Common Subsequence

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 19679 Accepted Submission(s): 8389

Problem Description

A subsequence of a given sequence is the given sequence with some elements (possible none) left out. Given a sequence X = <x1, x2, ..., xm> another sequence Z = <z1, z2, ..., zk> is a subsequence of X if there exists a strictly increasing sequence <i1, i2, ..., ik> of indices of X such that for all j = 1,2,...,k, xij = zj. For example, Z = <a, b, f, c> is a subsequence of X = <a, b, c, f, b, c> with index sequence <1, 2, 4, 6>. Given two sequences X and Y the problem is to find the length of the maximum-length common subsequence of X and Y.
The program input is from a text file. Each data set in the file contains two strings representing the given sequences. The sequences are separated by any number of white spaces. The input data are correct. For each set of data the program prints on the standard output the length of the maximum-length common subsequence from the beginning of a separate line.

Sample Input

abcfbc abfcab

programming contest

abcd mnp

Sample Output

　　题意就是求两个字符串的最长公共子串的长度。这题可以算是LCS的例题= =，所以直接写一个求两个字符串的LCS就可以了，但是这里没有告诉我们字符串的长度，所以字符串数组开了1000+，所以用来记录LCS的数组开不了这么大，只好用滚动数组，在原本的LCS上面稍微改一下就可以了。

上代码：

 1 #include <cstdio>
 2 #include <cstring>
 3 #define MAX 1100
 4 using namespace std;
 5 
 6 char a[MAX],b[MAX];
 7 int c[11][MAX];
 8 
 9 int main()
10 {
11     int lena,lenb,maxn,v;
12     while(scanf("%s %s",a+1,b+1)!=EOF){
13         lena=strlen(a+1);
14         lenb=strlen(b+1);
15         memset(c,0,sizeof(c));
16         maxn=0;
17         v=1;
18         for(int i=1;i<=lena;i++){
19             v=i%10;                 //这一句需要放在外面的循环里
20             for(int j=1;j<=lenb;j++){
21                 if(a[i]==b[j]) c[v][j]=c[(v-1+10)%10][j-1]+1;
22                 else if(c[v][j-1]>=c[(v-1+10)%10][j]){
23                     c[v][j]=c[v][j-1];
24                 }else{
25                     c[v][j]=c[(v-1+10)%10][j];
26                 }
27                 maxn = c[v][j] > maxn ? c[v][j] : maxn;
28             }
29         }
30         printf("%d
",maxn);
31 
32     }
33     return 0;
34 }
35 
36 
37 /**
38 abcfbc abfcab
39 programming contest
40 abcd mnp
41 
42 4
43 2
44 0
45 */

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