bzoj1717: [Usaco2006 Dec]Milk Patterns 产奶的模式(后缀数组+二分)

Posted 2020-08-09

 1 /*
 2 求可重叠的至少重复K次的最长字串
 3 以1为下标起点，因为a[i]最大到1000000，所以要先离散一下
 4 二分长度len
 5 然后O(n)检验
 6 后看h[i]是否有连续的一段h[i]大于len的，并且h[i]连续的长度大于K则满足 
 7 */
 8 #include<stdio.h>
 9 #include<string.h>
10 #include<algorithm>
11 using namespace std;
12 const int maxn = 20010;
13 int c[maxn],sa[maxn],t1[maxn],t2[maxn],n,m,K,tot,t[maxn],num[maxn],a[maxn],rank[maxn],height[maxn];
14 
15 bool cmp(int *r, int a, int b, int l){
16     return r[a]==r[b] && r[a+l]==r[b+l];
17 }
18 
19 void suffix(int *a, int n, int m){
20     int p=0, *x=t1, *y=t2;
21     for (int i=0; i<=m; i++) c[i]=0;
22     for (int i=1; i<=n; i++) c[x[i]=a[i]]++;
23     for (int i=1; i<=m; i++) c[i]+=c[i-1];
24     for (int i=n; i>=1; i--) sa[c[x[i]]--]=i;
25     for (int j=1; j<=n; j<<=1){
26         p=0;
27         for (int i=n-j+1; i<=n; i++) y[++p]=i;
28         for (int i=1; i<=n; i++) if (sa[i]>j) y[++p]=sa[i]-j;
29         for (int i=0; i<=m; i++) c[i]=0;
30         for (int i=1; i<=n; i++) c[x[y[i]]]++;
31         for (int i=1; i<=m; i++) c[i]+=c[i-1];
32         for (int i=n; i>=1; i--) sa[c[x[y[i]]]--]=y[i];
33         swap(x,y); x[sa[1]]=1; p=1;
34         for (int i=2; i<=n; i++)
35             x[sa[i]]=cmp(y,sa[i-1],sa[i],j)?p:++p;
36         m=p; if (p>=n) break;
37     }
38     //for (int i=1; i<=n; i++) printf("%d\n", sa[i]);
39 }
40 
41 void get_height(int *a){
42     int k=0,j;
43     for (int i=1; i<=n; i++) rank[sa[i]]=i;
44     for (int i=1; i<=n; i++){
45         j=sa[rank[i]-1];
46         k?k--:0;
47         while (a[j+k]==a[i+k]) k++;
48         height[rank[i]]=k;
49     }
50     //for (int i=1; i<=n; i++) printf("%d\n", height[i]);
51 }
52 
53 int find(int x){
54     int l=1, r=tot, ans;
55     while (l<=r){
56         int mid=l+r>>1;
57         if (t[mid]<=x) ans=mid,l=mid+1;
58         else r=mid-1;
59     }
60     return ans;
61 }
62 
63 bool check(int k){
64     int i,tot=0;
65     for (i=1; i<=n; i++){
66         if (height[i]>=k) tot++;
67         else{
68             if (tot+1>=K) return 1;
69             else tot=0;
70         }
71     }
72     if (tot+1>=K) return 1; return 0;
73 }
74 
75 int main(){
76     scanf("%d%d", &n, &K);
77     for (int i=1; i<=n; i++) scanf("%d", &a[i]),num[i]=a[i];
78     sort(num+1,num+1+n); tot=0;
79     t[++tot]=num[1];
80     for (int i=2; i<=n; i++)
81         if (num[i]!=num[i-1])
82             t[++tot]=num[i];
83     for (int i=1; i<=n; i++) a[i]=find(a[i]);
84     suffix(a,n,n);
85     get_height(a);
86     int l=1,r=n,ans;
87     while (l<=r){
88         int mid=l+r>>1;
89         if (check(mid)) ans=mid,l=mid+1;
90         else r=mid-1;
91     }
92     printf("%d\n", ans);
93     return 0;
94 }