经典DP题目：
状态转移方程：if(a[j] == b[i]) table[i][j] = table[i-1][j-1] + 1;
else table[i][j] = max(table[i-1][j],table[i][j-1]);
把a串看成横行，b串看成数列，依次相同加1，看斜角
1 #include<stdio.h>
2 #include<string.h>
3 char a[1003],b[1003];
4 int table[1003][1003];
5 int max(int a, int b)
6 {
7 return a>b?a:b;
8 }
9 int main()
10 {
11 int len1,len2,flag,i,j;
12 while(scanf("%s %s",a,b)!=EOF)
13 {
14 len1 = strlen(a);
15 len2 = strlen(b);
16 flag = 0;
17 for(i=0;i<len1;i++)
18 {
19 if(b[0] == a[i]) flag = 1;
20 if(flag) table[0][i] = 1;
21 else table[0][i] = 0;
22 }
23 flag = 0;
24 for(i=0;i<len2;i++)
25 {
26 if(a[0] == b[i]) flag = 1;
27 if(flag) table[i][0] = 1;
28 else table[i][0] = 0;
29 }
30 for(i=1;i<len2;i++)
31 for(j=1;j<len1;j++)
32 if(a[j] == b[i]) table[i][j] = table[i-1][j-1] + 1;
33 else table[i][j] = max(table[i-1][j],table[i][j-1]);
34 printf("%d\n",table[len2-1][len1-1]);
35 }
36 return 0;
37 }