Codeforces #123D: 后缀数组+单调栈

D. String

 

 

You are given a string s. Each pair of numbers l and r that fulfill the condition 1 ≤ l ≤ r ≤ |s|, correspond to a substring of the string s, starting in the position l and ending in the position r (inclusive).

Let's define the function of two strings F(x, y) like this. We'll find a list of such pairs of numbers for which the corresponding substrings of string x are equal to string y. Let's sort this list of pairs according to the pair's first number's increasing. The value of function F(x, y)equals the number of non-empty continuous sequences in the list.

For example: F(babbabbababbab, babb) = 6. The list of pairs is as follows:

(1, 4), (4, 7), (9, 12)

Its continuous sequences are:

• (1, 4)
• (4, 7)
• (9, 12)
• (1, 4), (4, 7)
• (4, 7), (9, 12)
• (1, 4), (4, 7), (9, 12)

Your task is to calculate for the given string s the sum F(s, x) for all x, that x belongs to the set of all substrings of a string s.

Input

The only line contains the given string s, consisting only of small Latin letters (1 ≤ |s| ≤ 105).

Output

Print the single number — the sought sum.

Please do not use the %lld specificator to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specificator.

Examples

input

Copy

aaaa

output

Copy

20

input

Copy

abcdef

output

Copy

21

input

Copy

abacabadabacaba

output

Copy

188

Note

In the first sample the function values at x equal to "a", "aa", "aaa" and "aaaa" equal 10, 6, 3 and 1 correspondingly.

In the second sample for any satisfying x the function value is 1.

题意：如果某一种子串s在原串中出现了k次，根据题目定义的函数，它产生的贡献是(k+1)*k/2

这个条件很奇怪，我们尝试转化模型，就会发现这个函数相当于我们将这k个s串排成一排，每个

串和它自己以及后面的串匹配一次，总次数就是题目要求的函数

于是我们可以上后缀数组+高度数组，对于每一个后缀，和后面的每一个后缀的算一个最长公共前缀，然后根据长度统计答案

这个东西可以用单调栈搞一搞，最后每个后缀和自己可以匹配一次，也就是说如果读入的串长度为n，ans+=(n+1)*n/2

代码：

 //#include"bits/stdc++.h"
 #include"cstdio"
 #include"map"
 #include"set"
 #include"cmath"
 #include"queue"
 #include"vector"
 #include"string"
 #include"ctime"
 #include"stack"
 #include"deque"
 #include"cstdlib"
 #include"cstring"
 #include"iostream"
 #include"algorithm"

 #define db double
 #define ll long long
 #define vec vector<ll>
 #define Mt  vector<vec>
 #define ci(x) scanf("%d",&x)
 #define cd(x) scanf("%lf",&x)
 #define cl(x) scanf("%lld",&x)
 #define pi(x) printf("%d\n",x)
 #define pd(x) printf("%f\n",x)
 #define pl(x) printf("%lld\n",x)
 //#define rep(i, x, y) for(int i=x;i<y;i++)
 #define rep(i, n) for(int i=0;i<n;i++)
 using namespace std;
 const int N   = 1e6 + ;
 const int mod = 1e9 + ;
 const int MOD = mod - ;
 const int inf = 0x3f3f3f3f;
 const db  PI  = acos(-1.0);
 const db  eps = 1e-;
 int sa[N];
 int rk[N];
 int tmp[N];
 int lcp[N];
 int n,k;
 bool cmp(int i,int j){
     if(rk[i] != rk[j]) return rk[i]<rk[j];
     else
     {
         int ri=i+k<=n?rk[i+k]:-;
         int rj=j+k<=n?rk[j+k]:-;
         return ri<rj;
     }
 }
 void bulid(string s,int *sa)
 {
     n=(int)s.size();
     for(int i=;i<=n;i++){
         sa[i]=i;
         rk[i]=i<n?s[i]:-;
     }
     for(k=;k<=n;k*=){
         sort(sa,sa+n+,cmp);
         tmp[sa[]]=;
         for(int i=;i<=n;i++){
             tmp[sa[i]]=tmp[sa[i-]]+(cmp(sa[i-],sa[i])?:);
         }
         for(int i=;i<=n;i++){
             rk[i]=tmp[i];
         }
     }
 }
 void LCP(string s,int *sa,int *lcp){
     n=(int)s.size();
     for(int i=;i<=n;i++) rk[sa[i]]=i;
     int h=;
     lcp[]=;
     for(int i=;i<n;i++){
         int j=sa[rk[i]-];
         for (h ? h-- : ; j + h < n&&i + h < n&&s[j + h] == s[i + h]; h++);
         lcp[rk[i]-] = h;
     }
 }
 #define x first
 #define y second
 #define Pair pair<int,int>
 #define mp make_pair

 stack<Pair> sta;
 int main ()
 {
     string s;
     cin>>s;
     n=s.length();
     bulid(s,sa);
     LCP(s,sa,lcp);
     ll ans=(ll)n*(ll)(n+)/;
     ll cnt=;
     for (int i=;i<=n;i++)
     {
         Pair ins=mp(lcp[i],);//贡献为lcp[i]*num
         while (!sta.empty() && sta.top().x>ins.x)
         {
             cnt-=(ll)sta.top().x*sta.top().y;
             ins.y+=sta.top().y;
             sta.pop();
         }
         cnt+=(ll)ins.x*ins.y;
         sta.push(ins);
         ans+=cnt;
     }
     cout<<ans<<endl;
     return ;
 }