510C Fox And Names (拓扑排序)

C. Fox And Names

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

Fox Ciel is going to publish a paper on FOCS (Foxes Operated Computer Systems, pronounce: "Fox"). She heard a rumor: the authors list on the paper is always sorted in the lexicographical order.

After checking some examples, she found out that sometimes it wasn't true. On some papers authors' names weren't sorted inlexicographical order in normal sense. But it was always true that after some modification of the order of letters in alphabet, the order of authors becomes lexicographical!

She wants to know, if there exists an order of letters in Latin alphabet such that the names on the paper she is submitting are following in the lexicographical order. If so, you should find out any such order.

Lexicographical order is defined in following way. When we compare s and t, first we find the leftmost position with differing characters: s_i ≠ t_i. If there is no such position (i. e. s is a prefix of t or vice versa) the shortest string is less. Otherwise, we compare characters s_i and t_iaccording to their order in alphabet.

Input

The first line contains an integer n (1 ≤ n ≤ 100): number of names.

Each of the following n lines contain one string name_i (1 ≤ |name_i| ≤ 100), the i-th name. Each name contains only lowercase Latin letters. All names are different.

Output

If there exists such order of letters that the given names are sorted lexicographically, output any such order as a permutation of characters 'a'–'z' (i. e. first output the first letter of the modified alphabet, then the second, and so on).

Otherwise output a single word "Impossible" (without quotes).

Sample test(s)

input

3
rivest
shamir
adleman

output

bcdefghijklmnopqrsatuvwxyz

input

10
tourist
petr
wjmzbmr
yeputons
vepifanov
scottwu
oooooooooooooooo
subscriber
rowdark
tankengineer

output

Impossible

input

10
petr
egor
endagorion
feferivan
ilovetanyaromanova
kostka
dmitriyh
maratsnowbear
bredorjaguarturnik
cgyforever

output

aghjlnopefikdmbcqrstuvwxyz

input

7
car
care
careful
carefully
becarefuldontforgetsomething
otherwiseyouwillbehacked
goodluck

output

acbdefhijklmnogpqrstuvwxyz

 

题意：给定n个字符串，问能否存在这样的字母表，使得字符串的排序满足字典序。即依据新的字母表，排序满足字典序大小。

思路：假设满足字典序，则我们可以依据已有的字符串得出各字母之间的大小关系，然后通过拓扑排序来判断是否存在可行解，输出任意解，因此只需要判断是否存在解即可。

代码：

#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<algorithm>
#include<iostream>
#include<stack>
#include<vector>
#include<queue>
using namespace std;
const int N = 200;
char now[N],pre[N];
int deg[26],ans[26];
vector<int> g[26];
queue<int> que;
int main()
{
    int n,tot = 0;
    cin >> n;
    for(int i=0; i<n; i++)
    {
        cin >> now;
        int len = min(strlen(now),strlen(pre));
        bool ok = false;
        for(int j=0; j<len; j++)
        {
            if(now[j] != pre[j])
            {
                ok = true;
                g[pre[j]-'a'].push_back(now[j]-'a');
                deg[now[j]-'a']++;
                break;
            }
        }
        if(!ok&&strlen(now) < strlen(pre))
        {
            cout << "Impossible" << endl;
            return 0;
        }
        strcpy(pre,now);
    }
    for(int i=0; i<26; i++)
        if(!deg[i])
            que.push(i);
    while(!que.empty())
    {
        int x = que.front();
        ans[tot++] = x;
        que.pop();
        for(int i=0; i<g[x].size(); i++)
        {
            if(deg[g[x][i]] == 1)
                que.push(g[x][i]);
            if(deg[g[x][i]] != 0)
                deg[g[x][i]]--;
        }
    }
    if(tot != 26)
        cout << "Impossible" << endl;
    else
    {
        for(int i=0; i<26; i++)
        {
            char o = 'a'+ ans[i];
            cout << o;
        }
        cout << endl;
    }
}