Project Euler 32

题目

Pandigital products

We shall say that an $n$-digit number is pandigital if it makes use of all the digits $1$ to $n$ exactly once; for example, the $5$-digit number, $15234$, is $1$ through $5$ pandigital.

The product $7254$ is unusual, as the identity, $39\times 186=7254$, containing multiplicand, multiplier, and product is $1$ through $9$ pandigital.

Find the sum of all products whose multiplicand/multiplier/product identity can be written as a $1$ through $9$ pandigital.

HINT: Some products can be obtained in more than one way so be sure to only include it once in your sum.

解决方案

先枚举第 $1$ 个因数，后枚举第 $2$ 个因数。再判断两个因数和积拼接后的长度是否会大于 $9$.

代码

from itertools import count

N = 1000
c = "123456789"
st = set()
for i in range(1, N):
    for j in count(i + 1, 1):
        s = str(i) + str(j) + str(i * j)
        if len(s) > 9:
            break
        t = "".join((lambda x: (x.sort(), x)[1])(list(s)))
        if t == c:
            st.add(i * j)
ans = sum(st)
print(ans)