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Project Euler, Problem #12, Python - Pastebin.com
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Project Euler, Problem #12, Python
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- # The sequence of triangle numbers is generated by adding the natural
- # numbers. So the 7th triangle number would be 1 + 2 + 3 + 4 + 5 + 6 +
- # 7 = 28. The first ten terms would be: 1, 3, 6, 10, 15, 21, 28, 36,
- # 45, 55, ... Let us list the factors of the first seven triangle
- # numbers: 1: 1; 3: 1, 3; 6: 1, 2, 3, 6; 10: 1, 2, 5, 10; 15: 1, 3, 5,
- # 15; 21: 1, 3, 7, 21; 28: 1, 2, 4, 7, 14, 28 We can see that 28 is
- # the first triangle number to have over five divisors. What is the
- # value of the first triangle number to have over five hundred
- # divisors?
- # Version 1: slightly shorter and faster
- cntr = 2
- ctn = 1
- dn = 0
- while True:
- ctn += cntr
- md = int(ctn ** 0.5)
- if md < ctn ** 0.5:
- cv = 0
- else:
- cv = 1
- if ctn % 2 == 0:
- dn = sum([2 if ctn % x == 0 else 0 for x in range(1, md + 1)])
- else:
- dn = sum([2 if ctn % x == 0 else 0 for x in range(1, md + 1, 2)])
- if dn - cv > 500:
- break
- dn = 0
- cntr += 1
- print(ctn)
- # 76576500
- # 24752 function calls in 9.839 seconds
- # Version 2
- cntr = 2
- ctn = 1
- dn = 0
- while True:
- ctn += cntr
- md = int(ctn ** 0.5)
- if md < ctn ** 0.5:
- cv = 0
- else:
- cv = 1
- if ctn % 2 == 0:
- for d in range(1, md + 1):
- if ctn % d == 0:
- dn += 2
- else:
- for d in range(1, md + 1, 2):
- if ctn % d == 0:
- dn += 2
- if dn - cv > 500:
- break
- dn = 0
- cntr += 1
- print(ctn)
- # 76576500
- # 12376 function calls in 10.944 seconds
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