Long Long Message POJ - 2774 后缀数组

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

 

 

题意：

题目这么长就是说，给你两个串，你需要找出来两个串的最长公共部分（听着好像dp的一种最长公共子序列，复杂度nlog(n)，不知道做这道题可不可以，应该会TLE）

 

题解：

你把这两个串连在一起然后找出来所有满足下面条件的所有height[i]的值，取最大那个输出

 

height[i]就表示排名第i和排名第i-1的后缀最长公共前缀，如果这两个后缀不属于一个串，那么这个长度就可以满足题意，又因为题目让我们找最大的，所以遍历一遍即可

 

代码：

#include <cstdlib>
#include <cstring>
#include <cstdio>
#include <algorithm>
using namespace std;

const int N = 200010;
int x[N], y[N], c[N];
int rank[N], height[N];
int sa[N],s[N],n,k;
char str1[N],str2[N];
bool pan(int *x,int i,int j,int k,int n)
{
    int ti=i+k<n?x[i+k]:-1;
    int tj=j+k<n?x[j+k]:-1;
    return x[i]==x[j]&&ti==tj;
}
void build_SA(int n,int r)
{
    int *x=rank,*y=height;
    for(int i=0; i<r; i++)c[i]=0;
    for(int i=0; i<n; i++)c[s[i]]++;
    for(int i=1; i<r; i++)c[i]+=c[i-1];
    for(int i=n-1; i>=0; i--)sa[--c[s[i]]]=i;
    r=1;
    x[sa[0]]=0;
    for(int i=1; i<n; i++)
        x[sa[i]]=s[sa[i]]==s[sa[i-1]]?r-1:r++;
    for(int k=1; r<n; k<<=1)
    {
        int yn=0;
        for(int i=n-k; i<n; i++)y[yn++]=i;
        for(int i=0; i<n; i++)
            if(sa[i]>=k)y[yn++]=sa[i]-k;
        for(int i=0; i<r; i++)c[i]=0;
        for(int i=0; i<n; i++)++c[x[y[i]]];
        for(int i=1; i<r; i++)c[i]+=c[i-1];
        for(int i=n-1; i>=0; i--)sa[--c[x[y[i]]]]=y[i];
        swap(x,y);
        r=1;
        x[sa[0]]=0;
        for(int i=1; i<n; i++)
            x[sa[i]]=pan(y,sa[i],sa[i-1],k,n)?r-1:r++;
    }
    for(int i=0; i<n; i++)rank[i]=x[i];
}
void get_height(int n)
{
    int i,j,k=0;
    for(i=1; i<=n; i++)rank[sa[i]]=i;
    for(i=0; i<n; i++)
    {
        if(k)k--;
        else k=0;
        j=sa[rank[i]-1];
        while(s[i+k]==s[j+k])k++;
        height[rank[i]]=k;
    }
}
int main()
{
    scanf("%s%s",str1,str2);
    int len=strlen(str1);
    n=0;
    for(int i=0;i<len;++i)
        s[n++]=str1[i];
    len=strlen(str2);
    for(int j=0;j<len;++j)
        s[n++]=str2[j];
    s[n]='0';

    build_SA(n+1,N);
    get_height(n);
    len=strlen(str1);
    int maxx=0;
    for(int i=2;i<=n;++i)
    {
        if(maxx<height[i])
        {
            if((sa[i]<len && sa[i-1]<len) || (sa[i]>=len && sa[i-1]>=len))
                continue;
            else maxx=height[i];
        }
    }
    printf("%d\n",maxx);
    return 0;
}