POJ 1458 Common Subsequence 简单DP

题目链接：http://poj.org/problem?id=1458

题目大意：最长公共子序列，不知道的话回去看书吧。。。算了， 就是他们共有的长度最大的子序列，可以是不连续的。问最大长度。

解题思路：dp[i][j]:=串A的前i个字符和串B的前j个字符的最长公共子序列长度

if(a[i] == b[j])

　　dp[i][j] = max(dp[i][j], dp[i - 1][j - 1] + 1);
else

　　dp[i][j] = max(dp[i][j], max(dp[i - 1][j], dp[i][j - 1]));

代码：

const int maxn = 1e3 + 5;
char a[maxn], b[maxn];
int dp[maxn][maxn];

int solve(){
    memset(dp, 0, sizeof(dp));
    int asz = strlen(a + 1), bsz = strlen(b + 1);
    for(int i = 1; i <= asz; i++){
        for(int j = 1; j <= bsz; j++){
            if(a[i] == b[j]) dp[i][j] = max(dp[i][j], dp[i - 1][j - 1] + 1);
            else dp[i][j] = max(dp[i][j], max(dp[i - 1][j], dp[i][j - 1]));
        }
    }
    printf("%d
", dp[asz][bsz]);
    return 0;
} 
int main(){
    while(scanf("%s %s", a + 1, b + 1) != EOF){
        solve();
    }
}

题目：

Common Subsequence

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 54425		Accepted: 22632

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, x_ij = 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

Source

Southeastern Europe 2003