EularProject 29: a^b的归并排序问题

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于 2015-06-17 20:13:33 发布

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分类专栏： # Eular 文章标签： EularProject python Python3

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本文探讨了在特定范围内整数幂次组合的唯一值数量问题，并给出了一段高效的Python代码实现，用于计算2到100之间所有可能的a的b次幂的不重复数值。

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Distinct powers

Problem 29

Consider all integer combinations of a^b for 2 ≤ a ≤ 5 and 2 ≤ b ≤ 5:

2²=4, 2³=8, 2⁴=16, 2⁵=32
3²=9, 3³=27, 3⁴=81, 3⁵=243
4²=16, 4³=64, 4⁴=256, 4⁵=1024
5²=25, 5³=125, 5⁴=625, 5⁵=3125

If they are then placed in numerical order, with any repeats removed, we get the following sequence of 15 distinct terms:

4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024, 3125

How many distinct terms are in the sequence generated by a^b for 2 ≤ a ≤ 100 and 2 ≤ b ≤ 100?

python code:

aindex=[i for i in range(2,101)]
bindex=[2 for i in range(2,101)]
value=[i*i for i in range(2,101)]
count=0
while len(value)>0:
    pointValue=min(value)
    count+=1
    for i in range(len(value)-1,-1,-1):
        if value[i]==pointValue:
            if bindex[i]==100:
                del aindex[i],bindex[i],value[i]
            else:
                bindex[i]+=1
                value[i]*=aindex[i]
print(count)

time: <1s