Euler #8, #9 y #10

https://projecteuler.net/problem=8

Sencillo problema, lo más fácil es tratar el número tan largo que proponen como un string e ir tomando "porciones" de 13 caracteres y sumándolas, guardándonos la mayor suma. Implementación en Python.

   1 
   2 number = "7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450"
   3 
   4 biggest = ""
   5 product = 0
   6 length = 13
   7 
   8 count = 0
   9 portion = number[count:count+length]
  10 while len(portion) == length:
  11     temp = 1
  12     for d in portion:
  13         temp *= int(d)
  14     if temp > product:
  15         product = temp
  16         biggest = portion
  17     count += 1
  18     portion = number[count:count+length]
  19 
  20 print ("Biggest: " + biggest + ", product: " + str(product))
  21 

---

https://projecteuler.net/problem=9

Implementación en JavaScript

   1 var SUM = 1000
   2 for (var a = 1; a < SUM; a++) {
   3   for (var b = a + 1; b < SUM; b++) {
   4     c2 = a*a + b*b;
   5     c = Math.sqrt(c2)
   6     if (Math.round(c) == c) { // Pythagorean triplet
   7       if (a + b +c == SUM) {
   8         console.log("Triplet: ", a, b, c, "Product: ", a*b*c);
   9         process.exit(0);
  10       }
  11     }
  12   }
  13 }
  14 

---

https://projecteuler.net/problem=10

Utilizamos la función sum de Python para efectuar la suma de todos los números. El problema principal es tener una función generadora de números primos. La que se propone es una sencilla criba de Eratóstenes.

   1 import math
   2 
   3 def isPrime(n):
   4   if n == 2:
   5       return True
   6   if n < 2 or n % 2 == 0:
   7       return False;
   8   max = int(math.sqrt(n));
   9   for i in range(3, max+1, 2):
  10       if n % i == 0:
  11           return False
  12   return True
  13 
  14 
  15 def primeGenerator(n):
  16     """Generates prime numbers < n"""
  17     primes = [2]
  18     if n > 2:
  19         candidates = [c for c in range(3, n, 2)]
  20         for test in range(3, int(math.sqrt(n))+1, 2):
  21             for c in candidates:
  22                 if c > test and c % test == 0:
  23                     candidates.remove(c)
  24         primes += candidates
  25     return primes
  26 
  27 if __name__ == '__main__':
  28     primes = primeGenerator(2000000)
  29     print sum(primes)
  30