Project Euler：Problem 92 Square digit chains

A number chain is created by continuously adding the square of the digits in a number to form a new number until it has been seen before.

For example,

44 → 32 → 13 → 10 → 1 → 1

85 → 89 → 145 → 42 → 20 → 4 → 16 → 37 → 58 → 89

Therefore any chain that arrives at 1 or 89 will become stuck in an endless loop. What is most amazing is that EVERY starting number will eventually arrive at 1 or 89.

How many starting numbers below ten million will arrive at 89?

对于10000000以内的数，其各数位的平方和最大为9*9*7， 即9999999的下一位数应该为9*9*7

声明一个大小为567的bool数组，在该数最终到达89时标记为true

def nextnum(a):
    res=0
    while a!=0:
        tmp=a%10
        res=res+tmp*tmp
        a=a//10
    return res

res=0
num=[False for i in range(9*9*7+2)]

for i in range(9*9*7+1):
    nextn=nextnum(i)

    while nextn>i and nextn!=89:
        nextn=nextnum(nextn)

    if num[nextn]==True or nextn==89:
       res=res+1
       num[i]=True

for i in range(9*9*7+1,10000000):
       if num[nextnum(i)]==True:
           res=res+1

print('res = ',res)

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