CF17C Balance

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    • 64提交
  • 题目来源 CodeForces 17C
  • 评测方式 RemoteJudge
  • 标签 字符串 枚举,暴力 概率论,统计
  • 难度 提高+/省选-
  • 时空限制 3000ms / 128MB

题解

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    题意翻译

    【题目描述】 一个仅由a,b,c三种字符组成的字符串,可以对其进行如下两种操作:

    1. 选择两个相邻字符,将第一个字符替换成第二个。
    2. 选择两个相邻字符,将第二个字符替换成第一个。 这样,通过任意多次的操作,可以得到许多不同的串,为了追求字符的平衡, 我们要求a,b,c三种字符在字符串中出现的次数两两之差都不能大于1。

    你的任 务是,统计给定字符串通过任意多次的操作,能够得到的不同的平衡串的个数。

    【输入格式】

    输入文件包含2行。 第一行包含1个正整数n,表示字符串长度。 第二行包含1个长度为n的字符串。

    【输出格式】

    输出共1行,包含1个正整数,表示能够得到的平衡串的数量。由于答案可 能很大,因此输出时要对51123987取模。

    题目描述

    Nick likes strings very much, he likes to rotate them, sort them, rearrange characters within a string... Once he wrote a random string of characters a, b, c on a piece of paper and began to perform the following operations:

    • to take two adjacent characters and replace the second character with the first one,
    • to take two adjacent characters and replace the first character with the second one

    To understand these actions better, let's take a look at a string «abc». All of the following strings can be obtained by performing one of the described operations on «abc»: «bbc», «abb», «acc». Let's denote the frequency of a character for each of the characters a, b and c as the number of occurrences of this character in the string. For example, for string «abc»: | $ a $ | = 1, | $ b $ | = 1, | $ c $ | = 1, and for string «bbc»: | $ a $ | = 0, | $ b $ | = 2, | $ c $ | = 1.

    While performing the described operations, Nick sometimes got balanced strings. Let's say that a string is balanced, if the frequencies of each character differ by at most 1. That is $ -1<=|a|-|b|<=1 $ , $ -1<=|a|-|c|<=1 $ и $ -1<=|b|-|c|<=1 $ .

    Would you help Nick find the number of different balanced strings that can be obtained by performing the operations described above, perhaps multiple times, on the given string $ s $ . This number should be calculated modulo $ 51123987 $ .

    输入输出格式

    输入格式:

    The first line contains integer $ n $ ( $ 1<=n<=150 $ ) — the length of the given string $ s $ . Next line contains the given string $ s $ . The initial string can be balanced as well, in this case it should be counted too. The given string $ s $ consists only of characters a, b and c.

    输出格式:

    Output the only number — the number of different balanced strings that can be obtained by performing the described operations, perhaps multiple times, on the given string $ s $ , modulo $ 51123987 $ .

    输入输出样例

    输入样例#1: 复制
    4
    abca
    
    输出样例#1: 复制
    7
    
    输入样例#2: 复制
    4
    abbc
    
    输出样例#2: 复制
    3
    
    输入样例#3: 复制
    2
    ab
    
    输出样例#3: 复制
    1
    

    说明

    In the first sample it is possible to get $ 51 $ different strings through the described operations, but only $ 7 $ of them are balanced: «abca», «bbca», «bcca», «bcaa», «abcc», «abbc», «aabc». In the second sample: «abbc», «aabc», «abcc». In the third sample there is only one balanced string — «ab» itself.

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