USACO 1.2.5 Dual Palindromes 双重回文数

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本博客介绍了一个算法，用于查找大于给定值且在两种或两种以上进制下为回文数的十进制数，涉及双进制转换与回文数判断。

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Dual Palindromes
Mario Cruz (Colombia) & Hugo Rickeboer (Argentina)

A number that reads the same from right to left as when read fromleft to right is called a palindrome. The number 12321 is a palindrome;the number 77778 is not. Of course, palindromes have neither leadingnor trailing zeroes, so 0220 is not a palindrome.

The number 21 (base 10) is not palindrome in base 10, but thenumber 21 (base 10) is, in fact, a palindrome in base 2 (10101).

Write a program that reads two numbers (expressed in base 10):

N (1 <= N <= 15)
S (0 < S < 10000)

and then finds and prints (in base 10) the first N numbers strictlygreater than S that are palindromic when written in two or morenumber bases (2 <= base <= 10).

Solutions to this problem do not require manipulating integerslarger than the standard 32 bits.

PROGRAM NAME: dualpal

INPUT FORMAT

A single line with space separated integers N and S.

SAMPLE INPUT (file dualpal.in)

3 25

OUTPUT FORMAT

N lines, each with a base 10 number that is palindromic when expressedin at least two of the bases 2..10. The numbers should be listedin order from smallest to largest.

SAMPLE OUTPUT (file dualpal.out)

26
27
28

解题思路：

该题要求我们，编一个程序，读入两个十进制数N (1 <= N <= 15)、S (0 < S < 10000)，然后找出前N个满足大于S且在两种或两种以上进制（二进制至十进制）上是回文数的十进制数，并输出。其基本思路仍然等同与前一道回文数问题，所不同的是，我们要转换的进制中可能会有10--20进制，这就会用到9以上数字Ａ、Ｂ、Ｃ......显然，整型数组已不能满足，那么我们就要用字符数组，而余数也处理成字符型。同样满足的数据要有两种或两种以上进制满足是回文数，同样从2进制转换到20进制依次进行，用一个变量记录满足情况，若大于2则跳出循环并输出。双重循环嵌套，复杂度Ｏ（nlogMn）。

代码如下：