PAT 甲级 1023 Have Fun with Numbers (20 分)（permutation是全排列题目没读懂）

1023 Have Fun with Numbers (20 分)

Notice that the number 123456789 is a 9-digit number consisting exactly the numbers from 1 to 9, with no duplication. Double it we will obtain 246913578, which happens to be another 9-digit number consisting exactly the numbers from 1 to 9, only in a different permutation. Check to see the result if we double it again!

Now you are suppose to check if there are more numbers with this property. That is, double a given number with k digits, you are to tell if the resulting number consists of only a permutation of the digits in the original number.

Input Specification:

Each input contains one test case. Each case contains one positive integer with no more than 20 digits.

Output Specification:

For each test case, first print in a line "Yes" if doubling the input number gives a number that consists of only a permutation of the digits in the original number, or "No" if not. Then in the next line, print the doubled number.

Sample Input:

1234567899


Sample Output:

Yes
2469135798

解题思路：
给定一个数，乘以2之后，各个数位的出现次数，是否与乘之前是否相同，相同输出Yes，否认输出No，然后下一行打印出乘2之后的各个数位。
这个题目是属于超大数运算的类型，题目给出的最高数位是20位，那么即便是用最高的unsigned long long 也会面临溢出的情况，所以输入和输出，只能用string，诸位乘2，然后再记录每一位出现的次数，相比较就行。

大数乘法！全排列的意思是：各个数字出现的次数分别相同！

AC代码：