poj 2774 Long Long Message 后缀数组基础题

Time Limit: 4000MS		Memory Limit: 131072K
Total Submissions: 24756		Accepted: 10130
Case Time Limit: 1000MS

Description

The little cat is majoring in physics in the capital of Byterland. A piece of sad news comes to him these days: his mother is getting ill. Being worried about spending so much on railway tickets (Byterland is such a big country, and he has to spend 16 shours on train to his hometown), he decided only to send SMS with his mother. 

The little cat lives in an unrich family, so he frequently comes to the mobile service center, to check how much money he has spent on SMS. Yesterday, the computer of service center was broken, and printed two very long messages. The brilliant little cat soon found out: 

1. All characters in messages are lowercase Latin letters, without punctuations and spaces. 
2. All SMS has been appended to each other – (i+1)-th SMS comes directly after the i-th one – that is why those two messages are quite long. 
3. His own SMS has been appended together, but possibly a great many redundancy characters appear leftwards and rightwards due to the broken computer. 
E.g: if his SMS is “motheriloveyou”, either long message printed by that machine, would possibly be one of “hahamotheriloveyou”, “motheriloveyoureally”, “motheriloveyouornot”, “bbbmotheriloveyouaaa”, etc. 
4. For these broken issues, the little cat has printed his original text twice (so there appears two very long messages). Even though the original text remains the same in two printed messages, the redundancy characters on both sides would be possibly different. 

You are given those two very long messages, and you have to output the length of the longest possible original text written by the little cat. 

Background: 
The SMS in Byterland mobile service are charging in dollars-per-byte. That is why the little cat is worrying about how long could the longest original text be. 

Why ask you to write a program? There are four resions: 
1. The little cat is so busy these days with physics lessons; 
2. The little cat wants to keep what he said to his mother seceret; 
3. POJ is such a great Online Judge; 
4. The little cat wants to earn some money from POJ, and try to persuade his mother to see the doctor :( 

Input

Two strings with lowercase letters on two of the input lines individually. Number of characters in each one will never exceed 100000.

Output

A single line with a single integer number – what is the maximum length of the original text written by the little cat.

Sample Input

yeshowmuchiloveyoumydearmotherreallyicannotbelieveit
yeaphowmuchiloveyoumydearmother

Sample Output

27

Source

POJ Monthly--2006.03.26,Zeyuan Zhu,"Dedicate to my great beloved mother."

 

思路：又是heigh数组的应用，我们把两个串链接起来，设第一个串的长度为ls，将连接起来的串s做一次后缀数组，然后就是二分一个答案M，通过扫描一遍heigh数组来判断M是否合法，将heigh按大于等于分组后，若该组中最小的sa值mi与最大的sa值mx满足：mi + M < ls && mx > ls  则M值合法（跟hdu3518一样一样的）

#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>
using namespace std;
const int INF = 0x3f3f3f3f;
const int maxn = 1000000 + 10;
int t1[maxn], t2[maxn], c[maxn];
bool cmp(int *r, int a, int b, int l) {
    return r[a] == r[b] && r[a + l] == r[b + l];
}
void da(char str[], int sa[], int Rank[], int heigh[], int n, int m)
{
    n++;
    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] = str[i] ]++;
    for(int i = 1; i < m; ++i) c[i] += c[i - 1];
    for(int i = n - 1; i >= 0; --i) sa[--c[x[i]]] = i;

    for(int 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] ] = cmp(y, sa[i - 1], sa[i], j) ? p - 1 : p++;
        if(p >= n) break;
        m = p;
    }
    int k = 0;
    n--;
    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(str[i + k] == str[j + k]) k++;
        heigh[ Rank[i] ] = k;
    }
}

int Rank[maxn], heigh[maxn], sa[maxn];
char s[maxn], s2[maxn];
void out(int n) {
    puts("Rank[]");
    ///Rank数组的有效范围是0~n-1， 值是1~n
    for(int i = 0; i <= n; ++i) printf("%d ", Rank[i]);
    puts("sa[]");
    ///sa数组的有效范围是1~n，值是0~n-1
    for(int i = 0; i <= n; ++i) printf("%d ", sa[i]);
    puts("heigh[]");
    ///heigh数组的有效范围是2~n
    for(int i = 0; i <= n; ++i) printf("%d ", heigh[i]);
}
int ls;
bool check(int x, int n) {
    int mi = INF, mx = -INF;
    for(int i = 2; i <= n; ++i) {
        if(heigh[i] >= x) {
            mi = min(mi, min(sa[i - 1], sa[i]));
            mx = max(mx, max(sa[i - 1], sa[i]));
        }else {
            if(mi + x < ls && mx >= ls) return true;
            mi = INF, mx = -INF;
        }
    }
    if(mi + x < ls && mx > ls) return true;
    return false;
}
int solve(int n) {
    int L = 0, R = n + 1;
    while(R - L > 1) {
        int M = (L + R) >> 1;
        if(check(M, n)) L = M;
        else R = M;
    }
    return L;
}
int main() {
    while(~scanf("%s%s", s, s2))
    {
        ls = strlen(s);
        strcat(s, s2);
        int n = strlen(s);
        da(s, sa, Rank, heigh, n, 128);
        printf("%d\n", solve(n));
    }
    return 0;
}

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