【后缀数组+二分】PKU 3294 Life Forms

【后缀数组+二分】PKU 3294 Life Forms

 

/**/ /*
【题目】给你N个字符串，输出若干个子串，满足大于N/2个字符串含有它。
【分析】先将N个字符串并成一个字符串，中间用不同的符号分割开。
        然后利用后缀数组求出Height数组，二分枚举答案X，将Height分为若干组（如何分组？
        若Height[I]大于等于X，则属于上一组，否则属于新的一组），
        若某个组里面的后缀的来源是大于N/2个字符串的，则可行，继续放大X，
        否则缩小X。若最后X=0则No Answer，否则再次分组，输出满足条件的组的前缀。
*/
#include < iostream >
#include < cmath >
#include < cstring >
#include < algorithm >
#include < set >
#include < string >
using   namespace  std;
#define  maxn 100000+105
char  s[maxn];
int  sa[maxn],h[maxn],height[maxn],rank[maxn];
int  k,n;
int  maxlen;
int  m;
int  belong[maxn];
set < string > outset;
bool  cmp1( const   int   &  a, const   int   &  b)
{
    return (s[a]<s[b]);
}
bool  cmp2( const   int   &  a, const   int   &  b)
{
    return (rank[a]<rank[b] || (rank[a]==rank[b]&&
        (a+k<n?rank[a+k]:-1)<(b+k<n?rank[b+k]:-1)));
}
void  suffixArray()
{
    int i,j;
    for(i=0;i<n;i++)
        sa[i]=i;
    sort(sa,sa+n,cmp1);
    for(i=0;i<n;i++)
    {
        if(i==0||s[sa[i]]!=s[sa[i-1]])
            rank[sa[i]]=i;
        else rank[sa[i]]=rank[sa[i-1]];
    }
    for(k=1;k<n;k*=2)
    {
        sort(sa,sa+n,cmp2);
        for(i=0;i<n;i++)
        {
            if( i==0 || (cmp2(sa[i],sa[i-1])||cmp2(sa[i-1],sa[i])) )
                h[sa[i]]=i;
            else h[sa[i]]=h[sa[i-1]];
        }
        memcpy(rank, h, n * sizeof(int)); 
    }

    height[0] = 0; 
    for(i = 0, j = 0; i < n; i++)   
    { 
        if(rank[i]>0)
        {
            while(s[sa[rank[i] - 1] + j] == s[i + j])  
                j++; 
            height[rank[i]] = j; 
            if(j > 0) j--; 
        }
     }
}
bool  ok( int  len)
{
    int count=0;
    bool visit[105]={0};
    for(int i=1;i<n;i++)
    {
        if(height[i]<len)
        {
            if(count>0)
            {
                count=0;
                memset(visit,0,sizeof(visit));
            }
        }
        else
        {
            if(!visit[belong[sa[i-1]]])
            {
                visit[belong[sa[i-1]]]=1;
                count++;
            }
            if(!visit[belong[sa[i]]])
            {
                visit[belong[sa[i]]]=1;
                count++;
            }
            //if(count>=ceil((double)m/2))
            if(count>m/2)
                return 1;
        }
    }
    return 0;
}
int  binarySearch()
{
    int l=0,r=maxlen;
    int mid;
    while(l<r)
    {
        mid=(l+r+1)>>1;
        if(ok(mid))
            l=mid;
        else r=mid-1;
    }
    return l;
}
void  search( int  len)
{
    outset.clear();
    bool visit[105]={0};
    int count=0;
    for(int i=1;i<n;i++)
    {
        if(height[i]<len)
        {
            if(count>0)
            {
                if(count>m/2)
                {
                    for(int j=0,index=sa[i-1];j<len;j++)
                        putchar(s[j+index]);
                    putchar('\n');
                }
                count=0;
                memset(visit,0,sizeof(visit));
            }
        }
        else
        {
            if(!visit[belong[sa[i-1]]])
            {
                visit[belong[sa[i-1]]]=1;
                count++;
            }
            if(!visit[belong[sa[i]]])
            {
                visit[belong[sa[i]]]=1;
                count++;
            }
        }
    }
}
int  main()
{
    int tmp,j,ans;
    bool first=1;
    while(scanf("%d", &m)!=EOF&&m)
    {
        if(!first)
        {
            printf("\n");
        }
        else first=0;

        n=0;
        maxlen=0;
        for(int i=0;i<m;i++)
        {
            scanf("%s",s+n);
            
            for(j=n;s[j];j++)
                belong[j]=i;

            tmp=j-n;
            if(tmp>maxlen)
                maxlen=tmp;
            
            n+=tmp;
            
            s[n++]='z'+i+1;
        }
        //s[n]='$';
        suffixArray();
        ans=binarySearch();
        if(!ans)
            printf("?\n");
        else
            search(ans);
    }
    return 0; 
}