题目链接:http://poj.org/problem?id=2774
后缀数组真的太强大了,原本dp是O(nm)的复杂度,在这里只需要O(n+m)。
做法:将两个串中间夹一个未出现过的字符接起来,然后做一次后缀数组,得到的height相邻两个排名的后缀,在串中的位置如果满足在分界符左右两侧,就更新最长公共前缀。最后得到的最大值就是最长公共子序列。
#include<algorithm>
#include<cstdio>
#include<cstring>
using namespace std; const int MAXN = *;
#define F(x) ((x)/3+((x)%3==1?0:tb))
#define G(x) ((x)<tb?(x)*3+1:((x)-tb)*3+2)
int wa[MAXN*],wb[MAXN*],wv[MAXN*],wss[MAXN*];
int c0(int *r,int a,int b)
{
return r[a] == r[b] && r[a+] == r[b+] && r[a+] == r[b+];
}
int c12(int k,int *r,int a,int b)
{
if(k == )
return r[a] < r[b] || ( r[a] == r[b] && c12(,r,a+,b+) );
else return r[a] < r[b] || ( r[a] == r[b] && wv[a+] < wv[b+] );
}
void sort(int *r,int *a,int *b,int n,int m)
{
int i;
for(i = ; i < n; i++)wv[i] = r[a[i]];
for(i = ; i < m; i++)wss[i] = ;
for(i = ; i < n; i++)wss[wv[i]]++;
for(i = ; i < m; i++)wss[i] += wss[i-];
for(i = n-; i >= ; i--)
b[--wss[wv[i]]] = a[i];
}
void dc3(int *r,int *sa,int n,int m)
{
int i, j, *rn = r + n;
int *san = sa + n, ta = , tb = (n+)/, tbc = , p;
r[n] = r[n+] = ;
for(i = ; i < n; i++)if(i % != )wa[tbc++] = i;
sort(r + , wa, wb, tbc, m);
sort(r + , wb, wa, tbc, m);
sort(r, wa, wb, tbc, m);
for(p = , rn[F(wb[])] = , i = ; i < tbc; i++)
rn[F(wb[i])] = c0(r, wb[i-], wb[i]) ? p - : p++;
if(p < tbc)dc3(rn,san,tbc,p);
else for(i = ; i < tbc; i++)san[rn[i]] = i;
for(i = ; i < tbc; i++) if(san[i] < tb)wb[ta++] = san[i] * ;
if(n % == )wb[ta++] = n - ;
sort(r, wb, wa, ta, m);
for(i = ; i < tbc; i++)wv[wb[i] = G(san[i])] = i;
for(i = , j = , p = ; i < ta && j < tbc; p++)
sa[p] = c12(wb[j] % , r, wa[i], wb[j]) ? wa[i++] : wb[j++];
for(; i < ta; p++)sa[p] = wa[i++];
for(; j < tbc; p++)sa[p] = wb[j++];
}
void da(int str[],int sa[],int rank[],int height[],int n,int m)
{
for(int i = n; i < n*; i++)
str[i] = ;
dc3(str, sa, n+, m);
int i,j,k = ;
for(i = ; i <= n; i++)rank[sa[i]] = i;
for(i = ; i < n; i++)
{
if(k) k--;
j = sa[rank[i]-];
while(str[i+k] == str[j+k]) k++;
height[rank[i]] = k;
}
} int str[MAXN*],sa[MAXN*],rk[MAXN],height[MAXN]; char s1[MAXN],s2[MAXN];
int l1,l2; int main()
{
while (~scanf("%s%s",s1,s2))
{
l1=strlen(s1);
l2=strlen(s2);
for (int i=; i<l1; i++) str[i]=s1[i]-'a'+;
str[l1]=;
for (int i=;i<l2;i++) str[l1++i]=s2[i]-'a'+;
str[l1+l2+]=;
da(str,sa,rk,height,l1+l2+,);
int ma=;
for (int i=;i<=l1+l2+;i++)
{
int p1=sa[i-];
int p2=sa[i];
if (p1<l1&&p2>l1 || p1>l1&&p2<l1) ma=max(ma,height[i]);
}
printf("%d\n",ma);
}
return ;
}