1458 Common Subsequence【lcs】
2015-08-10 10:41
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Common Subsequence
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.
Input
The program input is from the std input. Each data set in the input contains two strings representing the given sequences. The sequences are separated by any number of white spaces. The input data are correct.
Output
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
Sample Output
单纯的考察 lcs 的题目
lcs,用的是动态规划的思想,具体暂时不太清楚,就是一直打表记录状态,等到最后的时候,记录下来的就是最长的那个序列....
Time Limit: 1000MS | Memory Limit: 10000K | |
Total Submissions: 43175 | Accepted: 17501 |
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.
Input
The program input is from the std input. Each data set in the input contains two strings representing the given sequences. The sequences are separated by any number of white spaces. The input data are correct.
Output
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
4 2 0
单纯的考察 lcs 的题目
lcs,用的是动态规划的思想,具体暂时不太清楚,就是一直打表记录状态,等到最后的时候,记录下来的就是最长的那个序列....
#include<stdio.h> #include<string.h> #define max(a,b) (a>b?a:b) int x[1005][1005]; int main() { char a[1005],b[1005]; while(~scanf("%s%s",a,b)) { int i,j,lena=strlen(a),lenb=strlen(b); memset(x,0,sizeof(x)); for(i=1;i<=lena;++i)//双循环打表记录状态 { for(j=1;j<=lenb;++j) { if(a[i-1]==b[j-1]) { x[i][j]=x[i-1][j-1]+1; } else { x[i][j]=max(x[i-1][j],x[i][j-1]); } } } printf("%d\n",x[lena][lenb]);//输出... } return 0; }
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