bzoj 1717: [Usaco2006 Dec]Milk Patterns 产奶的模式

Posted 2020-10-24 Nico&11101001

题目链接

bzoj 1717: [Usaco2006 Dec]Milk Patterns 产奶的模式

题解

后缀排序
求出height之后一段区间[l,r]内,出现r-l+1次最长的串是\(min(height[i]) l<=i<=r\)
单调队列维护
代码

// luogu-judger-enable-o2
#include<cstdio>
#include<cstring>
#include<algorithm>
const int maxn = 600007;
int n,m,k;
char c[maxn];
int s[maxn],height[maxn],rank[maxn],sa[maxn],saf[maxn],cnt[maxn];
void rsort() {
    for(int i=0;i<=m;++i) cnt[i]=0;
    for(int i=1;i<=n;++i) cnt[rank[saf[i]]]++;
    for(int i=1;i<=m;++i) cnt[i]+=cnt[i-1];
    for(int i=n;i>=1;--i) sa[cnt[rank[saf[i]]]--]=saf[i];
}
bool cmp(int *f,int x,int y,int w) {
    return f[x]==f[y]&&f[x+w]==f[y+w];
}
void get_sa() {
    for(int i=1;i<=n;++i)rank[i]=s[i],saf[i]=i;m=127;rsort();
    for(int p=1,w=1,i;p<n;w<<=1,m=p) {
        for(i=n-w+1,p=0;i<=n;++i)saf[++p]=i;
        for(i=1;i<=n;++i)if(sa[i]>w)saf[++p]=sa[i]-w;
        rsort();std::swap(rank,saf);rank[sa[1]]=p=1;
        for(i=2;i<=n;++i)rank[sa[i]]=cmp(saf,sa[i],sa[i-1],w)?p:++p;
    }
    int j,k_=0;
    for(int i=1;i<=n;height[rank[i++]]=k_) 
        for(k_=k_?k_-1:k_,j=sa[rank[i]-1];s[i+k_]==s[j+k_];++k_);
}
void init() {
    scanf("%d%d",&n,&k);
    for(int i=1;i<=n;++i)scanf("%d",s+i);
}
int q[maxn];
void solve() {
    int h=1,t=0;
    k--;
    int ans=-1;height[1]=1;
    for(int i=2;i<=k;++i) {
        while(h<=t&&height[q[t]]>height[i])t--;
        q[++t]=i;
    }
    ans=std::max(ans,height[q[h]]);
    for(int i=k+1;i<=n;++i) {
        while(h<=t&&q[h]<i-k+1)h++;
        while(h<=t&&height[q[t]]>height[i])t--;
        q[++t]=i;
        ans=std::max(ans,height[q[h]]);
    }
    printf("%d\n",ans);
}
int main() {
    init();
    get_sa();
    solve();
    return 0;
}