【KMP】Blue Jeans

Time Limit: 1000MS Memory Limit: 65536K
Total Submissions: 21885 Accepted: 9712

Description

The Genographic Project is a research partnership between IBM and The National Geographic Society that is analyzing DNA from hundreds of thousands of contributors to map how the Earth was populated. 

As an IBM researcher, you have been tasked with writing a program that will find commonalities amongst given snippets of DNA that can be correlated with individual survey information to identify new genetic markers. 

A DNA base sequence is noted by listing the nitrogen bases in the order in which they are found in the molecule. There are four bases: adenine (A), thymine (T), guanine (G), and cytosine (C). A 6-base DNA sequence could be represented as TAGACC. 

Given a set of DNA base sequences, determine the longest series of bases that occurs in all of the sequences.

Input

Input to this problem will begin with a line containing a single integer n indicating the number of datasets. Each dataset consists of the following components:

  • A single positive integer m (2 <= m <= 10) indicating the number of base sequences in this dataset.
  • m lines each containing a single base sequence consisting of 60 bases.

Output

For each dataset in the input, output the longest base subsequence common to all of the given base sequences. If the longest common subsequence is less than three bases in length, display the string “no significant commonalities” instead. If multiple subsequences of the same longest length exist, output only the subsequence that comes first in alphabetical order.

Sample Input

3
2
GATACCAGATACCAGATACCAGATACCAGATACCAGATACCAGATACCAGATACCAGATA
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
3
GATACCAGATACCAGATACCAGATACCAGATACCAGATACCAGATACCAGATACCAGATA
GATACTAGATACTAGATACTAGATACTAAAGGAAAGGGAAAAGGGGAAAAAGGGGGAAAA
GATACCAGATACCAGATACCAGATACCAAAGGAAAGGGAAAAGGGGAAAAAGGGGGAAAA
3
CATCATCATCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
ACATCATCATAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
AACATCATCATTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTT

Sample Output

no significant commonalities
AGATAC
CATCATCAT

题目大意:

就是求k个长度为60的字符串的最长连续公共子串,2<=k<=10

限制条件:

1、  最长公共串长度小于3输出   no significant commonalities

2、  若出现等长的最长的子串,则输出字典序最小的串

解题分析:

将第一个字串的所有子串枚举出来,然后用KMP快速判断该子串是否在所有主串中出现,如果都出现过,那么就按该子串的长度和字典序,不断更新答案,直到得到最终的最优解。

#include <cstdio>
#include <cstring>
#include <string>
#include <iostream> 
#include <algorithm>
using namespace std;
const int N=10+5;
const int M=60+5;

string s[N];
int nxt[M];

void getnext(string str,int len){
    int i=0,j=-1;
    nxt[0]=-1;
    while(i<len){
        if(j==-1||str[i]==str[j])
            nxt[++i]=++j;
        else j=nxt[j];
    }
}
bool kmp(string s1,int len1,string s2,int len2){
    int i=0,j=0;
    while(i<len1){
        if(j==-1||s1[i]==s2[j])
            ++i,++j;
        else j=nxt[j];
        if(j==len2)return true;
    }
    return false;
}
int main()
{
    ios::sync_with_stdio(false);
    cin.tie(0);   
    int T,n;
    cin>>T;
    while(T--){
        cin>>n;
        for(int i=0;i<n;i++)cin>>s[i];
        string ans="";
        for(int i=0;i<s[0].size();i++) //起点
        {
            for(int j=1;i+j<=s[0].size();j++) //长度
            {
                string res=s[0].substr(i,j);
                getnext(res,res.size());
                bool flag=0;
                for(int k=1;k<n;k++)
                    if(!kmp(s[k],s[k].size(),res,res.size()))
                        flag=1;
                if(!flag)
                {
                    if(ans.size()<res.size())ans=res;  //优先长度更长的公共子串
                    else if(ans.size()==res.size())ans=min(ans,res); //长度相同,按字典序排序
                }
            }
        }
        if(ans.size()<3)cout<<"no significant commonalities"<<endl;
        else cout<<ans<<endl;
    }
    return 0;
}

引用自:https://www.cnblogs.com/00isok/p/9439897.html

【EX_CRT】Strange Way to Express Integers

Description

Elina is reading a book written by Rujia Liu, which introduces a strange way to express non-negative integers. The way is described as following:Choose k different positive integers a1a2…, ak. For some non-negative m, divide it by every ai (1 ≤ i ≤ k) to find the remainder ri. If a1a2, …, ak are properly chosen, m can be determined, then the pairs (airi) can be used to express m.

继续阅读【EX_CRT】Strange Way to Express Integers