poj 1743 Musical Theme 求不可重叠最长重复子串（二分答案+height分组）

题目可转化为一个经典问题：给定一个字符串，求最长重复子串，这两个子串不能重叠。

解题思路：二分答案。这就转化成判定性的问题。对于每一个答案需要判定该答案是否合法。把height数组分成若干组使得每一组的height都不小于答案k，如果有一组的后缀的sa值的最大值和最小值之差大于k（保证了两个子串不能重复），则答案k成立。

/*
 *Author:       Zhaofa Fang
 *Created time: 2013-04-18-16.24
 *Language:     C++
 */
#include <cstdio>
#include <cstdlib>
#include <sstream>
#include <iostream>
#include <cmath>
#include <cstring>
#include <algorithm>
#include <string>
#include <utility>
#include <vector>
#include <queue>
#include <map>
#include <set>
using namespace std;

typedef long long ll;
#define DEBUG(x) cout<< #x << ':' << x << endl
#define FOR(i,s,t) for(int i = (s);i <= (t);i++)
#define FORD(i,s,t) for(int i = (s);i >= (t);i--)
#define REP(i,n) FOR(i,0,n-1)
#define REPD(i,n) FORD(i,n-1,0)
#define PII pair<int,int>
#define PB push_back
#define MP make_pair
#define ft first
#define sd second
#define lowbit(x) (x&(-x))
#define INF (1<<30)

const int maxn = 22011;
int cha[maxn],a[maxn];
int sa[maxn],t1[maxn],t2[maxn],c[maxn];
int rank[maxn],height[maxn];

void getHeight(int n){
    int k = 0;
    for(int i=1;i<=n;i++)rank[sa[i]] = i;
    for(int i=0;i<n;i++){
        if(k)k --;
        int j = sa[rank[i]-1];
        while(cha[i+k] == cha[j+k])k++;
        height[rank[i]] = k;
    }
}
bool cmp(int *r,int a,int b,int l){
    return (r[a]==r[b] && r[a+l]==r[b+l]);
}
void build_sa(int m,int n){
    int i,*x = t1, *y = t2,k,p;
    for(i=0;i<m;i++)c[i] = 0;
    for(i=0;i<n;i++)c[x[i] = cha[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(k=1,p=0;p<n;m=p,k<<=1){
        p=0;
        for(i=n-k;i<n;i++)y[p++] = i;
        for(i=0;i<n;i++)if(sa[i]>=k)y[p++] = sa[i]-k;

        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]] = cmp(y,sa[i-1],sa[i],k)?p-1:p++;
    }
    getHeight(n-1);
}

bool check(int m,int n){
    int x=sa[1],y=sa[1];
    for(int i=2;i<=n;i++){
        if(height[i]>=m){
            x = min(x,sa[i]);
            y = max(y,sa[i]);
            if(y-x>m)return true;
        }else x = y = sa[i];
    }
    return false;
}
int solve(int n){
    int l=4,r=n/2,ans=0;
    while(l<=r){
        int m = (l + r) >> 1;
        if(check(m,n-1))l = m+1,ans = m;
        else r = m - 1;
    }
    if(ans<4)ans = -1;
    return ans+1;
}
int main(){
    //freopen("in","r",stdin);
    //freopen("out","w",stdout);
    int n;
    while(~scanf("%d",&n),n){
        REP(i,n)scanf("%d",&a[i]);
        REP(i,n-1)cha[i] = a[i+1] - a[i] + 87;
        cha[n-1] = 0;
        build_sa(175,n);
        printf("%d\n",solve(n));
    }
    return 0;
}