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p061.py
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p061.py
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# -*- coding: utf-8 -*-
"""
Created on Mon Jul 6 15:51:53 2020
@author: zhixia liu
"""
"""
Project Euler 61: Cyclical figurate numbers
Triangle, square, pentagonal, hexagonal, heptagonal, and octagonal numbers are all figurate (polygonal) numbers and are generated by the following formulae:
Triangle P3,n=n(n+1)/2 1, 3, 6, 10, 15, ...
Square P4,n=n2 1, 4, 9, 16, 25, ...
Pentagonal P5,n=n(3n−1)/2 1, 5, 12, 22, 35, ...
Hexagonal P6,n=n(2n−1) 1, 6, 15, 28, 45, ...
Heptagonal P7,n=n(5n−3)/2 1, 7, 18, 34, 55, ...
Octagonal P8,n=n(3n−2) 1, 8, 21, 40, 65, ...
The ordered set of three 4-digit numbers: 8128, 2882, 8281, has three interesting properties.
The set is cyclic, in that the last two digits of each number is the first two digits of the next number (including the last number with the first).
Each polygonal type: triangle (P3,127=8128), square (P4,91=8281), and pentagonal (P5,44=2882), is represented by a different number in the set.
This is the only set of 4-digit numbers with this property.
Find the sum of the only ordered set of six cyclic 4-digit numbers for which each polygonal type: triangle, square, pentagonal, hexagonal, heptagonal, and octagonal, is represented by a different number in the set.
"""
func = {'triangle':lambda x: x*(x+1)/2, 'square': lambda x: x**2, 'pentagonal': lambda x: x*(3*x-1)/2,
'hexagonal': lambda x: x*(2*x-1), 'heptagonal': lambda x: x*(5*x-3)/2, 'octagonal': lambda x: x*(3*x-2)}
graph = dict()
for k,f in func.items():
l =[n for n in map(f,range(150)) if n>1000 and n<10000]
graph[k] = dict()
for n in map(f,range(150)):
if n<1000:
continue
if n>10000:
break
head = str(n)[:2]
tail = str(n)[2:4]
graph[k].setdefault(head,[]).append(tail)
def findcircle(levels,tail,head):
if levels == []:
if tail==head:
return [tail]
else:
print('No')
return None
for l in levels:
if tail not in graph[l]:
continue
# print('here')
for newtail in graph[l][tail]:
con = findcircle([newl for newl in levels if newl != l],newtail,head)
if con is not None:
return [tail]+con
return None
for head in graph['triangle']:
result = findcircle(['triangle','square','pentagonal','hexagonal','heptagonal','octagonal'],head,head)
if result is not None:
break
print(result)