codeforces432D Prefixes and Suffixes(kmp+dp)

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D. Prefixes and Suffixes

You have a string s = s₁s₂...s_|s|, where |s| is the length of string s, and s_i its i-th character.

Let's introduce several definitions:

• A substring s[i..j] (1 ≤ i ≤ j ≤ |s|) of string s is string s_is_i + 1...s_j.
• The prefix of string s of length l (1 ≤ l ≤ |s|) is string s[1..l].
• The suffix of string s of length l (1 ≤ l ≤ |s|) is string s[|s| - l + 1..|s|].

Your task is, for any prefix of string s which matches a suffix of string s, print the number of times it occurs in string s as a substring.

Input

The single line contains a sequence of characters s₁s₂...s_|s| (1 ≤ |s| ≤ 10⁵) — string s. The string only consists of uppercase English letters.

Output

In the first line, print integer k (0 ≤ k ≤ |s|) — the number of prefixes that match a suffix of string s. Next print k lines, in each line print two integers l_i c_i. Numbers l_i c_i mean that the prefix of the length l_i matches the suffix of length l_i and occurs in string s as a substring c_i times. Print pairs l_i c_i in the order of increasing l_i.

Sample test(s)

Input

ABACABA

Output

3
1 4
3 2
7 1

Input

AAA

Output

3
1 3
2 2
3 1

题意：

　　给出一个字符串，问每种既是前缀，又是后缀的字符串出现的次数kmp+dp,利用kmp求出所有的前后缀，考虑到若第i位既是前缀又是后缀，则kmp中的p[i]位也一定是，由此可以得到一个状态转移的方程dp[p[i]]+=dp[i],初始化所有的dp[i]=1，因为还包括它本身。

我队友curs0r是用后缀数组做的。。。。。。

#include <iostream>
#include <sstream>
#include <ios>
#include <iomanip>
#include <functional>
#include <algorithm>
#include <vector>
#include <string>
#include <list>
#include <queue>
#include <deque>
#include <stack>
#include <set>
#include <map>
#include <cstdio>
#include <cstdlib>
#include <cmath>
#include <cstring>
#include <climits>
#include <cctype>
using namespace std;
#define XINF INT_MAX
#define INF 0x3FFFFFFF
#define MP(X,Y) make_pair(X,Y)
#define PB(X) push_back(X)
#define REP(X,N) for(int X=0;X<N;X++)
#define REP2(X,L,R) for(int X=L;X<=R;X++)
#define DEP(X,R,L) for(int X=R;X>=L;X--)
#define CLR(A,X) memset(A,X,sizeof(A))
#define IT iterator
typedef long long ll;
typedef pair<int,int> PII;
typedef vector<PII> VII;
typedef vector<int> VI;
#define MAXN 100010
char s[MAXN];
int p[MAXN];
int dp[MAXN];
int vis[MAXN];
void getp()
{
    p[1]=0;
    int len=strlen(s+1);
    for(int i=2,j=0;i<=len;i++)
    {
        while(j>0&&s[j+1]!=s[i])j=p[j];
        if(s[j+1]==s[i])j+=1;
        p[i]=j;
    }
}


int main()
{
    ios::sync_with_stdio(false);
    while(cin>>s+1)
    {
        int len=strlen(s+1);
        getp();
        for(int i=1;i<=len;i++)
        {
            dp[i]=1;
        }
        int i=len;
        int k=0;
        while(i)
        {
            vis[k]=i;
            k++;
            i=p[i];
        }
        for(i=len;i>0;i--)
        {
            dp[p[i]]+=dp[i];
        }
        cout<<k<<endl;
        for(i=k-1;i>=0;i--)
        {
            cout<<vis[i]<<" "<<dp[vis[i]]<<endl;
        }
    }
    return 0;
}