Problem C: 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
题意:给定两个序列,求最长公共子序列。
思路:dp中的LCS问题。。裸的很水。状态转移方程为
字符相同时: d[i][j] = d[i - 1][j - 1] + 1,不同时:d[i][j] = max(d[i - 1][j], d[i][j - 1])
代码:
#include <stdio.h> #include <string.h> char a[1005], b[1005]; int d[1005][1005], i, j; int max(int a, int b) { return a > b ? a : b; } int main() { while (gets(a) != NULL) { gets(b); memset(d, 0, sizeof(d)); int lena = strlen(a); int lenb = strlen(b); for (i = 1; i <= lena; i ++) for (j = 1; j <= lenb; j ++) { if (a[i - 1] == b[j - 1]) { d[i][j] = d[i - 1][j - 1] + 1; } else { d[i][j] = max(d[i - 1][j], d[i][j - 1]); } } printf("%d ", d[lena][lenb]); } return 0; }