POJ 3261 Milk Patterns (离散化+后缀数组可重叠k次最长重复子串)

Bertha 。 2021-11-16 10:06 194阅读 0赞

2014-6-23 更新

用DC3重写了此题，同时更换了height数组分组后的统计方法

原代码 4804K407MS

修改后 1048K32MS

————————————分割线——————————————

题意：给出一串长度为n的字符，再给出一个k值，要你求重复次数大于等于k次的最长子串长度

思路：首先离散化，二分答案，按照二分值k将height数组分组，对于k是否可行的判定：由height数组性质，同一组中个数大于等于k则可行。

#pragma warning(disable:4786)
    #include <set>
    #include <map>
    #include <cstdio>
    #include <cstring>
    #include <cstdlib>
    #include <algorithm>
    #include <vector>
    using namespace std;
    #define max(a,b) ((a)>(b)?(a):(b))
    #define min(a,b) ((a)<(b)?(a):(b))
    
    const int N = int(2e5)+10;
    
    int cmp(int *r,int a,int b,int l){
        return (r[a]==r[b]) && (r[a+l]==r[b+l]);
    }
    int wa[N],wb[N],ws[N],wv[N];
    int rank[N],height[N];
    
    void DA(int *r,int *sa,int n,int m){
        int i,j,p,*x=wa,*y=wb,*t;
        for(i=0;i<m;i++) ws[i]=0;
        for(i=0;i<n;i++) ws[x[i]=r[i]]++;
        for(i=1;i<m;i++) ws[i]+=ws[i-1];
        for(i=n-1;i>=0;i--) sa[--ws[x[i]]]=i;
        for(j=1,p=1;p<n;j*=2,m=p)
        {
            for(p=0,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<n;i++) wv[i]=x[y[i]];
            for(i=0;i<m;i++) ws[i]=0;
            for(i=0;i<n;i++) ws[wv[i]]++;
            for(i=1;i<m;i++) ws[i]+=ws[i-1];
            for(i=n-1;i>=0;i--) sa[--ws[wv[i]]]=y[i];
            for(t=x,x=y,y=t,p=1,x[sa[0]]=0,i=1;i<n;i++)
                x[sa[i]]=cmp(y,sa[i-1],sa[i],j)?p-1:p++;
            //printf("p = %d\n", p );
        }
    }
    void calheight(int *r,int *sa,int n){
      //  memset(height,0,sizeof(height));
      //  memset(rank,0,sizeof(rank));
        int i,j,k=0;
        for(i=1;i<=n;i++) rank[sa[i]]=i;
        for(i=0;i<n; height[rank[i++]] = k )
        for(k?k--:0,j=sa[rank[i]-1]; r[i+k]==r[j+k]; k++);
    }
    
    
    int data[N],sa[N],temp[N],n,k;
    map<int,int> mp;
    
    vector<int> S[N];
    
    bool Judge (int a)
    {
    	int i,cur = -1;
    	for (i=1;i<=n;i++)   //分组
    	{
    		if (height[i] < a)
    			S[++cur].clear();
    		S[cur].push_back(i);
    	}
    	for (i=0;i<=cur;i++)
    		if (S[i].size()>=k)
    			return true;
    	return false;
    }
    
    void Deal (int *data,int n,int m,int K)
    {
        DA(data,sa,n+1,m);
        calheight(data,sa,n);
    	int low=0,high=n,mid,ans=0;
    	while (low<high)   //注意二分的写法
    	{
    		mid = (low+high)>>1;
    		if ( Judge(mid) )
    			ans=mid,low=mid+1;
    		else high = mid;
    	}
    	printf("%d\n",ans);
    }
    
    int main ()
    {  
    #ifdef ONLINE_JUDGE
    #else
    	freopen("read.txt","r",stdin);
    #endif
    	while (~scanf("%d%d",&n,&k))
    	{
    		int i;
    		for (i=0;i<n;i++)
    		{
    			scanf("%d",&data[i]);
    			temp[i]=data[i];
    		}
    		if (n==1 && k==1)
    		{
    			printf("1\n");
    			continue;
    		}
    		sort(temp,temp+n);
    		int sz = unique(temp,temp+n)-temp;  //去重
    		mp.clear();
    		for (i=0;i<sz;i++)    //离散化
    			mp[ temp[i] ] = i+1;
    		for (i=0;i<n;i++)
    			data[i] = mp[ data[i] ];
    		data[n] = 0;
            Deal(data,n,sz+1,k-1);
    	}
    	return 0;
    }

#pragma warning(disable:4786)
    #include <set>
    #include <map>
    #include <cstdio>
    #include <cstring>
    #include <cstdlib>
    #include <algorithm>
    #include <vector>
    using namespace std;
    #define max(a,b) ((a)>(b)?(a):(b))
    #define min(a,b) ((a)<(b)?(a):(b))
    
    const int N = int(2e4)+10;
    
    #define F(x) ((x)/3+((x)%3==1?0:tb))
    #define G(x) ((x)<tb?(x)*3+1:((x)-tb)*3+2)
    
    int wa[N],wb[N],wv[N],ws[N];
    int c0 (int *r,int a,int b){
    	return r[a]==r[b] && r[a+1]==r[b+1] && r[a+2]==r[b+2];
    }
    int c12 (int k,int *r,int a,int b){
    	if (k==2) return r[a]<r[b] || r[a]==r[b] && c12(1,r,a+1,b+1);
    	else return r[a]<r[b] || r[a]==r[b] && wv[a+1]<wv[b+1];
    }
    void sort (int *r,int *a,int *b,int n,int m){
    	int i;
    	for(i=0;i<n;i++) wv[i]=r[a[i]];
    	for(i=0;i<m;i++) ws[i]=0;
    	for(i=0;i<n;i++) ws[wv[i]]++;
    	for(i=1;i<m;i++) ws[i]+=ws[i-1];
    	for(i=n-1;i>=0;i--) b[--ws[wv[i]]]=a[i];
    }
    void DC3 (int *r,int *sa,int n,int m){
    	int i,j,*rn=r+n,*san=sa+n,ta=0,tb=(n+1)/3,tbc=0,p;
    	r[n]=r[n+1]=0;
    	for(i=0;i<n;i++) if(i%3!=0) wa[tbc++]=i;
    	sort(r+2,wa,wb,tbc,m);
    	sort(r+1,wb,wa,tbc,m);
    	sort(r,wa,wb,tbc,m);
    	for(p=1,rn[F(wb[0])]=0,i=1;i<tbc;i++)
    		rn[F(wb[i])]=c0(r,wb[i-1],wb[i])?p-1:p++;
    	if(p<tbc) DC3(rn,san,tbc,p);
    	else for(i=0;i<tbc;i++) san[rn[i]]=i;
    	for(i=0;i<tbc;i++) if(san[i]<tb) wb[ta++]=san[i]*3;
    	if(n%3==1) wb[ta++]=n-1;
    	sort(r,wb,wa,ta,m);
    	for(i=0;i<tbc;i++) wv[wb[i]=G(san[i])]=i;
    	for(i=0,j=0,p=0;i<ta && j<tbc;p++)
    		sa[p]=c12(wb[j]%3,r,wa[i],wb[j])?wa[i++]:wb[j++];
    	for(;i<ta;p++) sa[p]=wa[i++];
    	for(;j<tbc;p++) sa[p]=wb[j++];
    }  
    int rank[N],height[N],sa[3*N],data[3*N];
    
    void calheight(int *r,int *sa,int n){
    //	memset(height,0,sizeof(height));
    //	memset(rank,0,sizeof(rank));
    	int i,j,k=0;
    	for(i=1;i<=n;i++) rank[sa[i]]=i;
    	for(i=0;i<n; height[rank[i++]] = k )
    	for(k?k--:0,j=sa[rank[i]-1]; r[i+k]==r[j+k]; k++);
    }
    
    int temp[N],n,k;
    
    bool Judge (int mid)  
    {  
    	int cnt=1;
    	for (int i=2;i<=n;i++)
    		if (height[i]<mid)
    			cnt=1;
    		else
    		{
                cnt++;
    			if (cnt >= k)  //同一组中个数大于等于k
    				return true;
    		}  
    	return false;
    }
    
    void Deal (int *data,int n,int m)
    {
        DC3(data,sa,n+1,m);
        calheight(data,sa,n);
    	int low=0,high=n,mid,ans=0;
    	while (low<high)   //注意二分的写法
    	{
    		mid = (low+high)>>1;
    		if ( Judge(mid) )
    			ans=mid,low=mid+1;
    		else high = mid;
    	}
    	printf("%d\n",ans);
    }
    
    int main ()
    {
    	while (~scanf("%d%d",&n,&k))
    	{
    		int i;
    		for (i=0;i<n;i++)
    		{
    			scanf("%d",&data[i]);
    			temp[i]=data[i];
    		}
    		if (n==1 && k==1)
    		{
    			printf("1\n");
    			continue;
    		}
    		sort(temp,temp+n);
    		int sz = unique(temp,temp+n)-temp;  //去重
    		map<int,int> mp;
    		for (i=0;i<sz;i++)    //离散化
    			mp[ temp[i] ] = i+1;
    		for (i=0;i<n;i++)
    			data[i] = mp[ data[i] ];
    		data[n] = 0;
    		Deal(data,n,sz+1);
    	}
    	return 0;
    }