poj1743 Musical Theme

Musical Theme

Time Limit: 1000MS		Memory Limit: 30000K
Total Submissions: 28409		Accepted: 9591

Description

A musical melody is represented as a sequence of N (1<=N<=20000)notes that are integers in the range 1..88, each representing a key on the piano. It is unfortunate but true that this representation of melodies ignores the notion of musical timing; but, this programming task is about notes and not timings.
Many composers structure their music around a repeating &qout;theme&qout;, which, being a subsequence of an entire melody, is a sequence of integers in our representation. A subsequence of a melody is a theme if it:

is at least five notes long
appears (potentially transposed -- see below) again somewhere else in the piece of music
is disjoint from (i.e., non-overlapping with) at least one of its other appearance(s)

Transposed means that a constant positive or negative value is added to every note value in the theme subsequence.
Given a melody, compute the length (number of notes) of the longest theme.
One second time limit for this problem's solutions!

Input

The input contains several test cases. The first line of each test case contains the integer N. The following n integers represent the sequence of notes.
The last test case is followed by one zero.

Output

For each test case, the output file should contain a single line with a single integer that represents the length of the longest theme. If there are no themes, output 0.

Sample Input

30
25 27 30 34 39 45 52 60 69 79 69 60 52 45 39 34 30 26 22 18
82 78 74 70 66 67 64 60 65 80
0

Sample Output

Hint

Use scanf instead of cin to reduce the read time.

Source

LouTiancheng@POJ

题意：

求两个最长相似子串（差分序列相同）的长度

/*
得出height数组后，二分答案x，将连续的>=x的段分组
如果一组内sa的最大值与最小值的差>=x，则x成立
*/
#include<cstdio>
#include<cstring>
#include<iostream>
using namespace std;
const int N=2e4+5;
int n,sa[N],tsa[N],rank[N],trank[N],c[N],h[N];
int s[N];
void DA(int maxx=256){
    memset(c,0,sizeof c);int p;
    for(int i=1;i<=n;i++) c[rank[i]=s[i]]++;
    for(int i=2;i<=maxx;i++) c[i]+=c[i-1];
    for(int i=n;i;i--) sa[c[rank[i]]--]=i;
    trank[sa[1]]=p=1;
    for(int i=2;i<=n;i++){
        if(rank[sa[i]]!=rank[sa[i-1]]) p++;
        trank[sa[i]]=p;
    }
    for(int i=1;i<=n;i++) rank[i]=trank[i];
    for(int k=1;p<n;k<<=1,maxx=p){
        p=0;
        for(int i=n-k+1;i<=n;i++) tsa[++p]=i;
        for(int i=1;i<=n;i++) if(sa[i]>k) tsa[++p]=sa[i]-k;
        memset(c,0,sizeof c);
        for(int i=1;i<=n;i++) trank[i]=rank[tsa[i]];
        for(int i=1;i<=n;i++) c[trank[i]]++;
        for(int i=2;i<=maxx;i++) c[i]+=c[i-1];
        for(int i=n;i;i--) sa[c[trank[i]]--]=tsa[i];
        trank[sa[1]]=p=1;
        for(int i=2;i<=n;i++){
            if(rank[sa[i]]!=rank[sa[i-1]]||rank[sa[i]+k]!=rank[sa[i-1]+k]) p++;
            trank[sa[i]]=p;
        }
        for(int i=1;i<=n;i++) rank[i]=trank[i];
    }
    for(int i=1,k=0;i<=n;i++){
        int j=sa[rank[i]-1];
        while(s[i+k]==s[j+k]) k++;
        h[rank[i]]=k;if(k>0) k--;
    }
}
bool judge(int k){
    int mn=sa[1],mx=sa[1];
    for(int i=2;i<=n;i++){
        if(h[i]<k){
            mn=mx=sa[i];
        }
        else{
            mx=max(mx,sa[i]);
            mn=min(mn,sa[i]);
            if(mx-mn>=k) return 1;
        } 
    }
    return 0;
}
void Clear(){
    memset(h,0,sizeof h);
    memset(sa,0,sizeof sa);
    memset(tsa,0,sizeof tsa);
    memset(rank,0,sizeof rank);
    memset(trank,0,sizeof trank);
}
int main(){
    while(scanf("%d",&n)==1){
        if(!n) break;
        Clear();
        for(int i=1;i<=n;i++) scanf("%d",&s[i]);n--;
        for(int i=1;i<=n;i++) s[i]=s[i+1]-s[i]+100;
        DA();
        int l=0,r=n/2,mid,ans=0;
        while(l<=r){
            mid=l+r>>1;
            if(judge(mid)) l=mid+1,ans=mid;
            else r=mid-1;
        }
        ans++;
        if(ans<5) ans=0;
        printf("%d
",ans);
    }
    return 0;
}