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)