POJ 1080 Human Gene Functions(LCS变形)

Human Gene Functions

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 17443		Accepted: 9707

DescriptionIt 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.InputThe 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.OutputThe 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

给你两个序列，A,G,C,T四个字母相同时值为5，其他的值如题中的图所示，不足的地方用空格去补，求最大可为多少。

如示例1 AGTGATG 与 GTTAG (空格用 '_' 表示)

AGTGATG

_GTTA_G

所以最后的结果为  (-3)+5+5+(-2)+5+(-1) +5=14

其实就是对LCS的一个利用，对于序列X( x1 ,x2 , x3, ....., xn  )  和序列 Y( y1 , y2 , y3,...., ym ) , dp[xn][ym] 来储存最后的结果

思考下就可以发现 dp[xn][ym] 可以由三种方式得到

1、 dp[xn][ym] = dp[xn-1][ym] + score( xn, '_' ) ;

2、 dp[xn][ym] = dp[xn][ym-1] + score( '_', ym) ;

3、 dp[xn][ym] = dp[xn-1][ym-1] + score( xn, ym) ;

对于dp[xn][ym] , 我们可以理解为在它的前一状态dp[xn-1][ym-1]时加上sorce(xn,ym)的值，或者是它的前一状态dp[xn][ym-1]时，序列X补上一个'_',序列Y加进去ym, 即加上score('_',ym)

同理dp[xn][ym]是dp[xn-1][ym] 是加上序列X中的xn和Y中的'_'所得

最后的结果就是这三个值中的最大值

#include <iostream>#include <cstdio>#include <cstring>#include <stdlib.h>using namespace std;const int N = 110;int dp;int score(char a,char b){    if((a=='A' && b=='C') || (a=='C' && b=='A'))        return -1;    if((a=='A' && b=='G') || (a=='G' && b=='A'))        return -2;    if((a=='A' && b=='T') || (a=='T' && b=='A'))        return -1;    if((a=='A' && b==' ') || (a==' ' && b=='A'))        return -3;    if((a=='C' && b=='G') || (a=='G' && b=='C'))        return -3;    if((a=='C' && b=='T') || (a=='T' && b=='C'))        return -2;    if((a=='C' && b==' ') || (a==' ' && b=='C'))        return -4;    if((a=='G' && b=='T') || (a=='T' && b=='G'))        return -2;    if((a=='G' && b==' ') || (a==' ' && b=='G'))        return -2;    if((a=='T' && b==' ') || (a==' ' && b=='T'))        return -1;    if(a==b)        return 5;}int main(){    int T;    scanf("%d",&T);    while(T--)    {        int n,m;        char s1,s2;        scanf("%d",&n);        for(int i=1; i<=n; i++)            cin>>s1[i];        scanf("%d",&m);        for(int i=1; i<=m; i++)            cin>>s2[i];        memset(dp,0,sizeof(dp));        char t=' ';        dp[0][0]=0;        for(int i=1; i<=n; i++)            dp[i][0]=dp[i-1][0] + score(s1[i],t);     //WA快哭了，初始化没考虑好        for(int i=1; i<=m; i++)            dp[0][i]=dp[0][i-1] + score(t,s2[i]);        for(int i=1; i<=n; i++)            for(int j=1; j<=m; j++)            {                int x1 = dp[i-1][j-1] + score(s1[i],s2[j]);                int x2 = dp[i-1][j] + score(s1[i],t);                x2=max(x1,x2);                int x3 = dp[i][j-1] + score(t,s2[j]);                dp[i][j]=max(x2,x3);            }        printf("%d\n",dp[m]);    }    return 0;}