题目链接
题意:
有N(1 <= N <=20000)个音符的序列来表示一首乐曲,每个音符都是1..88范围内的整数,现在要找一个重复的主题。“主题”是整个音符序列的一个子串,它需要满足如下条件:
1.长度至少为5个音符。
2.在乐曲中重复出现。(可能经过转调,“转调”的意思是主题序列中每个音符都被加上或减去了同一个整数值)
3.重复出现的同一主题在原序列中不能有重叠部分。
题目思路:
对于转调,因为a[i]-a[i-1]还是不变,所以我们可以构造a[i]-a[i-1]的后缀数组,从而用寻找最长不重叠子串的方法来写这个题。
#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
#define Max_N 20010
#define F(x) ((x)/3+((x)%3==1?0:tb))
#define G(x) ((x)<tb?(x)*3+1:((x)-tb)*3+2)
int wa1[Max_N*3], wb1[Max_N*3], wv1[Max_N*3], ws1[Max_N*3];
int c0(int *r, int a, int b)
{
return r[a] == r[b] && r[a+1] == r[b+1] && r[a+2] == r[b+2];
}
int c12(int k, int *r, int a, int b)
{
if(k == 2) return r[a] < r[b] || r[a] == r[b] && c12(1, r, a+1, b+1);
else return r[a] < r[b] || r[a] == r[b] && wv1[a+1] < wv1[b+1];
}
void sort(int *r, int *a, int *b, int n, int m)
{
int i;
for (i = 0; i < n; i++) wv1[i] = r[a[i]];
for (i = 0; i < m; i++) ws1[i] = 0;
for (i = 0; i < n; i++) ws1[wv1[i]]++;
for (i = 1; i < m; i++) ws1[i] += ws1[i-1];
for (i = n-1; i >= 0; i--) b[--ws1[wv1[i]]] = a[i];
return;
}
void dc3(int *r, int *sa, int n, int m)
{
int i, j, *rn = r + n, *san = sa + n,ta = 0,tb = (n + 1) / 3,tbc = 0,p;
r[n] = r[n+1] = 0;
for (i = 0; i < n; i++) if (i % 3 != 0) wa1[tbc++] = i;
sort(r+2, wa1, wb1, tbc, m);
sort(r+1, wb1, wa1, tbc, m);
sort(r, wa1, wb1, tbc, m);
for (p = 1,rn[F(wb1[0])] = 0,i = 1;i < tbc; i++)
rn[F(wb1[i])] = c0(r, wb1[i-1], wb1[i]) ? p - 1 : p++;
if (p < tbc) dc3(rn, san, tbc, p);
else for (i = 0; i < tbc; i++) san[rn[i]] = i;
for (i = 0; i < tbc; i++) if (san[i] < tb) wb1[ta++] = san[i] * 3;
if (n % 3 == 1) wb1[ta++] = n - 1;
sort(r, wb1, wa1, ta, m);
for (i = 0; i < tbc; i++) wv1[wb1[i] = G(san[i])] = i;
for (i = 0, j = 0, p = 0; i < ta && j < tbc; p++)
sa[p] = c12(wb1[j] % 3, r, wa1[i], wb1[j]) ? wa1[i++] : wb1[j++];
for(; i < ta; p++) sa[p] = wa1[i++];
for(; j < tbc; p++) sa[p] = wb1[j++];
return;
}
// str sa 都要开三倍的;
void da(int str[], int sa[], int rank1[], int height1[], int n, int m)
{
for (int i = n; i < n*3; i++)
str[i] = 0;
dc3(str, sa, n+1, m);
int i, j, k = 0;
for (i = 0; i <= n; i++) rank1[sa[i]] = i;
for (i = 0; i < n; i++)
{
if (k) k--;
j = sa[rank1[i] - 1];
while (str[i+k] == str[j+k]) k++;
height1[rank1[i]] = k;
}
return;
}
int a[Max_N];
int str[3*Max_N];
int sa[3*Max_N];//sa[i]表示将所有后缀排序后第i小的后缀的编号。
int rank1[3*Max_N];//rank1[i]表示后缀i的排名。
int height1[3*Max_N]; //LCP(sa[i],sa[i-1]);
int n;
bool judge(int c)
{
int Max=sa[0],Min=sa[0];
for(int i=1;i<=n;i++)
{
if(height1[i]>=c)
Max=max(Max,sa[i]),Min=min(Min,sa[i]);
else
Max=sa[i],Min=sa[i];
if(Max-Min>=c+1)
return true;
}
return false;
}
int main()
{
while(~scanf("%d",&n))
{
if(n==0)
break;
int m=0;
str[0]=0;
for(int i=0;i<n;i++)
{
scanf("%d",&a[i]);
if(i)
{
str[i-1]=a[i]-a[i-1]+100;
m=max(m,str[i-1]);
}
}
n--;
m+=10;
str[n]=0;
da(str, sa, rank1, height1, n, m);
int L=0;
int R=n;
int ans=0;
/* for(int i=0;i<=n;i++)
{
printf("%d ",height1[i]);
}
printf("
");*/
while(L<=R)
{
int mid=(L+R)/2;
if(judge(mid))
{
L=mid+1;
ans=max(ans,mid);
}
else
{
R=mid-1;
}
}
if(ans>=4)
{
printf("%d
",ans+1);
}
else
{
printf("0
");
}
}
}