C. Fox And Names

C. Fox And Names

https://codeforces.com/problemset/problem/510/C

 

思路

使用拓扑序算法，找出前后的依赖的可能情况。

如果拓扑序未找到所有的节点，表明存在依赖环，这种情况不满足。

Code

https://codeforces.com/problemset/submission/510/195396844

#include <iomanip>
#include <bits/stdc++.h>
#include <iostream>
using namespace std;
#include <limits.h>
#include <math.h>
#include <vector>
#include <set>
#include <map>
#include <stack>
#include <queue>

typedef long long LL;
typedef pair<int, int> pii;
typedef pair<LL, LL> pll;
typedef pair<string, string> pss;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<pii> vii;
typedef vector<LL> vl;
typedef vector<vl> vvl;

double EPS = 1e-9;
int INF = 1000000005;
long long INFF = 1000000000000000005LL;
double PI = acos(-1);
int dirx[8] = { -1, 0, 0, 1, -1, -1, 1, 1 };
int diry[8] = { 0, 1, -1, 0, -1, 1, -1, 1 };

#ifdef TESTING
#define DEBUG fprintf(stderr, "====TESTING====\n")
#define VALUE(x) cerr << "The value of " << #x << " is " << x << endl
#define debug(...) fprintf(stderr, __VA_ARGS__)
#else
#define DEBUG
#define VALUE(x)
#define debug(...)
#endif

#define FOR(a, b, c) for (int(a) = (b); (a) < (c); ++(a))
#define FORN(a, b, c) for (int(a) = (b); (a) <= (c); ++(a))
#define FORD(a, b, c) for (int(a) = (b); (a) >= (c); --(a))
#define FORSQ(a, b, c) for (int(a) = (b); (a) * (a) <= (c); ++(a))
#define FORC(a, b, c) for (char(a) = (b); (a) <= (c); ++(a))
#define FOREACH(a, b) for (auto&(a) : (b))
#define REP(i, n) FOR(i, 0, n)
#define REPN(i, n) FORN(i, 1, n)
#define MAX(a, b) a = max(a, b)
#define MIN(a, b) a = min(a, b)
#define SQR(x) ((LL)(x) * (x))
#define RESET(a, b) memset(a, b, sizeof(a))
#define fi first
#define se second
#define mp make_pair
#define pb push_back
#define ALL(v) v.begin(), v.end()
#define ALLA(arr, sz) arr, arr + sz
#define SIZE(v) (int)v.size()
#define SORT(v) sort(ALL(v))
#define REVERSE(v) reverse(ALL(v))
#define SORTA(arr, sz) sort(ALLA(arr, sz))
#define REVERSEA(arr, sz) reverse(ALLA(arr, sz))
#define PERMUTE next_permutation
#define TC(t) while (t--)

/******************************** COMMON FUNC START ***************************************/

LL quick_pow(LL x,LL n,LL m){
    LL res = 1;
    while(n > 0){
        if(n & 1)    res = res * x % m;
        x = x * x % m;
        n >>= 1;//相当于n=n/2.详情请参考位移运算符。
    }

    return res;
}

inline string IntToString(LL a)
{
    char x[100];
    sprintf(x, "%lld", a);
    string s = x;
    return s;
}

inline LL StringToInt(string a)
{
    char x[100];
    LL res;
    strcpy(x, a.c_str());
    sscanf(x, "%lld", &res);
    return res;
}

inline string GetString(void)
{
    char x[1000005];
    scanf("%s", x);
    string s = x;
    return s;
}

inline string uppercase(string s)
{
    int n = SIZE(s);
    REP(i, n)
    if (s[i] >= 'a' && s[i] <= 'z')
        s[i] = s[i] - 'a' + 'A';
    return s;
}

inline string lowercase(string s)
{
    int n = SIZE(s);
    REP(i, n)
    if (s[i] >= 'A' && s[i] <= 'Z')
        s[i] = s[i] - 'A' + 'a';
    return s;
}

inline void OPEN(string s)
{
#ifndef TESTING
    freopen((s + ".in").c_str(), "r", stdin);
    freopen((s + ".out").c_str(), "w", stdout);
#endif
}

/******************************** COMMON FUNC END ***************************************/

/******************************** GRAPH START ***************************************/
// Graph class represents a directed graph
// using adjacency list representation
class Graph {
public:
    map<int, bool> visited;
    map<int, list<int> > adj;

    // function to add an edge to graph
    void addEdge(int v, int w);

    // DFS traversal of the vertices
    // reachable from v
    void DFS(int v);
};

void Graph::addEdge(int v, int w)
{
    adj[v].push_back(w); // Add w to v’s list.
}

void Graph::DFS(int v)
{
    // Mark the current node as visited and
    // print it
    visited[v] = true;
    cout << v << " ";

    // Recur for all the vertices adjacent
    // to this vertex
    list<int>::iterator i;
    for (i = adj[v].begin(); i != adj[v].end(); ++i)
        if (!visited[*i])
            DFS(*i);
}

/******************************** GRAPH END ***************************************/

/*
https://atcoder.jp/contests/abcxxx/tasks/abcxxx_d
*/

int n;

int main()
{
    cin >> n;
    vector<string> names(n+1);
    
    for(int i=0; i<n; i++){
        cin >> names[i];
    }
    
    map<char, vector<char> > mp;
    map<char, int> indgree;
    
    for(int i=1; i<n; i++){
        string& prev = names[i-1];
        string& now = names[i];
        
        int prevlen = prev.size();
        int nowlen = now.size();
        
        bool found = false;
        int minlen = min(prevlen, nowlen);
        
        for(int j=0; j<minlen; j++){
            char prev_char = prev[j];
            char now_char = now[j];
            
            if (prev_char == now_char){
                continue;
            }
            
            // find the first nonequal char
            found = true;
            
            // record in graph
            mp[prev_char].push_back(now_char);
            indgree[now_char]++;
            
            break;
        }
        
        if (!found && prevlen>nowlen){
            cout << "Impossible" << endl;
            return 0;
        }
    }

    string ans;
    
    // output topological order
    queue<char> topo;
    for(char c='a'; c<='z'; c++){
        if (indgree[c] == 0){
            topo.push(c);
            
            ans += c;
        }
    }

    while(!topo.empty()){
        char now = topo.front();
        topo.pop();
        
        vector<char> nexts = mp[now];
        for(auto next: nexts){
            indgree[next]--;
            
            if (indgree[next] == 0){
                topo.push(next);

                ans += next;
            }
        }
    }
    
    if (ans.size() != 26){
        cout << "Impossible" << endl;
        return 0;
    }

    cout << ans << endl;
    return 0;
}