euler_challenges.rb

require 'mathn'
# def time_logger(function)
#   start = Time.now
# 	function
# 	puts "It took #{(Time.now - start)/60} minutes to run #{function}" 
# end

# PROBLEM 2
# def fibonacci
# 	fib_array = [1,2]
# 	i = 1
# 	while (fib_array[i] + fib_array[i-1]) < 4000000
# 		fib_array << fib_array[i] + fib_array[i-1]
# 		i += 1
# 	end
# 	even_array = fib_array.find_all(&:even?)
# 	puts even_array.inject(:+)
# end

# start = Time.now
# fibonacci
# puts Time.now - start


# PROBLEM 3 -> NOT SOLVED YET
# require 'mathn'

class Fixnum

	def prime?
		factors = []
		(1..self).each do |num|
			factors << num if self % num == 0
		end
		return factors.length == 2
	end
end

# def largest_prime(n)	
# 	prime_factors = []
# 	(1..n).each do |i|
# 		prime_factors << i if n % i == 0 && i.prime?
# 	end
# 	puts prime_factors.max
# end

# largest_prime(600851475143)

# PROBLEM 4

# def palindrome_num
# 	a = *(100...1000)
# 	b = *(100...1000)
# 	pals = []
# 	i = 0
# 	while i < b.length
# 		a.each { |num| pals << num * b[i] if (num * b[i]).to_s == (num * b[i]).to_s.reverse }
# 		i += 1
# 	end

# 	puts pals.max
# end


# PROBLEM 5

# class Fixnum

# 	def divisible_by_those?
# 		i = 1 
# 		verdict = true
# 		while i <= 20 && verdict == true
# 			if self % i == 0
# 				verdict = true
# 			else
# 				verdict = false
# 			end
# 			i += 1
# 		end
# 		verdict

# 	end
# end

# start = Time.now
# i = 1
# while i < 1000000000
# 	puts i if i.divisible_by_those?
# 	i += 1
# end
# puts Time.now - start



# PROBLEM 6

# array = *(1..100)
# sum_of_square = array.map { |i| i**2 }.inject(:+)
# square_of_sum = (array.inject(:+))**2
# puts square_of_sum - sum_of_square

# PROBLEM 7

class Fixnum

	def is_prime?
		for i in 2..(self - 1)
			if self % i == 0
				return false
			end
		end
	end

# end

# def find_the_x_prime(prime_in_list_of_primes)
# 	array_of_primes = []
# 	i = 1
# 	while array_of_primes.length <= prime_in_list_of_primes
# 		array_of_primes << i if i.is_prime? 
# 		i += 1
# 	end
# 	puts array_of_primes.last
# end

# start = Time.now
# find_the_x_prime(10001)
# puts (Time.now - start)/60



	
# PROBLEM 8

# number = "73167176531330624919225119674426574742355349194934
# 96983520312774506326239578318016984801869478851843
# 85861560789112949495459501737958331952853208805511
# 12540698747158523863050715693290963295227443043557
# 66896648950445244523161731856403098711121722383113
# 62229893423380308135336276614282806444486645238749
# 30358907296290491560440772390713810515859307960866
# 70172427121883998797908792274921901699720888093776
# 65727333001053367881220235421809751254540594752243
# 52584907711670556013604839586446706324415722155397
# 53697817977846174064955149290862569321978468622482
# 83972241375657056057490261407972968652414535100474
# 82166370484403199890008895243450658541227588666881
# 16427171479924442928230863465674813919123162824586
# 17866458359124566529476545682848912883142607690042
# 24219022671055626321111109370544217506941658960408
# 07198403850962455444362981230987879927244284909188
# 84580156166097919133875499200524063689912560717606
# 05886116467109405077541002256983155200055935729725
# 71636269561882670428252483600823257530420752963450"
# number = number.gsub("\n", '')
# num_array = number.split(//).map! { |i| i.to_i }


# new_array = []
# i = 0
# while i < num_array.length - 4
# 	new_array << num_array[i..i+4]
# 	i += 1
# end

# p new_array.map! { |num| num.inject(:*) }.sort


# PROBLEM 9

# a,b,c = 0,0,0
# for a in 1..1000
# 	for b in 1..1000
# 		for c in 1..1000
# 			puts "a = #{a}, b = #{b}, c = #{c}" if a + b + c == 1000 && a**2 + b**2 == c**2
# 		end
# 	end
# end


# PROBLEM 10 LONG LONG LONG LONG RUNTIME

# class Fixnum

# 	def is_prime?
# 		for i in 2..(self - 1)
# 			if self % i == 0
# 				return false
# 			end
# 		end
# 	end

# end

# def sum_primes	
# 	array_of_primes= []
# 	j = 2
# 	while j < 1000
# 		array_of_primes << j if j.is_prime?
# 		j += 1
# 	end
# 	p array_of_primes
# 	puts array_of_primes.inject(:+)
# end

# start = Time.now
# sum_primes
# puts (Time.now - start)/60


# PROBLEM 11


# PROBLEM 12

# Fixnum.class_eval do
# 	def factors
# 		factor_array = []
# 		for i in 1..self
# 			factor_array << i if self % i == 0
# 		end
# 		factor_array
# 	end
# end

# triangular_array = []
# j = 443520
# counted = 0
# while counted < 500
# 	number = (1..j).inject(:+)
# 	triangular_array << number
# 	counted = number.factors.count
# 	j += 1
# end
# p triangular_array



# PROBLEM 13

# number = "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"
# numarray = number.split(/\n/).map! { |w| w.to_i }
# num_array.inject(:+).to_s[0..9]



# PROBLEM 14

def collatz(initial_num)
	hash = {}
	for i in 1..initial_num
		a = [i]
		while a.last != 1
			if a.last.even?
				a << a.last/2
			else
				a << a.last*3+1
			end
		end
		hash[i.to_s] = a.count
	end
	p hash.sort_by { |number, length| length }.last
	
end

start = Time.now
collatz(1000000)
puts Time.now - start
# a = [9]
# while a.last != 1
# 	if a.last.even?
# 		a << a.last/2
# 	else
# 		a << a.last*3+1
# 	end
# end

# p a 
# p a.count


# PROBLEM