Project Euler 45

problem

Triangular numbers, pentagonal numbers, and hexagonal numbers are generated as follows.

Triangular number Tn = n (n + 1) / 2 1, 3, 6, 10, 15, ... Pentagonal number Pn = n (3n-1) / 2 1, 5, 12, 22, 35, ... Hexagonal number Hn = n (2n-1) 1, 6, 15, 28, 45, ... It turns out that T285 = P165 = H143 = 40755.

Find the following triangular, pentagonal, and hexagonal numbers. http://odz.sakura.ne.jp/projecteuler/index.php?cmd=read&page=Problem%2045

Answer policy

Each term of a hexagonal number is an odd term of a triangular number, but I ignored this fact and thought about a mechanism that makes all terms equal for the time being.

Make a list ang_list by combining the generator gene and the value value of each angle.
The generator updates the value less than the maximum value ang_max until each value is equal. When the value is updated, set the flag to False.
If the value value is not updated for all the corner numbers, the value value of each corner number is equal to the maximum value ang_max, that is, the values of all the corner numbers are equal, so the process ends.

code

from mytools import *


def t(n):
  return n*(n+1)/2

def p(n):
  return n*(3*n-1)/2

def h(n):
  return n*(2*n-1)

@get_time
@main_start
def main():
  #(TRI_START,PEN_START,HEX_START) = (2, 2, 2) 
  (TRI_START,PEN_START,HEX_START) = (286, 166, 144) 
  MAX = 10**8

  tri_gene = ( t(n) for n in xrange(TRI_START, MAX))
  pen_gene = ( p(n) for n in xrange(PEN_START, MAX))
  hex_gene = ( h(n) for n in xrange(HEX_START, MAX))
  ang_list = [
              {'value': tri_gene.next(), 'gene': tri_gene},
              {'value': pen_gene.next(), 'gene': pen_gene},
              {'value': hex_gene.next(), 'gene': hex_gene}
             ]

  ang_max = max(ang_list[0]['value'], ang_list[1]['value'], ang_list[2]['value']) 
  flag = False  
  while not flag:
    flag = True
    for ang in ang_list:
      if ang['value'] < ang_max:
         ang['value'] = ang['gene'].next()
         flag = False
         if ang['value'] > ang_max:
           ang_max = ang['value']
  print ang_max

main()