PKU ACM 1080-human gene function
テーマの出所:http://acm.pku.edu.cn/JudgeOnline/problem?id=1080
问题解释报告:最近アルゴリズム导论の动态计画の一章をぼんやり见て、理解したようで、结果的に问题を作る时、やはりすることができないことを発见して、いつも子の问题が见つからないで、どのように最优秀の子の构造を设けるか分からないで、もともと1本の简単なことを探して、1080を见つけて、结果はやはり考えがなくて、他の人のコードを见て、やっと少し理解しました.やはりもっと練習しなければならないようですね.
この問題は2つの文字列の類似度を求めて、第1の文字列s 1[0]、s 1[1]、s 1[2],.....s 1[len 1-1]、第2の文字列s 2[0]、s 2[1],.....s 2[len 2-1]を設定し、2つの文字列の最後の文字の関係を見ると、3つの可能性がある.
1.s 1[len 1-1]s 2[len 2-1]に対応
2.s 1[len 1-1]は「-」に対応
3.s 2[len 2-1]は'-'に対応
第1の場合、文字列の類似度は、s 1[0]、s 1[1]、s 1[2],....s 1[len 1-2]とs 2[0]、s 2[1],....s 2[len 2-2]の類似度+s 1[len 1-1]とs 2[len 2-1]との類似度である.明らかに、最大値に達するには、s 1[0],s 1[1],s 1[2],....s 1[len 1-2]とs 2[0],s 2[1],....s 2[len 2-2]の2つの文字列の類似度も最大値に達する必要がある.
2つ目の場合、2つの文字列の類似度は、s 1[0],s 1[1],s 1[2],....s 1[len 1-2]とs 2[0],s 2[1],....s 2[len 2-1]の類似度+s 1[len 1-1]と「-」の類似度である.明らかに、最大値に達するには、s 1[0],s 1[1],s 1[2],....s 1[len 1-2]とs 2[0],s 2[1],....s 2[len 2-1]の2つの文字列の類似度も最大値に達しなければならない.
3つ目の場合、2つの文字列の類似度は、s 1[0],s 1[1],s 1[2],....s 1[len 1-1]とs 2[0],s 2[1],....s 2[len 2-2]の類似度+'-'とs 2[len 2-1]との類似度である.明らかに、最大値に達するには、s 1[0],s 1[1],s 1[2],....s 1[len 1-1]とs 2[0],s 2[1],....s 2[len 2-2]の2つの文字列の類似度も最大値に達しなければならない.
動的計画を用いてボトムアップからf[i][j]が文字列s 1の前i文字からなる文字列と文字列s 2の前j文字からなる文字列との類似度を表すとすると、
f[i][j]=max(
f[i-1][j-1]+value(s 1[i-1],s 2[j-1])//第1のケース
f[i-1][j]+value(s 1[i-1],'-'),//第2のケース
f[i][j-1]+value('-',s 2[j-1])/第3のケース
)
#include using namespace std; #define INF 100 int f[102][102]; int v[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,-INF }; int toInt(char c) { int i; switch(c) { case 'A': i=0;break; case 'C': i=1;break; case 'G': i=2;break; case 'T': i=3;break; case '-': i=4;break; default: break; } return i; } int value(char a, char b) { int m=toInt(a); int n=toInt(b); return v[m][n]; } int max(int a,int b, int c) { int m=a> caseNum; while(caseNum--) { int len1,len2; cin >> len1; char *s1=new char[len1+1]; cin >> s1; cin >> len2; char *s2=new char[len2+1]; cin >> s2; for(int i=0;i<=len1;i++) { for(int j=0;j<=len2;j++) { if(i==0 && j==0) f[i][j]=0; else if(i==0) f[i][j]=f[i][j-1]+value('-',s2[j-1]); else if(j==0) f[i][j]=f[i-1][j]+value(s1[i-1],'-'); else { f[i][j]=max(f[i-1][j-1]+value(s1[i-1],s2[j-1]), f[i-1][j]+value(s1[i-1],'-'), f[i][j-1]+value('-',s2[j-1])); } } } cout << f[len1][len2] << endl; } }
付録:
Human Gene Functions
Time Limit: 1000MS
Memory Limit: 10000K
Total Submissions: 9149
Accepted: 5045
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.
対応する表1枚で、画像が表示されません.
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
Sample Output
问题解释报告:最近アルゴリズム导论の动态计画の一章をぼんやり见て、理解したようで、结果的に问题を作る时、やはりすることができないことを発见して、いつも子の问题が见つからないで、どのように最优秀の子の构造を设けるか分からないで、もともと1本の简単なことを探して、1080を见つけて、结果はやはり考えがなくて、他の人のコードを见て、やっと少し理解しました.やはりもっと練習しなければならないようですね.
この問題は2つの文字列の類似度を求めて、第1の文字列s 1[0]、s 1[1]、s 1[2],.....s 1[len 1-1]、第2の文字列s 2[0]、s 2[1],.....s 2[len 2-1]を設定し、2つの文字列の最後の文字の関係を見ると、3つの可能性がある.
1.s 1[len 1-1]s 2[len 2-1]に対応
2.s 1[len 1-1]は「-」に対応
3.s 2[len 2-1]は'-'に対応
第1の場合、文字列の類似度は、s 1[0]、s 1[1]、s 1[2],....s 1[len 1-2]とs 2[0]、s 2[1],....s 2[len 2-2]の類似度+s 1[len 1-1]とs 2[len 2-1]との類似度である.明らかに、最大値に達するには、s 1[0],s 1[1],s 1[2],....s 1[len 1-2]とs 2[0],s 2[1],....s 2[len 2-2]の2つの文字列の類似度も最大値に達する必要がある.
2つ目の場合、2つの文字列の類似度は、s 1[0],s 1[1],s 1[2],....s 1[len 1-2]とs 2[0],s 2[1],....s 2[len 2-1]の類似度+s 1[len 1-1]と「-」の類似度である.明らかに、最大値に達するには、s 1[0],s 1[1],s 1[2],....s 1[len 1-2]とs 2[0],s 2[1],....s 2[len 2-1]の2つの文字列の類似度も最大値に達しなければならない.
3つ目の場合、2つの文字列の類似度は、s 1[0],s 1[1],s 1[2],....s 1[len 1-1]とs 2[0],s 2[1],....s 2[len 2-2]の類似度+'-'とs 2[len 2-1]との類似度である.明らかに、最大値に達するには、s 1[0],s 1[1],s 1[2],....s 1[len 1-1]とs 2[0],s 2[1],....s 2[len 2-2]の2つの文字列の類似度も最大値に達しなければならない.
動的計画を用いてボトムアップからf[i][j]が文字列s 1の前i文字からなる文字列と文字列s 2の前j文字からなる文字列との類似度を表すとすると、
f[i][j]=max(
f[i-1][j-1]+value(s 1[i-1],s 2[j-1])//第1のケース
f[i-1][j]+value(s 1[i-1],'-'),//第2のケース
f[i][j-1]+value('-',s 2[j-1])/第3のケース
)
#include
付録:
Human Gene Functions
Time Limit: 1000MS
Memory Limit: 10000K
Total Submissions: 9149
Accepted: 5045
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.
対応する表1枚で、画像が表示されません.
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