQueue(ProblemArguments arguments)
{
Queue <long> queue = new Queue <long>();
foreach (long l in arguments.Numbers)
{
queue.EnQueue(l);
}
Console.WriteLine("Queue [{0}] without first element {1} has size {2}", queue.ToString(), queue.DeQueue(), queue.Size);
}
public static void Launch(Problem problem, ProblemArguments arguments)
{
Stopwatch stopWatch = new Stopwatch();
Console.WriteLine("Problem {0}:", arguments.ID);
stopWatch.Start();
problem(arguments);
stopWatch.Stop();
double elapsedTime = stopWatch.Elapsed.TotalMilliseconds;
Console.WriteLine("Problem execution duration: {0}ms", elapsedTime);
}
static void Main(string[] arguments)
{
Problem[] problem = new Problem[] {
//ProblemSandbox,
//Problem1,
//Problem2,
//Problem3,
//Problem4,
//Problem5,
//Problem6,
//Problem7,
//Problem7b,
//Problem8,
//Problem9,
//Problem10,
//Problem11,
//Problem12
Problem13
//ProblemTree,
//ProblemQueue
};
ProblemArguments[] arg = new ProblemArguments[] {
//new ProblemArguments(0,1),
//new ProblemArguments(1,10,"",new long[] {3,5}),
//new ProblemArguments(2,4000000),
//new ProblemArguments(3,600851475143),
//new ProblemArguments(4,3),
//new ProblemArguments(5,20),
//new ProblemArguments(6,100),
//new ProblemArguments(7,10001),
//new ProblemArguments(7,1000),
//new ProblemArguments(8,13,"7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450",null),
//new ProblemArguments(9,1000),
//new ProblemArguments(10,2000000),
//new ProblemArguments(11,4,"08,02,22,97,38,15,00,40,00,75,04,05,07,78,52,12,50,77,91,08:49,49,99,40,17,81,18,57,60,87,17,40,98,43,69,48,04,56,62,00:81,49,31,73,55,79,14,29,93,71,40,67,53,88,30,03,49,13,36,65:52,70,95,23,04,60,11,42,69,24,68,56,01,32,56,71,37,02,36,91:22,31,16,71,51,67,63,89,41,92,36,54,22,40,40,28,66,33,13,80:24,47,32,60,99,03,45,02,44,75,33,53,78,36,84,20,35,17,12,50:32,98,81,28,64,23,67,10,26,38,40,67,59,54,70,66,18,38,64,70:67,26,20,68,02,62,12,20,95,63,94,39,63,08,40,91,66,49,94,21:24,55,58,05,66,73,99,26,97,17,78,78,96,83,14,88,34,89,63,72:21,36,23,09,75,00,76,44,20,45,35,14,00,61,33,97,34,31,33,95:78,17,53,28,22,75,31,67,15,94,03,80,04,62,16,14,09,53,56,92:16,39,05,42,96,35,31,47,55,58,88,24,00,17,54,24,36,29,85,57:86,56,00,48,35,71,89,07,05,44,44,37,44,60,21,58,51,54,17,58:19,80,81,68,05,94,47,69,28,73,92,13,86,52,17,77,04,89,55,40:04,52,08,83,97,35,99,16,07,97,57,32,16,26,26,79,33,27,98,66:88,36,68,87,57,62,20,72,03,46,33,67,46,55,12,32,63,93,53,69:04,42,16,73,38,25,39,11,24,94,72,18,08,46,29,32,40,62,76,36:20,69,36,41,72,30,23,88,34,62,99,69,82,67,59,85,74,04,36,16:20,73,35,29,78,31,90,01,74,31,49,71,48,86,81,16,23,57,05,54:01,70,54,71,83,51,54,69,16,92,33,48,61,43,52,01,89,19,67,48")
//new ProblemArguments(12,500)
new ProblemArguments(13, 10, "37107287533902102798797998220837590246510135740250,46376937677490009712648124896970078050417018260538,74324986199524741059474233309513058123726617309629,91942213363574161572522430563301811072406154908250,23067588207539346171171980310421047513778063246676,89261670696623633820136378418383684178734361726757,28112879812849979408065481931592621691275889832738,44274228917432520321923589422876796487670272189318,47451445736001306439091167216856844588711603153276,70386486105843025439939619828917593665686757934951,62176457141856560629502157223196586755079324193331,64906352462741904929101432445813822663347944758178,92575867718337217661963751590579239728245598838407,58203565325359399008402633568948830189458628227828,80181199384826282014278194139940567587151170094390,35398664372827112653829987240784473053190104293586,86515506006295864861532075273371959191420517255829,71693888707715466499115593487603532921714970056938,54370070576826684624621495650076471787294438377604,53282654108756828443191190634694037855217779295145,36123272525000296071075082563815656710885258350721,45876576172410976447339110607218265236877223636045,17423706905851860660448207621209813287860733969412,81142660418086830619328460811191061556940512689692,51934325451728388641918047049293215058642563049483,62467221648435076201727918039944693004732956340691,15732444386908125794514089057706229429197107928209,55037687525678773091862540744969844508330393682126,18336384825330154686196124348767681297534375946515,80386287592878490201521685554828717201219257766954,78182833757993103614740356856449095527097864797581,16726320100436897842553539920931837441497806860984,48403098129077791799088218795327364475675590848030,87086987551392711854517078544161852424320693150332,59959406895756536782107074926966537676326235447210,69793950679652694742597709739166693763042633987085,41052684708299085211399427365734116182760315001271,65378607361501080857009149939512557028198746004375,35829035317434717326932123578154982629742552737307,94953759765105305946966067683156574377167401875275,88902802571733229619176668713819931811048770190271,25267680276078003013678680992525463401061632866526,36270218540497705585629946580636237993140746255962,24074486908231174977792365466257246923322810917141,91430288197103288597806669760892938638285025333403,34413065578016127815921815005561868836468420090470,23053081172816430487623791969842487255036638784583,11487696932154902810424020138335124462181441773470,63783299490636259666498587618221225225512486764533,67720186971698544312419572409913959008952310058822,95548255300263520781532296796249481641953868218774,76085327132285723110424803456124867697064507995236,37774242535411291684276865538926205024910326572967,23701913275725675285653248258265463092207058596522,29798860272258331913126375147341994889534765745501,18495701454879288984856827726077713721403798879715,38298203783031473527721580348144513491373226651381,34829543829199918180278916522431027392251122869539,40957953066405232632538044100059654939159879593635,29746152185502371307642255121183693803580388584903,41698116222072977186158236678424689157993532961922,62467957194401269043877107275048102390895523597457,23189706772547915061505504953922979530901129967519,86188088225875314529584099251203829009407770775672,11306739708304724483816533873502340845647058077308,82959174767140363198008187129011875491310547126581,97623331044818386269515456334926366572897563400500,42846280183517070527831839425882145521227251250327,55121603546981200581762165212827652751691296897789,32238195734329339946437501907836945765883352399886,75506164965184775180738168837861091527357929701337,62177842752192623401942399639168044983993173312731,32924185707147349566916674687634660915035914677504,99518671430235219628894890102423325116913619626622,73267460800591547471830798392868535206946944540724,76841822524674417161514036427982273348055556214818,97142617910342598647204516893989422179826088076852,87783646182799346313767754307809363333018982642090,10848802521674670883215120185883543223812876952786,71329612474782464538636993009049310363619763878039,62184073572399794223406235393808339651327408011116,66627891981488087797941876876144230030984490851411,60661826293682836764744779239180335110989069790714,85786944089552990653640447425576083659976645795096,66024396409905389607120198219976047599490197230297,64913982680032973156037120041377903785566085089252,16730939319872750275468906903707539413042652315011,94809377245048795150954100921645863754710598436791,78639167021187492431995700641917969777599028300699,15368713711936614952811305876380278410754449733078,40789923115535562561142322423255033685442488917353,44889911501440648020369068063960672322193204149535,41503128880339536053299340368006977710650566631954,81234880673210146739058568557934581403627822703280,82616570773948327592232845941706525094512325230608,22918802058777319719839450180888072429661980811197,77158542502016545090413245809786882778948721859617,72107838435069186155435662884062257473692284509516,20849603980134001723930671666823555245252804609722,53503534226472524250874054075591789781264330331690")
//new ProblemArguments(13,3,"222,222,222,222,222")
//new ProblemArguments(0,new long[] { 8, 3, 10, 1, 6, 14, 4, 7, 13 }),
//new ProblemArguments(0,new long[] { 3, 5, 1, 2 })
};
int numberOfProblems = problem.Length;
for (int i = 0; i < numberOfProblems; i++)
{
Launch(problem[i], arg[i]);
}
Console.WriteLine("------------------------------------------------------------------------");
Console.WriteLine("Complete");
Console.ReadKey();
}
public static void Problem10(ProblemArguments arguments)
{
long sum = 0, limit = arguments.Number;
for (long i = 2; i <= limit; i++)
{
if (UtilityMath.IsPrime(i))
{
sum += i;
}
}
Console.WriteLine("The sum of all the primes below {0} is {1}.", limit, sum);
}
public static void Problem13(ProblemArguments arguments)
{
string sequence = arguments.Sequence;
int digits = Convert.ToInt32(arguments.Number);
string[] numbers = sequence.Split(',').ToArray <string>();
int height = numbers.Length;
int width = numbers[0].Length;
int[,] matrix = LoadMatrix(numbers, height, width);
string sum = AddMatrix(matrix);
if (digits < sum.Length)
{
Console.WriteLine("The first {0} digits of the large sum are {1}.", digits, sum.Substring(0, digits));
}
}
public static void Problem12(ProblemArguments arguments)
{
long count = arguments.Number;
long number = (long)Math.Pow((double)count, 2);
long number_of_divisors = 0;
do
{
number++;
if (UtilityMath.IsTriangularNumber(number))
{
number_of_divisors = 0;// UtilityMath.NumberOfDivisor(number);
}
} while (number_of_divisors < count);
Console.WriteLine("The value of the first triangle number to have over {0} divisors is {1}.", count, number);
}
static void Problem4(ProblemArguments arguments)
{
long digits = arguments.Number;
long limit = (long)Math.Pow(10, digits) - 1;
long number = 0;
long i, j, pi = 0, pj = 0;
bool found = false;
long palindrome = UtilityMath.GenericLimit <long> .MinValue;
i = limit;
j = limit;
while (i > Math.Pow(10, digits - 1))
{
j = limit;
while (!found && j > Math.Pow(10, digits - 1))
{
number = i * j;
found = UtilityMath.IsPalindrome(number);
j--;
}
i--;
if (found && number > palindrome)
{
pi = i + 1;
pj = j + 1;
palindrome = number;
found = false;
}
}
if (palindrome == UtilityMath.GenericLimit <long> .MinValue && i == Math.Pow(10, digits - 1) && j == Math.Pow(10, digits - 1))
{
Console.WriteLine("No palindrome found");
}
else
{
Console.WriteLine("The largest palindrome made from the product of two 3-digit numbers is {0} = {1} x {2}", palindrome, pi, pj);
}
//int digit = sequence[1]-48; //convert character to it's integer representation
}
static void Problem3(ProblemArguments arguments)
{
//n=600851475143;143;8462696833;
long number = arguments.Number;
Tree <long> factors = new Tree <long>();
UtilityMath.GetPrimeFactors(arguments.Number, factors);
bool isPrime = factors.Size == 0;
long max = (long)factors.Max();
if (isPrime)
{
Console.WriteLine("The prime factors of {0} are [{1}], maximum is {2}", number, factors.ToString(), max);
}
else
{
Console.WriteLine("{0} is not a prime, but its prime factors are [{1}] with maximum {2}", number, factors.ToString(), max);
}
}
public static void Problem7(ProblemArguments arguments)
{
long index = arguments.Number;
long count = 1;
long number = 2;
long prime = long.MinValue;
Tree <long> factors = new Tree <long>();
while (count < index + 1)
{
if (UtilityMath.IsPrime(number))
{
count++;
prime = number;
}
number++;
}
Console.WriteLine("The {0}st/nd prime number is {1}.", index, prime);
}
static void Problem1(ProblemArguments arguments)
{
long limit = arguments.Number;
long[] numbers = arguments.Numbers; //new long[] { 3, 5 };
long n = 1;
Tree <long> multiples = new Tree <long>();
while (n < limit)
{
for (int i = 0; i < numbers.Length; i++)
{
if ((n % numbers[i]) == 0)
{
multiples.Add(n);
}
}
n++;
}
Console.WriteLine("The sum of the multiples of ({0}) is {1}", string.Join(",", numbers.Select(v => v.ToString())), multiples.Sum);
}
public static void Problem7b(ProblemArguments arguments)
{
long index = arguments.Number;
long number = 2;
Tree <long> factors = new Tree <long>();
while (factors.Size < index)
{
UtilityMath.GetPrimeFactors(number, factors);
number++;
}
string prime = string.Empty;
Node <long> node = factors[index];
if (node != null)
{
prime = node.Item.ToString();
}
Console.WriteLine("The {0}st/nd prime number is {1}.", index, prime);
}
public static void Problem6(ProblemArguments arguments)
{
int[] numbers = new int[arguments.Number];
long sum = 0;
long length = arguments.Number;
//initialize natural numbers array
for (int i = 0; i < length; i++)
{
numbers[i] = i + 1;
}
for (int i = 0; i < length - 1; i++)
{
for (int j = i + 1; j < length; j++)
{
sum += 2 * numbers[i] * numbers[j];
}
}
Console.WriteLine("The difference between the sum of the squares of the first one hundred natural numbers and the square of the sum is {0}.", sum);
}
public static void Problem8(ProblemArguments arguments)
{
string sequence = arguments.Sequence;
int digits = Convert.ToInt32(arguments.Number);
string segment = string.Empty, digit = string.Empty;
int start = 0;
long product = long.MinValue;
while (start + digits < sequence.Length)
{
segment = sequence.Substring(start, digits);
start++;
long p = GetProduct(segment);
if (p > product)
{
product = p;
digit = segment;
}
}
Console.WriteLine("The adjacent digits [{0}] in the 1000-digit number that have the greatest product which is {1}.", string.Join("x", digit.ToArray()), product);
}
public static void ProblemSandbox(ProblemArguments arguments)
{
}