Colored Sticks - poj2513(trie + 并查集)

问题便转化为：给定一个图，是否存在“一笔画”经过涂中每一点，以及经过每一边一次。这样就是求图中是否存在欧拉路Euler-Path。
由图论知识可以知道，无向图存在欧拉路的充要条件为：
① 图是连通的；
② 所有节点的度为偶数，或者有且只有两个度为奇数的节点。

trie 和 并查集

 #include <iostream>
 #include <vector>
 #include <string.h>
 #include<stdlib.h>
 #include<stdio.h>
 using namespace std;
 typedef struct trie{
     int trie_index;
     bool flag;
     trie* next[];

 } Trie;
 void trie_init(Trie* tr){
     tr->trie_index = -;
     tr->flag = false;
     for(int i = ; i< ; i ++)
         tr->next[i] = NULL;
 }
 int trie_index;
 Trie *root;
 vector<int> trie_set;
 vector<int> trie_rank;

 int trie_hash(char *input){
     int i = ;
     Trie* path = root;
     while(input[i] != ){
         if(path->next[input[i] - 'a'] == NULL){
             path->next[input[i] - 'a'] = (Trie*)malloc(sizeof(Trie));
             trie_init(path->next[input[i] - 'a']);
         }
         path = path->next[input[i] - 'a'];
         i ++;
     }
     if(path->flag == true){
         return path->trie_index;
     }else{
         path->flag = true;
         path->trie_index = trie_index ++;
         return path->trie_index;
     }

 }
 int find_set(int i){
     if(trie_set[i] == i)
         return i;
     return  find_set(trie_set[i]);

 }
 void union_set(int i, int j){
     int i_p = find_set(i);
     int j_p = find_set(j);
     if(i_p == j_p) return;
     if(trie_rank[i_p] > trie_rank[j_p])
         trie_set[j_p] = i_p;
     else{
         if(trie_rank[i_p] == trie_rank[j_p])
             trie_rank[j_p]++;
         trie_set[i_p] = j_p;
     }

 }
 int main(int argc, char* argv[]){
     trie_index = ;
     vector<int> trie_degree(,);
     char a[], b[];
     root = (Trie*)malloc(sizeof(Trie));
     trie_init(root);
     for(int i = ; i < ; i ++){
         trie_set.push_back(i);
         trie_rank.push_back();
     }
     while (scanf("%s%s",a,b)!=EOF){
         int i = trie_hash(a);
         int j = trie_hash(b);
         trie_degree[i] += ;
         trie_degree[j] += ;

         union_set(i, j);

     }
     int pre = find_set();
     bool result = true;
     for(int i = ; i < trie_index; i ++)
         if(find_set(i) != pre)
             result = false;
     int odd_num = ;
     for(int i = ; i < trie_index; i ++){
         if((trie_degree[i] & ) == )
             odd_num += ;
     }
     if(odd_num==  || odd_num > )
             result = false;
     if(result == true)
         cout << "Possible" << endl;
     else
         cout << "Impossible" << endl;
     return ;
 }

样本输入

Sample Input

blue red
red violet
cyan blue
blue magenta
magenta cyan
Sample Output

Possible