2021ccpc网络赛 Nun Heh Heh Aaaaaaaaaaa

字符串子序列与排列组合

最新推荐文章于 2021-11-25 23:37:35 发布

原创最新推荐文章于 2021-11-25 23:37:35 发布 · 455 阅读

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#动态规划

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该博客主要讨论字符串子序列的计数问题，特别是寻找具有特定前缀和后缀（非零数字）的子序列数量。作者介绍了动态规划（DP）方法来解决这个问题，并给出了代码实现，特别强调了在状态转移过程中防止整型溢出的问题。博客内容涉及字符串处理、动态规划和组合数学。

Problem Description

Vasily Tadokorov is a stringologist. He thinks a string is fragrant if it can be divided into two parts — nunhehheh as the prefix and a number of (excluding 0) a as the suffix. For example, nunhehhehaaaaaa is fragrant, but nunhehheh and nunhehhehoooaaa are not fragrant.

Today Vasily Tadokorov has some strings consisting of lowercase English letters. For each string, he wants to know how many subsequences of this string are fragrant. A string a is a subsequence of a string b if a can be obtained from b by deletion of several (including 0) characters.

Input

The first line contains an integer T (1≤T≤1000), denoting the number of strings.

Each of the next T lines contains a string S (1≤|S|≤105) consisting of lowercase English letters.

The total length of the strings in the input will not exceed 106.

Output

For each of the given T strings, output the answer modulo 998244353.

题解

dp[j][i] 表示s串中0 ~ i - 1中子序列为 nunhehheh的0 ~ j - 1的个数，对于当前位置i求得新增加的子序列个数（dp[9][i] - dp[9][i]) * i后面a的排列组合(2^(pre[s.size()] - pre[i]) - 1, (pre[s.size()] - pre[i])个 'a’每个选或者不选的方案 - 都不选的方案）

注意dp状态转移过程会爆long long 要边转移边取模,差值也要取模如
( dp[9][i] - dp[9][i - 1] + mod )%mod;，比赛的时候因为忘了这个wa惨了

code

#include <bits/stdc++.h>
using namespace std;
#define IOS std::ios_base::sync_with_stdio(false), std::cin.tie(0), std::cout.tie(0);

typedef long long ll;


ll mod = 998244353;
ll qq(ll b){
    ll ans = 1;
    ll a = 2;
    while(b > 0){
        if(b&1){
            ans = (ans * a) % mod;
        }
        a = (a * a)%mod;
        b >>= 1;
    }
    return ans;
}

string s,t = "nunhehheh";
             
const int N = 1E5 + 10;
ll dp[11][N];
ll pre[N];

int main()
{   
    IOS
    int T;  cin >> T;
    for(int k = 1; k <= T; ++k){
        cin >> s;
        int sz = s.size(),tz = t.size();
        for(int i = 1; i <= sz; ++i){
            pre[i] = 0;
            if(s[i-1] == 'a')
                pre[i] = 1;
            pre[i] += pre[i - 1];
        }

        ll ans = 0;
        memset(dp,0,sizeof dp);
      
        for(int i = 0; i <= sz; ++i)
            dp[0][i] = 1;
        for(int i = 1; i <= sz; ++i)
        {
            for(int j = 1; j <= tz; ++j)
            {
                /* 根据是否相等执行不同操作，因为此时需要匹配t[0 : j]，而只有相等是才可以允许只匹配t[0 : j-1] */
                if(s[i - 1] == t[j - 1])
                    dp[j][i] = (dp[j - 1][i - 1] + dp[j][i-1])%mod;
                else
                    dp[j][i] = dp[j][i-1];
            }
            ll x = pre[sz] - pre[i];
            ll y = ( dp[tz][i] - dp[tz][i - 1] + mod )%mod;
            y%=mod;
            if( y && x){    
              
                y =  y * ( ( qq(x) - 1 + mod )%mod ) % mod;
                ans += y;
                ans %= mod;
            }
            
        }
        cout << ans << '\n';

    }
      
      return 0;
}