D. Artsem and Saunders
题目连接：
http://codeforces.com/contest/765/problem/D
Description
Artsem has a friend Saunders from University of Chicago. Saunders presented him with the following problem.
Let [n] denote the set {1, ..., n}. We will also write f: [x] → [y] when a function f is defined in integer points 1, ..., x, and all its values are integers from 1 to y.
Now then, you are given a function f: [n] → [n]. Your task is to find a positive integer m, and two functions g: [n] → [m], h: [m] → [n], such that g(h(x)) = x for all , and h(g(x)) = f(x) for all , or determine that finding these is impossible.
Input
The first line contains an integer n (1 ≤ n ≤ 105).
The second line contains n space-separated integers — values f(1), ..., f(n) (1 ≤ f(i) ≤ n).
Output
If there is no answer, print one integer -1.
Otherwise, on the first line print the number m (1 ≤ m ≤ 106). On the second line print n numbers g(1), ..., g(n). On the third line print m numbers h(1), ..., h(m).
If there are several correct answers, you may output any of them. It is guaranteed that if a valid answer exists, then there is an answer satisfying the above restrictions.
Sample Input
3
1 2 3
Sample Output
3
1 2 3
1 2 3
Hint
题意
给你n个数f(i)
现在让你构造一个长度为n的g(i)，和一个长度为m的h(i),m由你自己定。
要求g(h(x))=x,h(g(x))=f(x)
题解：
g(h(x))= x
h(g(x)) = f(x)
得h(x) = f(h(x))
继而得到f(x) = f(f(x))
从而能够判断是否能够构造成功
然后h(x)就是f(x)的去重排序
从而得到g
代码
#include<bits/stdc++.h>
using namespace std;
const int maxn = 1e5+7;
int a[maxn],n,b[maxn],c[maxn],m;
map<int,int> H;
int main(){
scanf("%d",&n);
for(int i=1;i<=n;i++)
scanf("%d",&a[i]);
for(int i=1;i<=n;i++)
if(a[a[i]]!=a[i]){
cout<<"-1"<<endl;
return 0;
}
for(int i=1;i<=n;i++){
if(!H[a[i]]){
m++;
H[a[i]]=m;
c[m]=a[i];
}
b[i]=H[a[i]];
}
cout<<m<<endl;
for(int i=1;i<=n;i++)
cout<<b[i]<<" ";
cout<<endl;
for(int i=1;i<=m;i++)
cout<<c[i]<<" ";
cout<<endl;
}