【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=,f=;
    char c=getchar();
    while(c<||<c) {if(c=='-') f=-; c=getchar();}
    while(<=c&&c<=) v=(v<<)+v+v+c-,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=;i<n;i++) wc[x[i]=r[i]]++;
     for(i=;i<m;i++) wc[i]+=wc[i-];
     for(i=n-;i>=;i--) sa[--wc[x[i]]]=i;
     for(j=,p=;p<n;j*=,m=p)
     {
         p=;
         for(i=n-j;i<n;i++) y[p++]=i;
         for(i=;i<n;i++)
          if(sa[i]>=j) y[p++]=sa[i]-j;
         for(i=;i<n;i++) wd[i]=x[y[i]];
         for(i=;i<m;i++) wc[i]=;
         for(i=;i<n;i++) wc[wd[i]]++;
         for(i=;i<m;i++) wc[i]+=wc[i-];
         for(i=n-;i>=;i--) sa[--wc[wd[i]]]=y[i];
         swap(x,y);
         p=; x[sa[]]=;
         for(i=;i<n;i++) x[sa[i]]=cmp(y,sa[i-],sa[i],j)?p-:p++;
     }
 }    

 void getheight(int *r,int *sa,int n)
 {
     int i,j,k=;
     for(i=;i<=n;i++) rank[sa[i]]=i;
     for(i=;i<n;height[rank[i++]]=k)
     {
         if(k) k--;
         j=sa[rank[i]-];
         while(r[i+k]==r[j+k]) k++;
     }
 }

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

 void solve(ll f,int L,int R)
 {
     //printf("%lld %d %d\n",f,L,R);
     for(int i=L-;i<=R+;i++) H[i]=height[i];
     for(int i=L;i<=R;i++) c[i]=d[i]=;
     stk[]=L-; H[L-]=-oo;
     int top=;
     for(int i=L;i<=R;i++)
     {
         while(top&&H[i]<H[stk[top]]) top--;
         if(stk[top]==L-) c[i]=L;
          else c[i]=stk[top]+;
         stk[++top]=i;
     }
     stk[]=R+; H[R+]=-oo;
     top=;
     for(int i=R;i>=L;i--)
     {
         while(top&&H[i]<=H[stk[top]]) top--;
         if(stk[top]==R+) d[i]=R;
          else d[i]=stk[top]-;
         stk[++top]=i;
     }
     ll tmp=;
     for(int i=L;i<=R;i++) tmp=tmp+(-c[i]+i+)*(d[i]-i+)*height[i];
 //    printf("%lld\n",tmp);
     ll t=R-L+;
     tmp=tmp-K*(t+)*t/;
 //    printf("%lld\n",tmp);
     for(int i=L;i<=R;i++) tmp=tmp+(-c[i]+i+)*(d[i]-i+);
 //    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==) break;
         ans=;
         init();
         scanf("%s",a);
         int n1=strlen(a);
         scanf("%s",b);
         int n2=strlen(b);
         for(int i=;i<n1;i++)
          if('A'<=a[i]&&a[i]<='Z') s[i]=a[i]-'A'+;
           else s[i]=a[i]-'a'+;
         s[n1]=;
         n=n1;
         getsa(s,sa,n+,);
         getheight(s,sa,n);

         int i=;
         while(i<n)
         {
             i++;
             if(height[i]>=K)
             {
                 int st=i;
                 while(i<=n&&height[i]>=K) i++;
                 if(st<=i-) solve(-,st,i-);
             }
         }
         //printf("%lld\n",ans);

         init();
         for(int i=;i<n2;i++)
          if('A'<=b[i]&&b[i]<='Z') s[i]=b[i]-'A'+;
           else s[i]=b[i]-'a'+;
         s[n2]=;
         n=n2;
         getsa(s,sa,n+,);
         getheight(s,sa,n);
         i=;
         while(i<n)
         {
             i++;
             if(height[i]>=K)
             {
                 int st=i;
                 while(i<=n&&height[i]>=K) i++;
                 if(st<=i-) solve(-,st,i-);
             }
         }
     //    printf("%lld\n",ans);

         init();
         for(int i=;i<n1;i++)
          if('A'<=a[i]&&a[i]<='Z') s[i]=a[i]-'A'+;
           else s[i]=a[i]-'a'+;
         s[n1]=;
         for(int i=;i<n2;i++)
          if('A'<=b[i]&&b[i]<='Z') s[n1+i+]=b[i]-'A'+;
           else s[n1+i+]=b[i]-'a'+;
         s[n1+n2+]=;
         n=n1+n2+;
         getsa(s,sa,n+,);
         getheight(s,sa,n);
     //    for(int i=1;i<=n;i++) printf("%d\n",sa[i]);
         i=;
         while(i<n)
         {
             i++;
             if(height[i]>=K)
             {
                 int st=i;
                 while(i<=n&&height[i]>=K) i++;
                 if(st<=i-) solve(,st,i-);
             }
         }
         //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 ;
 }