Day 4 -E - Catenyms POJ - 2337

A catenym is a pair of words separated by a period such that the last letter of the first word is the same as the last letter of the second. For example, the following are catenyms:

dog.gopher

gopher.rat

rat.tiger

aloha.aloha

arachnid.dog

A compound catenym is a sequence of three or more words separated by periods such that each adjacent pair of words forms a catenym. For example,

aloha.aloha.arachnid.dog.gopher.rat.tiger

Given a dictionary of lower case words, you are to find a compound catenym that contains each of the words exactly once.

Input

The first line of standard input contains t, the number of test cases. Each test case begins with 3 <= n <= 1000 - the number of words in the dictionary. n distinct dictionary words follow; each word is a string of between 1 and 20 lowercase letters on a line by itself.

Output

For each test case, output a line giving the lexicographically least compound catenym that contains each dictionary word exactly once. Output "***" if there is no solution.

Sample Input

2
6
aloha
arachnid
dog
gopher
rat
tiger
3
oak
maple
elm

Sample Output

aloha.arachnid.dog.gopher.rat.tiger
***

思路：
可以将每个单词看作是两点一边，就变成判断欧拉路径(回路)了，从连通性和出度入度两方面判断，然后打印欧拉路径即可，代码如下(注释

int in[30], out[30], ans[1005], start, fa[30], n, k;

struct edge {
    int u, v, vis;
    string s;
    bool operator<(const edge &a) const {
        return s<a.s;
    }
} Edge[1005];

void init() {
    memset(in, 0, sizeof(in)), memset(out, 0, sizeof(out));
    memset(ans, 0, sizeof(ans));
    k = 0;
    for(int i = 1; i <= 28; ++i)
        fa[i] = i;
}

// Find-Union
int Find(int u) {
    if(fa[u] != u)
        return fa[u] = Find(fa[u]);
    return fa[u];
}

void Union(int x, int y) {
    x = Find(x), y = Find(y);
    if(x != y) fa[x] = y;
}

// judge whether connected

bool Connect() {
    int now = Find(start);
    for(int i = 1; i <= 26; ++i)
        if(in[i] || out[i])
            if(Find(i) != now)
                return false;
    return true;
}

// judge the in and out and set the start

bool check() {
    int t1 = 0, t2 = 0, i;
    for(i = 1; i <= 26; ++i) {
        if(in[i] == out[i]) continue;
        else if(in[i] == out[i] + 1) 
            t1++;
        else if(in[i] == out[i] - 1) {
            t2++;
            start = i;
        }
        else 
            break;
    }
    if(i == 27 && t1 == t2 && (t1 == 0 || t1 == 1)) {
        return true;
    }
    return false;
}

//print the euler path
void dfs(int v) {
    for(int i = 1; i <= n; ++i) {
        if(Edge[i].vis == 0 && Edge[i].u == v) {
            Edge[i].vis = 1;
            dfs(Edge[i].v);
            ans[k++] = i;
        }
    }
}

int main() {
    ios::sync_with_stdio(false);
    int T;
    cin >> T;
    while(T--) {
        cin >> n;
        init();
        for(int i = 1; i <= n; ++i) {
            int u, v;
            cin >> Edge[i].s;
            u = Edge[i].s[0] - 'a' + 1;
            v = Edge[i].s[Edge[i].s.size()-1] - 'a' + 1;
            in[v]++, out[u]++;
            Edge[i].u = u, Edge[i].v = v, Edge[i].vis = 0;
            Union(u, v);
        }
        sort(Edge+1, Edge+1+n);
        start = Edge[1].u;
        if(check() && Connect()) {
            dfs(start);
            for(int i = n-1; i >= 1; --i)
                cout << Edge[ans[i]].s << ".";
            cout << Edge[ans[0]].s << "\n";
        } else {
            cout <<"***\n";
        }
    }
    return 0;
}