uva 10405 Longest Common Subsequence

Sequence 1:

Sequence 2:

Given two sequences of characters, print the length of the longest common subsequence of both sequences. For example, the longest common subsequence of the following two sequences:

abcdgh
aedfhr

is adh of length 3.

Input consists of pairs of lines. The first line of a pair contains the first string and the second line contains the second string. Each string is on a separate line and consists of at most 1,000 characters

For each subsequent pair of input lines, output a line containing one integer number which satisfies the criteria stated above.
Sample input

a1b2c3d4e
zz1yy2xx3ww4vv
abcdgh
aedfhr
abcdefghijklmnopqrstuvwxyz
a0b0c0d0e0f0g0h0i0j0k0l0m0n0o0p0q0r0s0t0u0v0w0x0y0z0
abcdefghijklmnzyxwvutsrqpo
opqrstuvwxyzabcdefghijklmn

Output for the sample input

4
3
26
14

题目大意：最长公共子序列。

解题思路：递推。

#include<stdio.h>
#include<string.h>
#include<stdlib.h>
#include<algorithm>
#define N 1005
using namespace std;
char s1[N], s2[N];
int dp[N][N];
int main() {
    while (gets(s1)) {
        gets(s2);
        int l1 = strlen(s1), l2 = strlen(s2);
        memset(dp, 0, sizeof(dp));
        for (int i = 1; i <= l1; i++) {
            for (int j = 1; j <= l2; j++) {
                if (s1[i - 1] == s2[j - 1]) {
                    dp[i][j] = dp[i - 1][j - 1] + 1;
                }
                else {
                    dp[i][j] = max(dp[i - 1][j], dp[i][j - 1]);
                }
            }
        }
        printf("%d\n", dp[l1][l2]);
    }
    return 0;
}