UVaOJ10405 - Longest Common Subsequence

[title3]
10405 - Longest Common Subsequence[/title3]

Time limit: 3.000 seconds

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
aedfhrabcdefghijklmnopqrstuvwxyz
a0b0c0d0e0f0g0h0i0j0k0l0m0n0o0p0q0r0s0t0u0v0w0x0y0z0
abcdefghijklmnzyxwvutsrqpo
opqrstuvwxyzabcdefghijklmn

Output for the sample input

4
3
26
14

Problem Setter: Piotr Rudnicki

题目大意：

求两个字符串的最大相同子序列

题目分析：

动态规划经典问题，求最大共同子序列。状态转移方程是：

源代码：

#include <iostream>
#include <cstdio>
#include <cstring>
using namespace std;

const int MAXN = 1010;
char a[MAXN], b[MAXN];
int dp[MAXN][MAXN];
int main() {
while (gets(a) && gets(b)) {
memset(dp, 0, sizeof(dp));
for (int i = 1; i <= strlen(a); i ++) {
for (int j = 1; j <= strlen(b); j ++) {
if (a[i - 1] == b[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[strlen(a)][strlen(b)]);
}
return 0;
}