[POJ3080 Blue Jeans]

[题目来源]：South Central USA 2006

[关键字]：字符串

[题目大意]：找出给所有字符串的最长公共字串。

//=====================================================================================================

[分析]：暴力枚举+KMP。最近刚学了后缀数组，发现用它也可以解出这道题，所以就试了试，但说实话很失败……输出错了还以为算法错了白调了半天，后缀数组做这道题代码很长（也许是我写坏了），基本思路就是连在一起然后二分答案对后缀数组分组。

[代码]：

KMP

 1 var
 2   tc, n: longint;
 3   p: array[0..100] of longint;
 4   w: array[0..100] of string;
 5 
 6 procedure init;
 7 var
 8   i: longint;
 9 begin
10   readln(n);
11   for i := 1 to n do
12     readln(w[i]);
13   //for i := 1 to n do writeln(w[i]);
14 end;
15 
16 function KMP(s1, s2: string):boolean;
17 var
18   t1, t2, k, i: longint;
19 begin
20   t1 := length(s1);
21   t2 := length(s2);
22   fillchar(p,sizeof(p),0);
23   k := 0;
24   p[1] := 0;
25   for i := 2 to t2 do
26     begin
27       while (k > 0) and (s2[i] <> s2[k+1]) do k := p[k];
28       if s2[i] = s2[k+1] then inc(k);
29       p[i] := k;
30     end;
31   k := 0;
32   for i := 1 to t1 do
33     begin
34       while (k > 0) and (s2[k+1] <> s1[i]) do k := p[k];
35       if s2[k+1] = s1[i] then inc(k);
36       if k = t2 then exit(true);
37     end;
38   exit(false);
39 end;
40 
41 procedure work;
42 var
43   len, i, j: longint;
44   s, ans: string;
45   f: boolean;
46 begin
47   ans := '';
48   for len := 60 downto 2 do
49     begin
50       for i := 1 to 60-len+1 do
51         begin
52           f := true;
53           s := copy(w[1],i,len);
54           //writeln(s);
55           for j := 2 to n do
56             if not KMP(w[j],s) then
57               begin f := false; break; end;
58           if f then
59             if (ans = '') or (ans > s) then ans := s;
60         end;
61       if ans <> '' then break;
62     end;
63 //  writeln(ans);
64   if ans = '' then writeln('no significant commonalities') else writeln(ans);
65 end;
66 
67 begin
68 //  assign();reset(input);
69 //  assign(output,'d:\1.out');rewrite(output);
70   readln(tc);
71   while tc <> 0 do
72     begin
73       init;
74       work;
75       //readln(w[1]);
76       //readln(w[2]);
77       //writeln(KMP(w[2],w[1]));
78       dec(tc);
79     end;
80  // close(output);
81 end.

后缀数组

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

const int MAXL=70;
const int MAXN=800;

int n,test,x,df;
int top[MAXN],r[MAXN],height[MAXN],sa[MAXN],temp[MAXN];
int s[MAXN],belong[MAXN];
char s1[MAXL],q[MAXL];
bool v[MAXL];
set<string> p;

void Make()
{
    int i,j,m,len;
    memset(top,0,sizeof(top));
    m=n<256?256:n;
    for (i=0;i<n;++i) ++top[r[i]=s[i]&0xff];
    for (i=1;i<m;++i) top[i]+=top[i-1];
    for (i=0;i<n;++i) sa[--top[r[i]]]=i;
    for (len=1;len<n;len<<=1)
    {
        for (i=0;i<n;++i)
        {
            j=sa[i]-len;
            if (j<0) j+=n;
            temp[top[r[j]]++]=j;
        }
        sa[temp[top[0]=0]]=j=0;
        for (i=1;i<n;++i)
        {
            if (r[temp[i]]!=r[temp[i-1]] ||
                r[temp[i]+len]!=r[temp[i-1]+len])
                top[++j]=i;
            sa[temp[i]]=j;
        }
        memcpy(r,sa,sizeof(sa));
        memcpy(sa,temp,sizeof(sa));
        if (j>=n-1) break;
    }
}

void Lcp()
{
    int i,j,k;
    for (j=r[height[i=k=0]=0];i<n-1;++i,++k)
        while (k>=0 && s[i]!=s[sa[j-1]+k])
            height[j]=k--,j=r[sa[j]+1];
}

bool Judge(int limit)
{
    int i,d=0;
    memset(v,0,sizeof(v));
    v[0]=1;
    if (!v[belong[sa[0]]]) ++d;
    v[belong[sa[0]]]=1;
    for (i=1;i<n;++i)
    {
        if (height[i]<limit)
        {
            d=0;
            memset(v,0,sizeof(v));
            v[0]=1;
        }
        if (!v[belong[sa[i]]]) ++d;
        v[belong[sa[i]]]=1;
        if (d>=x) return 1;
    }
    return 0;
}

void Print(int limit)
{
     int i,d=0,j,len;
     memset(v,0,sizeof(v));
     v[0]=1;
     if (!v[belong[sa[i]]]) ++d;
     v[belong[sa[0]]]=1;
     for (int i=1;i<n;++i)
     {
         if (height[i]<limit)
         {
                             d=0;
                             memset(v,0,sizeof(v));
                             v[0]=1;
         }
         if (!v[belong[sa[i]]]) ++d;
         v[belong[sa[i]]]=1;
         if (d>=x)
         {
                  len=0;
                  memset(q,0,sizeof(q));
                  for (int j=sa[i];j<sa[i]+limit;++j)
                      q[len++]=s[j];
                  p.insert(q);
         }
     }
}

void Solve()
{
    int l=1,r=60,mid,ans=0;
    while (l<=r)
    {
        mid=(l+r)/2;
        if (Judge(mid)) ans=mid,l=mid+1; else r=mid-1;
    }
    if (ans<3) printf("no significant commonalities\n"); else printf(""),Print(ans),cout<<*p.begin()<<endl;
}

int main()
{
    freopen("in.txt","r",stdin);
    freopen("out.txt","w",stdout);
    scanf("%d",&test);
    while (test--)
    {
        n=df=0;
        p.clear();
        scanf("%d",&x);
        for (int i=1;i<=x;++i)
        {
            scanf("%s",s1);
            int len=strlen(s1);
            //printf("%d\n",len);
            for (int j=0;j<len;++j)
                s[n++]=(int)s1[j],belong[n-1]=i;
            s[n++]=++df,belong[n-1]=0;
        }
        s[n-1]=0;
        Make();
        Lcp();
        //printf("%d\n",n);
        //for (int i=0;i<n;++i) printf("%d ",height[i]);
        //printf("\n");
        Solve();
    }
    return 0;
}