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
Source
這是一道較爲容易的動態規劃問題，假設前後兩個字符串cgene1和cgene2的長度分別爲igene1和igene2，令ic[i][j]表示字符串cgene1的前i個字符和字符串cgene2的前j個字符的最大相似度，1≤i≤igen1且1≤j≤igen2, 則必定有如下關係：
ic[i][j] = max(ic[i-1][j-1]+iCost[igene1[i]][igene2[j]], ic[i][j-1]+iCost[4][igene2[j]],ic[i-1][j]+iCost[igene1[i][4]);
iCost是題目中給定的得分矩陣(scoring matrix)。根據上述公式，可以容易的求得需要的結果ic[igene1][igene2]。
在初始化的時候，有一點需要特別注意：因爲這道題目，類似於一道求取兩字符串最大公共子串的題目，在剛開始做這題目時，作者想當然地進行了如下初始化：
for(i = 1; i <= igene1; i ++) ic[i][0] = ０;
for(i = 1; i <= igene2; i ++) ic[0][i] = ０;
後來，仔細想想，這是完全錯誤的，因爲當一某個字符串中沒有字符與另一字符串中的字符對應時，其得分（代價）是不爲零的。因此，需要進行如下初始化：
for(i = 1; i <= igene1; i ++) ic[i][0] = ic[i-1][0] + iCost[CharToInt(cgene1[i])][4];
for(i = 1; i <= igene2; i ++) ic[0][i] = ic[0][i-1] + iCost[4][CharToInt(cgene2[i])];
具體實現如下：
#include "iostream"
using namespace std;
int iCost[5][5] = {
5, -1, -2, -1, -3,
-1, 5, -3, -2, -4,
-2, -3, 5, -2, -2,
-1, -2, -2, 5, -1,
-3, -4, -2, -1, 0
};
int CharToInt(char ch)
{
switch(ch)
{
case 'A': return 0;
case 'C': return 1;
case 'G': return 2;
case 'T': return 3;
default: return 4;
}
}
int Similarity(char *cgene1, int igene1, char *cgene2, int igene2)
{
int ic[110][110];
int i, j, max;
ic[0][0] = 0;
for(i = 1; i <= igene1; i ++) ic[i][0] = ic[i-1][0] + iCost[CharToInt(cgene1[i])][4];
for(i = 1; i <= igene2; i ++) ic[0][i] = ic[0][i-1] + iCost[4][CharToInt(cgene2[i])];
for(i = 1; i <= igene1; i ++)
{
for(j = 1; j <= igene2; j ++)
{
max = ic[i-1][j-1] + iCost[CharToInt(cgene1[i])][CharToInt(cgene2[j])];
if(max < ic[i-1][j] + iCost[CharToInt(cgene1[i])][4])
{
max = ic[i-1][j] + iCost[CharToInt(cgene1[i])][4];
}
if(max < ic[i][j-1] + iCost[4][CharToInt(cgene2[j])])
{
max = ic[i][j-1] + iCost[4][CharToInt(cgene2[j])];
}
ic[i][j] = max;
}
}
return ic[igene1][igene2];
}
int main(void)
{
int T, igene1, igene2;
char cgene1[105], cgene2[105];
cin >> T;
while(T--)
{
int i;
cin >> igene1;
for(i = 1; i <= igene1; i++)
{
cin >> cgene1[i];
}
cgene1[igene1+1] = '/0';
cin >> igene2;
for(i = 1; i <= igene2; i++)
{
cin >> cgene2[i];
}
cgene2[igene2+1] = '/0';
cout << Similarity(cgene1, igene1, cgene2, igene2) << endl;;
}
return 0;
}
執行結果：