HDU1116

有向图欧拉道路的判定，与欧拉回路类似，但要注意入度和出度的不同。

#include<iostream>
#include<cstring>
#include<cstdio>
using namespace std;

const int MAX = 26;
int T;
int N;
int graph[MAX][MAX];
int in_degree[MAX];
int out_degree[MAX];
int parent[MAX];

void initialize();
int ancestor(int x);
bool union_find_sets();
bool euler();

void initialize(){
	for (int i = 0; i < MAX; i++){
		parent[i] = i;
	}
}

int ancestor(int x){
	return parent[x] == x ? x : parent[x] = ancestor(parent[x]);
}

bool union_find_sets(){

	int ai;
	int aj;
	for (int i = 0; i < MAX; i++){
		for (int j = 0; j < MAX; j++){
			if (graph[i][j]){
				ai = ancestor(i);
				aj = ancestor(j);
				if (ai != aj){
					parent[ai] = aj;
				}
			}
		}
	}

	int p = 0;
	for (int i = 0; i < MAX; i++){
		if (in_degree[i]+out_degree[i]){
			p = ancestor(i);
			break;
		}
	}

	for (int i = 0; i < MAX; i++){
		if (in_degree[i]+out_degree[i]){
			if (p != ancestor(i))
				return false;
		}
	}
	return true;
}

bool euler(){
	int odd_point = 0;
	int in_and_out = 0;
	for (int i = 0; i < MAX; i++){
		if (in_degree[i] - out_degree[i] == 1){
			in_and_out++;
			odd_point++;
		}
		else if (out_degree[i] - in_degree[i] == 1){
			in_and_out--;
			odd_point++;
		}
		else if (in_degree[i] != out_degree[i]){
			return false;
		}
	}

	if (odd_point == 0 || (odd_point = 2 && in_and_out == 0))
		return true;
	return false;
}

int main() {
	cin >> T;
	for (int i = 0; i < T; i++){
		memset(graph,0,sizeof(graph));
		memset(in_degree,0,sizeof(in_degree));
		memset(out_degree,0,sizeof(out_degree));
		initialize();
		cin >> N;
		int x;
		int y;
		int length;
		char str[1002];
		getchar();
		for (int j = 0; j < N; j++){
			memset(str,0,sizeof(str));
			gets(str);
			length = strlen(str);
			x = str[0] - 'a';
			y = str[length-1] - 'a';
			graph[x][y]++;
			out_degree[x]++;
			in_degree[y]++;
		}

		if (union_find_sets() && euler()){
			cout << "Ordering is possible." << endl;
		}
		else{
			cout << "The door cannot be opened." << endl;
		}
	}
	return 0;
}