POJ topic 3261 Milk Patterns (suffix array for longest overlap at least k-times substring length)

Milk Patterns

Time Limit: 5000MS		Memory Limit: 65536K
Total Submissions: 12128		Accepted: 5387
Case Time Limit: 2000MS

Description

Farmer John has noticed, the quality of milk given by he cows varies from day to day. On further investigation, he discovered so although he can ' t predict the quality of milk from one day to the next, there is some regular patterns in the daily milk quality.

To perform a rigorous study, he had invented a complex classification scheme by which each milk sample was recorded as an I Nteger between 0 and 1,000,000 inclusive, and have recorded data from a single cow overn (1≤ n ≤20,000) Days. He wishes to find the longest pattern of samples which repeats identically at least K (2≤k ≤ N) times. This could include overlapping patterns--1 2 3 2 3 2 3 1 repeats 2 3 2 3 twice, for example.

Help Farmer John by finding the longest repeating subsequence in the sequence of samples. It is guaranteed, at least one subsequence are repeated at leastK times.

Input

Line 1:two space-separated integers: Nand K
Lines 2.. N+ 1: NIntegers, one per line, the quality of the milk on day IAppears on the ITh line.

Output

Line 1:one Integer, the length of the longest pattern which occurs at least KTimes

Sample Input

8 212323231

Sample Output

4

Source

Usaco 2006 December Gold

AC Code

problem:3261  user:kxh1995 memory:680k  time:47ms language:c++  

#include <stdio.h> #include <string.h> #include <algorithm> #include <iostream> using Namespac  e std;  int s[20020];  int sa[20020],t1[20020],t2[20020],c[20020];  int rank[20020],height[20020];      void Build_sa (int s[],int n,int m) {int i,j,p,*x=t1,*y=t2;      for (i=0;i<m;i++) c[i]=0;      for (i=0;i<n;i++) c[x[i]=s[i]]++;      for (i=1;i<m;i++) c[i]+=c[i-1];      for (i=n-1;i>=0;i--) sa[--c[x[i]]]=i;          for (j=1;j<=n;j<<=1) {p=0;          for (i=n-j;i<n;i++) y[p++]=i;          for (i=0;i<n;i++) if (sa[i]>=j) y[p++]=sa[i]-j;          for (i=0;i<m;i++) c[i]=0;          for (i=0;i<n;i++) c[x[y[i]]]++;          for (i=1;i<m;i++) c[i]+=c[i-1];          for (i=n-1;i>=0;i--) sa[--c[x[y[i]]]]=y[i];          Swap (x, y);          P=1;          x[sa[0]]=0;     for (i=1;i<n;i++)         x[sa[i]]=y[sa[i-1]]==y[sa[i]]&&y[sa[i-1]+j]==y[sa[i]+j]?p-1:p++;          if (p>=n) break;      M=p;      }} void GetHeight (int s[],int n) {int i,j,k=0;      for (i=0;i<=n;i++) rank[sa[i]]=i;          for (i=0;i<n;i++) {if (k) k--;          J=SA[RANK[I]-1];          while (S[i+k]==s[j+k]) k++;      Height[rank[i]]=k; }} int judge (int n,int k,int len) {int num=1;for (int i=1;i<=n;i++) {if (Height[i]>=len) {num++;if (num>=k) return 1 ;} Elsenum=1;} return 0;} int main () {int n,k;while (scanf ("%d%d", &n,&k)!=eof) {int i;int num=-1;for (i=0;i<n;i++) {scanf ("%d", &s[ I]); if (Num<s[i]) num=s[i];} S[n]=0;build_sa (s,n+1,num+1); getheight (s,n); int ans=0;int L=0,r=n;while (l<=r) {int mid= (L+R) >>1;if (judge ( N,k,mid)) {ans=mid;l=mid+1;} Elser=mid-1;} printf ("%d\n", ans);}}

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POJ topic 3261 Milk Patterns (suffix array for longest overlap at least k-times substring length)