LRJ-Example-06-16-Uva10129

#include <cstdio>
#include <cstring>
#include <vector>

using namespace std;

const int maxn =  + ; // at most 1000 lowercase characters

// union find set, each set is a tree
// only letters 'a' through 'z' will appear, so totally 26 nodes
const int maxc = ;

int parent[maxc]; // parent of each node

// find the root node of the set of node x
int findSet(int x) {
    return parent[x] == x ? x : findSet(parent[x]);
}

int used[maxc];
int degree[maxc]; // degree = out degree - in degree

int main() {
    int T;
    int N; // 1 <= N <= 100000
    char word[maxn]; 

    scanf("%d", &T);
    while(T--) {
        scanf("%d", &N);

        memset(used, , sizeof(used));
        memset(degree, , sizeof(degree));

        // init the sets
        for(int i = ; i < maxc; i++) parent[i] = i;
        int numSet = maxc;

        for(int i = ; i < N; i++) {

            // read each word
            scanf("%s", word);
            int first = word[] - 'a';
            int last = word[strlen(word) - ] - 'a';
            // there is an edge first --> last
            degree[first]++;// out degree
            degree[last]--;// in degree

            used[first] = used[last] = ;

            int setFirst = findSet(first);
            int setLast = findSet(last);

            if(setFirst != setLast) {
                // union
                parent[setFirst] = setLast;
                numSet--;
            }
        }

        vector<int> d;
        for(int i = ; i < maxc; i++) {
            if(!used[i])
                numSet--;
                else if (degree[i] != )
                    d.push_back(degree[i]);
            }

            bool ok = false;
            if(numSet ==  && // all nodes are connected
                    // Euler circuit, all nodes have degree 0
                   (d.empty() ||
                    // Euler path, if d[0] == 1, then d[1] == -1, and vice versa
                   (d.size() ==  && (d[] ==  || d[] == -))))
                ok = true;

            if(ok) printf("Ordering is possible.\n");
            else printf("The door cannot be opened.\n");
    }

    return ;
}