【POJ3415】Common Substrings（后缀数组，单调栈）

题意：

n<=1e5

思路：

我的做法和题解有些不同

题解是维护A的单调栈算B的贡献，反过来再做一次

我是去掉起始位置不同这个限制条件先算总方案数，再把两个串内部不合法的方案数减去

式子展开之后是 sigma(lcp(i,j))-K*L*(L+1)/2+合法(i,j)对数，其中L为连续的height[i]>=K的区域长度

sigma(lcp(i,j))计算部分与BZOJ3238类似

#include<cstdio>
#include<cstring>
#include<string>
#include<cmath>
#include<iostream>
#include<algorithm>
#include<map>
#include<set>
#include<queue>
#include<vector>
using namespace std;
typedef long long ll;
typedef unsigned int uint;
typedef unsigned long long ull;
typedef pair<int,int> PII;
typedef vector<int> VI;
#define fi first
#define se second 
#define MP make_pair
#define N   210000
#define MOD 1000000007
#define eps 1e-8 
#define pi acos(-1)
#define oo  1000000000

char a[N],b[N];
int n,i,s[N],sa[N],wa[N],wb[N],wc[N],wd[N],height[N],rank[N],
    H[N],stk[N];
ll ans,K,c[N],d[N];

int read()
{ 
   int v=0,f=1;
   char c=getchar();
   while(c<48||57<c) {if(c=='-') f=-1; c=getchar();}
   while(48<=c&&c<=57) v=(v<<3)+v+v+c-48,c=getchar();
   return v*f;
}

bool cmp(int *r,int a,int b,int l)
{
    return r[a]==r[b]&&r[a+l]==r[b+l];
}

void getsa(int *r,int *sa,int n,int m)
{
    int *x=wa,*y=wb,j,p;
    for(i=0;i<n;i++) wc[x[i]=r[i]]++;
    for(i=1;i<m;i++) wc[i]+=wc[i-1];
    for(i=n-1;i>=0;i--) sa[--wc[x[i]]]=i;
    for(j=1,p=1;p<n;j*=2,m=p)
    {
        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<n;i++) wd[i]=x[y[i]];
        for(i=0;i<m;i++) wc[i]=0;
        for(i=0;i<n;i++) wc[wd[i]]++; 
        for(i=1;i<m;i++) wc[i]+=wc[i-1];
        for(i=n-1;i>=0;i--) sa[--wc[wd[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++;
    }
}    
    
void getheight(int *r,int *sa,int n)
{
    int i,j,k=0;
    for(i=1;i<=n;i++) rank[sa[i]]=i;
    for(i=0;i<n;height[rank[i++]]=k)
    {
        if(k) k--;
        j=sa[rank[i]-1];
        while(r[i+k]==r[j+k]) k++;
    }
}

void init()
{    
        memset(s,0,sizeof(s));
        memset(sa,0,sizeof(sa));
        memset(wa,0,sizeof(wa));
        memset(wb,0,sizeof(wb));
        memset(wc,0,sizeof(wc));
        memset(wd,0,sizeof(wd));
        memset(height,0,sizeof(height));
        memset(rank,0,sizeof(rank));
}

void solve(ll f,int L,int R)
{
    //printf("%lld %d %d\n",f,L,R);
    for(int i=L-1;i<=R+1;i++) H[i]=height[i];
    for(int i=L;i<=R;i++) c[i]=d[i]=0;
    stk[1]=L-1; H[L-1]=-oo; 
    int top=1;
    for(int i=L;i<=R;i++)
    {
        while(top&&H[i]<H[stk[top]]) top--;
        if(stk[top]==L-1) c[i]=L;
         else c[i]=stk[top]+1;
        stk[++top]=i;
    }
    stk[1]=R+1; H[R+1]=-oo;
    top=1;
    for(int i=R;i>=L;i--)
    {
        while(top&&H[i]<=H[stk[top]]) top--;
        if(stk[top]==R+1) d[i]=R;
         else d[i]=stk[top]-1;
        stk[++top]=i;
    } 
    ll tmp=0;
    for(int i=L;i<=R;i++) tmp=tmp+(-c[i]+i+1)*(d[i]-i+1)*height[i];
//    printf("%lld\n",tmp);
    ll t=R-L+1;
    tmp=tmp-K*(t+1)*t/2;
//    printf("%lld\n",tmp);
    for(int i=L;i<=R;i++) tmp=tmp+(-c[i]+i+1)*(d[i]-i+1);
//    printf("%lld\n",tmp);
    ans=ans+f*tmp;
} 
    

int main()
{
    freopen("poj3415.in","r",stdin);
    freopen("poj3415.out","w",stdout); 
    while(scanf("%lld",&K)!=EOF)
    {
        if(K==0) break;
        ans=0;
        init();
        scanf("%s",a);
        int n1=strlen(a);
        scanf("%s",b);
        int n2=strlen(b);
        for(int i=0;i<n1;i++) 
         if('A'<=a[i]&&a[i]<='Z') s[i]=a[i]-'A'+2;
          else s[i]=a[i]-'a'+28;
        s[n1]=1;
        n=n1;
        getsa(s,sa,n+1,100);
        getheight(s,sa,n);
    
        int i=1;
        while(i<n)
        {
            i++;
            if(height[i]>=K)
            {
                int st=i;
                while(i<=n&&height[i]>=K) i++;
                if(st<=i-1) solve(-1,st,i-1);
            }
        }
        //printf("%lld\n",ans);
    
         
        init();
        for(int i=0;i<n2;i++) 
         if('A'<=b[i]&&b[i]<='Z') s[i]=b[i]-'A'+2;
          else s[i]=b[i]-'a'+28;
        s[n2]=1;
        n=n2;
        getsa(s,sa,n+1,100);
        getheight(s,sa,n);
        i=1;
        while(i<n)
        {
            i++;
            if(height[i]>=K)
            {
                int st=i;
                while(i<=n&&height[i]>=K) i++;
                if(st<=i-1) solve(-1,st,i-1);
            }
        }
    //    printf("%lld\n",ans);
    
        init();
        for(int i=0;i<n1;i++) 
         if('A'<=a[i]&&a[i]<='Z') s[i]=a[i]-'A'+2;
          else s[i]=a[i]-'a'+28;
        s[n1]=1;
        for(int i=0;i<n2;i++)
         if('A'<=b[i]&&b[i]<='Z') s[n1+i+1]=b[i]-'A'+2;
          else s[n1+i+1]=b[i]-'a'+28;
        s[n1+n2+1]=0;
        n=n1+n2+1;
        getsa(s,sa,n+1,100);
        getheight(s,sa,n);
    //    for(int i=1;i<=n;i++) printf("%d\n",sa[i]);
        i=1;
        while(i<n)
        {
            i++;
            if(height[i]>=K)
            {
                int st=i;
                while(i<=n&&height[i]>=K) i++;
                if(st<=i-1) solve(1,st,i-1);
            }
        }
        //for(int i=0;i<=n1+n2;i++) printf("%d\n",sa[i]);
        //for(int i=2;i<=n1+n2+2;i++) printf("%d\n",height[i]);
        printf("%lld\n",ans);
    } 
    return 0;
}