probleme_27.groovy

// courtesy of http://www.nearinfinity.com/blogs/seth_schroeder/project_euler_problem_10_meets.html and others
def primes(upto) {
	def primes = []
	def range = 2..upto
	for(i in range) {
		primes[i] = true
	}
	primes.remove(0)
	for(def index=2; index<upto; index++) {
		if(primes[index]) {
			def increment = 2
			def value
			while((value = index*increment)<=upto) {
				primes[value] = false
				increment++
			}
		}
	}
	def returned = []
	for(i in range) {
		if(primes[i])
			returned << i
	}
	return returned
}

/**
 * Small optimization : directly compute squares for easier formula writing
 */
def squares(upto) {
	returned = []
	for(i in 1..upto) {
		returned[i]=i*i
	}
	return returned
}

def maxN = 1000
def maxFactors = 1000

long start = System.currentTimeMillis();


def primes = primes(maxN)
println "primes computed"
def squares = squares(maxFactors)
println "squares computed"

def workingFactors = [:]

for(a in -1*maxFactors..maxFactors) {
	for(b in -1*maxFactors..maxFactors) {
		boolean isPrime = true
		def matching = []
		for(def n=1; n<maxN && isPrime; n++) {
			result = squares[n]+n*a+b;
			isPrime=primes.contains(result)
			if(isPrime) {
				matching << result
			}
		}
		if(matching.size()>0) {
			workingFactors[[a,b]]=matching
		}
	}
	if(a%100==0)
		println "reached ${a}"
}

bestEntry = workingFactors.max { e ->
	e.value.size()
}
println "best entry is ${bestEntry.key} product is ${bestEntry.key.inject(1, {result, entry -> result*entry})} and sequence length is ${bestEntry.value.size()}"

long end = System.currentTimeMillis();
println "duration "+((end-start)/1000.0)+" s";