poj 1080 Human Gene Functions（lcs，较难）

Human Gene Functions

Description

It is well known that a human gene can be considered as a sequence, consisting of four nucleotides, which are simply denoted by four letters, A, C, G, and T. Biologists have been interested in identifying human genes and determining their functions, because these can be used to diagnose human diseases and to design new drugs for them.

A human gene can be identified through a series of time-consuming biological experiments, often with the help of computer programs. Once a sequence of a gene is obtained, the next job is to determine its function. 
One of the methods for biologists to use in determining the function of a new gene sequence that they have just identified is to search a database with the new gene as a query. The database to be searched stores many gene sequences and their functions – many researchers have been submitting their genes and functions to the database and the database is freely accessible through the Internet.

A database search will return a list of gene sequences from the database that are similar to the query gene. 
Biologists assume that sequence similarity often implies functional similarity. So, the function of the new gene might be one of the functions that the genes from the list have. To exactly determine which one is the right one another series of biological experiments will be needed.

Your job is to make a program that compares two genes and determines their similarity as explained below. Your program may be used as a part of the database search if you can provide an efficient one. 
Given two genes AGTGATG and GTTAG, how similar are they? One of the methods to measure the similarity 
of two genes is called alignment. In an alignment, spaces are inserted, if necessary, in appropriate positions of 
the genes to make them equally long and score the resulting genes according to a scoring matrix.

For example, one space is inserted into AGTGATG to result in AGTGAT-G, and three spaces are inserted into GTTAG to result in –GT--TAG. A space is denoted by a minus sign (-). The two genes are now of equal 
length. These two strings are aligned:

AGTGAT-G 
-GT--TAG

In this alignment, there are four matches, namely, G in the second position, T in the third, T in the sixth, and G in the eighth. Each pair of aligned characters is assigned a score according to the following scoring matrix. 

denotes that a space-space match is not allowed. The score of the alignment above is (-3)+5+5+(-2)+(-3)+5+(-3)+5=9.

Of course, many other alignments are possible. One is shown below (a different number of spaces are inserted into different positions):

AGTGATG 
-GTTA-G

This alignment gives a score of (-3)+5+5+(-2)+5+(-1) +5=14. So, this one is better than the previous one. As a matter of fact, this one is optimal since no other alignment can have a higher score. So, it is said that the 
similarity of the two genes is 14.

Input

The input consists of T test cases. The number of test cases ) (T is given in the first line of the input file. Each test case consists of two lines: each line contains an integer, the length of a gene, followed by a gene sequence. The length of each gene sequence is at least one and does not exceed 100.

Output

The output should print the similarity of each test case, one per line.

Sample Input

2
7 AGTGATG
5 GTTAG
7 AGCTATT
9 AGCTTTAAA 

Sample Output

14
21 

题目大意是就是求两基因的相似度，先要在每个基因对中加入若干空格，然后再依次加上匹配度，详见上表，则相似度就是最大的匹配度和

例如对于测试数据一，加上空格则变成

AGTGAT--G

-GT----TAG

则相似度就是（-3）+5+5+（-2）+5+（-1）+5=14，可以证明这是最大的，故为所求

此题为dp,详见代码

 1 #include<iostream>
 2 #include<cstdlib>
 3 #include<cstdio>
 4 #include<cstring>
 5 #include<algorithm>
 6 #include<cmath>
 7 using namespace std;
 8 int map[][5]={    {5,-1,-2,-1,-3},
 9                 {-1,5,-3,-2,-4},
10                 {-2,-3,5,-2,-2},
11                 {-1,-2,-2,5,-1},
12                 {-3,-4,-2,-1,0} };
13 char str1[105];
14 char str2[105];
15 int f[256];
16 bool vis[105][105];
17 int ans[105][105];
18 int DFS ( int x , int y )
19 {
20
21     int i ;
22     int xy=0;
23     if ( x == -1 )
24     {
25         for ( i = 0 ; i <= y ; i ++ )
26             xy += map[str2[i]][4] ;
27         return xy ;
28     }
29     if ( y == -1 )
30     {
31         for ( i = 0 ; i <= x ; i ++ )
32             xy += map[str1[i]][4] ;
33         return xy ;
34     }
35     if ( vis[x][y] )
36         return ans[x][y] ;
37     vis[x][y]=true;
38     ans[x][y] = max ( DFS ( x - 1 , y - 1 ) + map[str1[x]][str2[y]] , max ( DFS(x,y-1)+map[4][str2[y]] , DFS(x-1,y)+map[str1[x]][4] )) ;
39     return ans[x][y] ;
40 }
41 int main()
42 {
43     f[‘A‘]=0;
44     f[‘C‘]=1;
45     f[‘-‘]=4;
46     f[‘G‘]=2;
47     f[‘T‘]=3;
48     int t ;
49     cin >> t ;
50     while ( t -- )
51     {
52         int i , j ;
53         int len1 , len2 ;
54         cin >> len1 >> str1 ;
55         for ( i = 0 ; i < len1 ; i ++ )
56             str1[i]=f[str1[i]];
57
58         cin >> len2 >> str2 ;
59         for ( i = 0 ; i < len2 ; i ++ )
60             str2[i]=f[str2[i]];
61         memset ( vis , 0 , sizeof ( vis ) ) ;
62         cout << DFS(len1-1,len2-1) << endl ;
63     }
64     return 0;
65 }

 1 #include<cstdio>
 2 #include<cstdlib>
 3 #include<iostream>
 4 #include<algorithm>
 5
 6 using namespace std;
 7 /*dp，poj1080*/
 8
 9 int dp[105][105];//动态规划数据存放
10  int map[105][105];//用来存放原始数据
11
12  void map_init()
13  {
14      map[‘A‘][‘A‘]=map[‘C‘][‘C‘]=map[‘G‘][‘G‘]=map[‘T‘][‘T‘]=5;
15      map[‘A‘][‘C‘]=map[‘C‘][‘A‘]=map[‘A‘][‘T‘]=map[‘T‘][‘A‘]=map[‘T‘][‘ ‘]=map[‘ ‘][‘T‘]=-1;
16      map[‘A‘][‘G‘]=map[‘G‘][‘A‘]=map[‘C‘][‘T‘]=map[‘T‘][‘C‘]=map[‘G‘][‘T‘]=map[‘T‘][‘G‘]=map[‘G‘][‘ ‘]=map[‘ ‘][‘G‘]=-2;
17      map[‘A‘][‘ ‘]=map[‘ ‘][‘A‘]=map[‘G‘][‘C‘]=map[‘C‘][‘G‘]=-3;
18      map[‘C‘][‘ ‘]=map[‘ ‘][‘C‘]=-4;
19  }
20
21  int max_X3(int a,int b,int c)
22  {
23      if(a>b)
24      {
25          if(a>c)
26              return a;
27          else
28              return c;
29      }
30      else
31      {
32          if(b>c)
33              return b;
34          else
35              return c;
36      }
37  }
38
39  int    main()
40  {
41      int y;//全局次数
42      int i,j;//循环变量
43      int a,b;//用户输入
44      char str1[105];
45      char str2[105];
46
47      //初始化
48      map_init();
49
50      cin>>y;
51      while (y--)
52      {
53          scanf("%d %s",&a,str1);
54          scanf("%d %s",&b,str2);
55
56          //初始化第一行第一列
57          dp[0][0]=0;
58          for (i = 0; i < a; i++)
59              dp[0][i+1] = dp[0][i] + map[str1[i]][‘ ‘];
60
61          for (j = 0; j < b; j++)
62              dp[j+1][0] = dp[j][0] + map[str2[j]][‘ ‘];
63
64          for (i = 1; i <= a; i++)
65          {
66              for (j = 1; j <= b; j++)
67              {
68                  dp[j][i] = max_X3(dp[j-1][i-1]+map[str2[j-1]][str1[i-1]],
69                      dp[j-1][i]+map[str2[j-1]][‘ ‘],
70                      dp[j][i-1]+map[str1[i-1]][‘ ‘]);
71              }
72          }
73
74          cout<<dp[b][a]<<endl;
75      }
76      return 0;
77  }