EularProject 29: a^b的归并排序问题

Distinct powers

Problem 29

Consider all integer combinations of ab 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 ab for 2 ≤ a ≤ 100 and 2 ≤ b ≤ 100?

Answer: 9183 Completed on Wed, 17 Jun 2015, 13:10

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