DNA sequence（映射+BFS）

时间 2019-11-08

原文原文链接

Problem Description

The twenty-first century is a biology-technology developing century. We know that a gene is made of DNA. The nucleotide bases from which DNA is built are A(adenine), C(cytosine), G(guanine), and T(thymine). Finding the longest common subsequence between DNA/Protein sequences is one of the basic problems in modern computational molecular biology. But this problem is a little different. Given several DNA sequences, you are asked to make a shortest sequence from them so that each of the given sequence is the subsequence of it.

For example, given "ACGT","ATGC","CGTT" and "CAGT", you can make a sequence in the following way. It is the shortest but may be not the only one.

Input

The first line is the test case number t. Then t test cases follow. In each case, the first line is an integer n ( 1<=n<=8 ) represents number of the DNA sequences. The following k lines contain the k sequences, one per line. Assuming that the length of any sequence is between 1 and 5.

Output

For each test case, print a line containing the length of the shortest sequence that can be made from these sequences.

SampleInput

1
4
ACGT
ATGC
CGTT
CAGT

SampleOutput

8

题意就是给你几个DNA序列，要求找到一个序列，使得全部序列都是它的子序列（不必定连续）。
直接搜MLE、TLE、RE，因此不能直接搜索，通常处理这种序列问题，都是把序列映射到整数或其余便于处理的东西上。
题目还说了每一个DNA的序列长度不会超过5，因此咱们能够按位处理映射到一个整数上，并且题目只须要咱们输出最短的序列长度，因此咱们也没必要去映射字符，映射长度便够了。
最多8个字符，每一个字符1-5长度，因此最大数为6^8。好为何是6^8，不明明是5^8么，这个我暂时先不解释，我加在了代码注释里。
代码：

  1 #include <iostream>
  2 #include <string>
  3 #include <cstdio>
  4 #include <cstdlib>
  5 #include <sstream>
  6 #include <iomanip>
  7 #include <map>
  8 #include <stack>
  9 #include <deque>
 10 #include <queue>
 11 #include <vector>
 12 #include <set>
 13 #include <list>
 14 #include <cstring>
 15 #include <cctype>
 16 #include <algorithm>
 17 #include <iterator>
 18 #include <cmath>
 19 #include <bitset>
 20 #include <ctime>
 21 #include <fstream>
 22 #include <limits.h>
 23 #include <numeric>
 24 
 25 using namespace std;
 26 
 27 #define F first
 28 #define S second
 29 #define mian main
 30 #define ture true
 31 
 32 #define MAXN 1000000+5
 33 #define MOD 1000000007
 34 #define PI (acos(-1.0))
 35 #define EPS 1e-6
 36 #define MMT(s) memset(s, 0, sizeof s)
 37 typedef unsigned long long ull;
 38 typedef long long ll;
 39 typedef double db;
 40 typedef long double ldb;
 41 typedef stringstream sstm;
 42 const int INF = 0x3f3f3f3f;
 43 
 44 int t,n;
 45 map<int,int>vis;
 46 char s[10][10];    //保存序列
 47 int len[10];    //保存每一个序列的长度
 48 int p[10] = {1,6,36,216,1296,7776,46656,279936,1679616,10077696};    //6的k次方表
 49 char temp[4]={'A','C','G','T'};
 50 
 51 struct node{
 52     int step;    //长度
 53     int st;    //也就是映射数
 54     node(){}
 55     node(int _step, int _st):step(_step),st(_st){}
 56 };
 57 
 58 int bfs(int res){
 59     vis.clear();
 60     queue<node>q;
 61     q.push(node(0,0));
 62     vis[0] = 1;
 63     while(!q.empty()){
 64         node nxt,k = q.front();
 65         q.pop();
 66         if(k.st == res){    //当映射等于结果时 返回长度
 67             return k.step;
 68         }
 69         for(int i = 0; i < 4; i++){
 70             nxt.st = 0;
 71             nxt.step = k.step+1;
 72             int tp = k.st;
 73             for(int j = 1; j <= n; j++){
 74                 int x = tp%6;    //获得位数
 75                 tp /= 6;
 76                 if(x == len[j] || s[j][x+1] != temp[i]){    //判断字符是否匹配
 77                     nxt.st += x*p[j-1];
 78                 }
 79                 else{
 80                     nxt.st += (x+1)*p[j-1];
 81                 }
 82             }
 83             if(vis[nxt.st] == 0){    //标记是否已经搜过
 84                 q.push(nxt);
 85                 vis[nxt.st] = 1;
 86             }
 87         }
 88     }
 89 }
 90 
 91 int main(){
 92     ios_base::sync_with_stdio(false);
 93     cout.tie(0);
 94     cin.tie(0);
 95     cin>>t;
 96     while(t--){
 97         cin>>n;
 98         int res = 0;
 99         for(int i = 1; i <= n; i++){    //由于数组从0开始计数，但咱们映射以及后面操做都是基于位置，因此从1开始
100             cin>>s[i]+1;    //同理从一开始
101             len[i] = strlen(s[i]+1);
102             res += len[i]*p[i-1];    //这也就是为何是6^8，由于咱们是从1开始有5个状态而不是0
103         }
104         cout << bfs(res) <<endl;
105     }
106     return 0;
107 }

因此这题你非要从0位置搞，弄5^8确实没错，也能够作出来，可是操做会繁琐不少，还不如从方便的角度多加一个长度。node

这道题的难度就是不知道怎么入手，即便知道转换处理也不知道该如何转换以及如何搜索，这里咱们避免了去从字符开始搜索，而是直接基于长度搜。ios

值得一提的是，我问了队友后，他们表示这道题作法不少，还能够用IDA*算法或者启发式搜索，甚至不用搜索用AC自动机加矩阵也能够作。但这些作法都是基于字符去搜索的，也不能说谁好谁坏，只是咱们的思惟就不同了，不少题目其实都不止一种解法，多想一想，颇有用的。至于其余作法我也就懒得作了（实际上是不会23333）算法