CF1120C Compress String

朴素算法n^2求最长公共后缀

#include <bits/stdc++.h>
using namespace std;
const int N=5e3+5;
int n,a,b;
int f[N],g[N][N];
char str[N];int main(){
    scanf("%d%d%d",&n,&a,&b);scanf("%s",str+1);for (register int i=1; i<n; ++i)for (register int j=i+1; j<=n; ++j) if (str[i]==str[j]) g[i][j]=g[i-1][j-1]+1;else g[i][j]=0;memset(f,60,sizeof(f));f[1]=a;for (register int i=2; i<=n; ++i){
    f[i]=f[i-1]+a;for (register int j=1; j<i; ++j)if (j<i-g[j][i]+1) f[i]=min(f[i],f[i-g[j][i]]+b);}printf("%d\n",f[n]);
return 0;	
}

现在我们可以通过SA来完成这项操作。同时用st表维护height数组，得到答案。

#include <bits/stdc++.h>
using namespace std;
const int N=5e3+5;
int n,m,a,b;
int sum[N],rk[N],rk2[N],tp[N],sa[N],height[N];
char s[N];
int LOG[N],minn[N][14],f[N];inline void qsort()
{
    for (register int i=0; i<=m; ++i) sum[i]=0;for (register int i=1; i<=n; ++i) sum[rk[i]]++;for (register int i=1; i<=m; ++i) sum[i]+=sum[i-1];for (register int i=n; i>=1; --i) sa[sum[rk[tp[i]]]]=tp[i],sum[rk[tp[i]]]--;
}inline void SA()
{
    m=130;for (register int i=1; i<=n; ++i) rk[i]=s[i]-'0'+1,tp[i]=i;qsort();int p=0;for (register int len=1; p<n; m=p,len<<=1){
    p=0;for (register int i=n-len+1; i<=n; ++i) tp[++p]=i;for (register int i=1; i<=n; ++i) if (sa[i]>len) tp[++p]=sa[i]-len;qsort();memcpy(rk2,rk,sizeof(rk2));p=1; rk[sa[1]]=1;for (register int i=2; i<=n; ++i){
    if (rk2[sa[i]]==rk2[sa[i-1]] && rk2[sa[i]+len]==rk2[sa[i-1]+len]) p=p; else p++;rk[sa[i]]=p;}}
}inline void LCP()
{
    for (register int i=1; i<=n; ++i) rk[sa[i]]=i;int k=0;for (register int i=1; i<=n; ++i){
    if (rk[i]==1) continue;if (k) k--;int j=sa[rk[i]-1];while (i+k<=n && j+k<=n && s[i+k]==s[j+k]) k++;height[rk[i]]=k; }
// for (register int i=1; i<=n; ++i) printf("%d ",height[i]); puts("");
}inline void ST()
{
    LOG[0]=-1;for (register int i=1; i<=n; ++i) LOG[i]=LOG[i>>1]+1;for (register int i=1; i<=n; ++i) minn[i][0]=height[i];for (register int j=1; j<=13; ++j) for (register int i=1; i+(1<<j)-1<=n; ++i){
    minn[i][j]=min(minn[i][j-1],minn[i+(1<<(j-1))][j-1]);	}
}inline void dp()
{
    memset(f,60,sizeof(f));f[0]=0;for (register int i=0; i<n; ++i){
    f[i+1]=min(f[i+1],f[i]+a);int maxn=0;for (register int j=1; j<=i; ++j){
    int x=rk[j],y=rk[i+1];if (x>y) swap(x,y);int s=LOG[y-(x+1)+1];maxn=max(maxn,min(min(minn[x+1][s],minn[y-(1<<s)+1][s]),i-j+1));}f[i+maxn]=min(f[i+maxn],f[i]+b);}
}int main(){
    scanf("%d%d%d",&n,&a,&b);scanf("%s",s+1);SA();LCP();ST();dp();printf("%d\n",f[n]);
return 0;	
}