Swapping Digits

本文探讨了一个有趣的数学问题:如何通过交换字符串中两个数字的位置来获得最小可能的整数,同时确保新字符串仍然表示一个有效的正整数且不包含前导零。文章详细解释了输入输出格式,并给出了示例。

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Description

Let S be a string containing the digits of a (possibly large) positive integer. For example, S="1147" represents the integer 1147. S will not have any leading zeros.

You are allowed to swap one pair of digits in the given number. In other words, you may choose a pair of distinct indices i and j, and swap the characters S[i] and S[j]. Note that you may also leave the original number unchanged. The new string must again describe a valid positive integer, i.e., it must not have any leading zeros.

Your task is to find out the string that represents the smallest possible integer that can be obtained.

Input

The input begins with a line containing an integer T (T<=150), which indicates the number of test cases. Each case contains a string S. S contains only digits (‘0’-‘9’), and its length is between 2 and 50, inclusive.

Output

For each case, output the smallest possible integer in a line.

Sample Input
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459693561549172751410234
Sample Output
56913569149172755410234

Problem Source: Training 3


A-1 Intersection Set of Prime Factors(c++题解,禁止有注释,请严格按找题目要求,输出末尾没有空格) 分数 20 作者 陈越 单位 浙江大学 Given a positive integer n. Select two distinct digits from the decimal repersentation(十进制表示)of n, we obtain another integer m. What is the size of the intersection set(交集)of the prime factors of n and m? For example, given n=623457198, its prime factor set is A = {2, 3, 7, 13, 380621}. Swapping 2 and 9 gives us m=693457128, of which the prime factor set is B = {2, 3, 7, 13, 109, 971}. Then the intersection set of A and B is {2, 3, 7, 13}, with 4 factors. Input Specification: Each input file contains one test case, which gives a positive integer n (10<n≤10 9 ). It is guaranteed that there are at least 2 distinct digits in n. Output Specification: Swap any pair of digits in n to obtain m, you are supposed to find the m with the largest intersection set of the prime factors of n and m. Output in a line the number of the prime factors in the intersection set, together with m. The numbers must be separated by 1 space, and there must be no extra space at the beginning or the end of the line. In case such an m is not unique, output the one with the smallest value. Sample Input: 623457198 Sample Output: 4 123457698 Hint: There are two m's with 4 common factors. Besides the one given in the problem description, we can also swap 6 and 1 to obtain 123457698. This number has a prime factor set {2, 3, 7, 13, 23, 29, 113}, and so the intersection set is also {2, 3, 7, 13}. This number is in the ouput because it is smaller than 693457128. 代码长度限制 16 KB 时间限制 400 ms 内存限制 64 MB 栈限制 8192 KB
最新发布
08-11
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