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  • project euler 12 Highly divisible triangular number

    
    
    Highly divisible triangular number
    
    
    Problem 12
    
    
    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?
    
    
    
    


    def
    divisor(num,j): count1 = 1 count2 = 1 if num%2 == 0: lst1 = [num//2] lst2 = [num+1] else: lst1 = [(num+1)//2] lst2 = [num] for i in range(2,lst1[0]): if lst1[0] % i ==0: count1 += 1 # print(i) lst1.append(i) for i in range(2,lst2[0]): if lst2[0] % i ==0: count2 += 1 lst2.append(i) count = count1 + count2 + count1*count2 return count n = 1 import time print(time.time()) while True: j = n*(n+1)//2 if str(j)[-1] != '0': #print(n) n += 1 continue count = divisor(n,j) # print(j,n,count) n += 1 if count >= 500: print(j,n,count) break print(time.time()) 1462342495.953848 76576500 12376 575 1462342499.651143

    约4S

    对求因子的算法进行一点改进,能提高一半效率。

        for i in range(2,lst1[0]//2+1):
    
    
        for i in range(2,lst2[0]//2+1):


    >>> 
    1462414510.288464
    76576500 12376 575
    1462414512.207313
    

    再次对求因子进行改进,效率提高10倍!!

        for i in range(2,int(sqrt(lst1[0])+1)):
            if lst1[0] % i ==0:
                count1 += 2
    1462415389.778016
    76576500 12376 575
    1462415389.91842
    >>> 


     

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  • 原文地址:https://www.cnblogs.com/zhourong1104/p/5458243.html
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