Euler/problem_044_02.py at master · dsmdavid/Euler · GitHub

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##Pentagonal numbers are generated by the formula,
##Pn=n(3n−1)/2. The first ten pentagonal numbers are:
##
##1, 5, 12, 22, 35, 51, 70, 92, 117, 145, ...
##
##It can be seen that P4 + P7 = 22 + 70 = 92 = P8.
##However, their difference, 70 − 22 = 48, is not pentagonal.
##
##Find the pair of pentagonal numbers, Pj and Pk,
##for which their sum and difference are pentagonal and
##D = |Pk − Pj| is minimised; what is the value of D?


import numpy as np
import itertools
import math
import time
import eulertools as et


def createpent(n):
    pn = n * (3 * n - 1) / 2
    return pn


## 1. Find the first couple of pentagonal numbers whose difference is also
## a pentagonal number.
## 1.a. Create a list of pentagonal numbers.
## 1.b. Create the next pentagonal number.
## 1.c. Test if the new pentagonal number, minus any of the pentagonal numbers
## in the list yields a pentagonal number, if so, add it to a set of combinations.

def euler44():
    setpent = set()
    listpent = set()
    listdif = []
    dictdif = {}
    proceed = 1
    current_n = 1
    while proceed == 1:
        #1.b
        pn = createpent(current_n)
        listpent.add(pn)
##        print(listpent)
##        input("a")
        #1.c
##        print(current_n)
##        if pn == 92:
##            input(92)
        for i in listpent:
##            print(i)
            try:
                dif = pn - i

##                print("dif " + str(dif))
                if dif in listpent:
##                    print(dif,pn,i,current_n)
##                    sv = frozenset[pn, i, dif]
##                    print(sv)
                    if isPentagonal(pn+i) != 3:
##                            setpent.add(sv)
##                            print(setpent)
                        print(dif, pn, i)
##                        input("b " + str(current_n))
                        proceed = 0
                else:
                    pass
            except:
                pass
        current_n += 1
##        if current_n % 1000 == 0:
##            print(current_n)
##        input("c " + str(current_n))
##        listpent
##        input("listpent")

        #print(current_n, listpent)


def isPentagonal(number):

    conditionplus = (1+np.sqrt(1+24*number))/6
##    conditionminus = (1-np.sqrt(1+24*number))/6
    if int(conditionplus) == conditionplus:
        m = 1

##    elif int(conditionminus) == conditionminus:
##        m = 2

    else:
        m = 3

    return m


##def convertfiletolist(filename):
##    f = open(filename)
##    lw = f.read().replace('"',"").split(",")
##    f.close()
##    return lw
##
##def maxvalue(listw):
##    maxl = 0
##    maxv = ord("Z") - 64
##    for i in listw:
##        maxl = max(maxl, len(i))
##    return maxl*maxv
##
##def valueword(word):
##    value = 0
##    for i in word:
##        value += ord(i)
##    value = value -(64*len(word))
####    print("value = ", value, end = " ")
##    return value
##
##def evaluatelist(lw,st):
##    count = 0
##    for i in lw:
####        print(i, end = " ")
##        vw = valueword(i)
####        print(vw, end = "\n")
##        if vw in st:
##            count +=1
####            print("new", i, vw, "\n")
##    return count
##
##def evaluaten(n,lp):
##    sn = str(n)
##    c = 0
##    d = 0
##    for i in range(2,9):
##        if int(sn[i-1:i+2]) % lp[d] == 0:
##            c += 0
##        else:
##            c += 1
##        d += 1
##
##    if c == 0: return True
##    else: return False
##
##def euler43():
##    """Generates listofprimes < 18, evaluates permutations 0-9 for Euler43"""
##
##    lp = et.primesfrom2to(18)
##    print(lp)
##    s = ""
##    for x in range(0,10):
##        s += str(x)
##
##
##
##    listes=[]
##    lv = []
##    for n in itertools.permutations(s):
##        sn = createseq(n)
##        if evaluaten(sn,lp):
##            listes.append(int(sn))
##
##
##    print(sum(listes))
##    print(listes[1])
##    print(evaluate(str(listes[1]),lp))
##
####
####print(evaluaten("1406357289",et.primesfrom2to(18)))
####input("result")


def main():
    start = time.time()
    euler44()
##    print(evaluatelist(["SKY","REGIONAL"], triangles(1000)))
##    print(valueword("ABOUT"))
##    print(valueword("SKY"))
    end = time.time()
    print(end-start)


main()