/*
欧拉路径 之 poj 2513 Colored Sticks
欧拉路径： 若图G中存在这样一条路径，使得它恰通过G中每条边一次,则称该路径为欧拉路径。
无向图存在欧拉路径 充要条件：
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。
题目要求：
align the sticks in a straight line such that the colors of the endpoints that touch are of the same color.
模型转换：
木棒看作边，木棒两端看作节点（相同的颜色即为同一个节点），这样便可构成无向图G。
align the sticks in a straight line 即：在无向图G中，通过每条边一次。
即：判定无向图G是否存在欧拉路径
实现：
字典树 + 并查集
*/
1 #include <crtdbg.h>
2 #include <iostream>
3 #include <fstream>
4 #include <sstream>
5 #include <cstdlib>
6 #include <cstdio>
7 #include <cstddef>
8 #include <iterator>
9 #include <algorithm>
10 #include <string>
11 #include <locale>
12 #include <cmath>
13 #include <vector>
14 #include <cstring>
15 #include <map>
16 #include <utility>
17 #include <queue>
18 #include <stack>
19 #include <set>
20 #include <functional>
21 using namespace std;
22 typedef pair<int, int> PII;
23 typedef long long int64;
24 const int INF = 0x3f3f3f3f;
25 const int modPrime = 3046721;
26 const double eps = 1e-9;
27 const int MaxN = 500010;
28 const int MaxM = 10010;
29
30
31 int degree[MaxN];
32 int ftr[MaxN];
33 int rnk[MaxN];
34
35 //Union-Find Sets
36 void ufsIni()
37 {
38 for (int i = 0; i < MaxN; ++i)
39 {
40 ftr[i] = i;
41 rnk[i] = 0;
42 }
43 }
44 int ufsFind(int x)
45 {
46 if (x == ftr[x]) return x;
47 return ftr[x] = ufsFind(ftr[x]);
48 }
49 void ufsUnite(int x, int y)
50 {
51 x = ufsFind(x);
52 y = ufsFind(y);
53 if (x == y) return;
54
55 if (rnk[x] > rnk[y])
56 {
57 ftr[y] = x;
58 }
59 else
60 {
61 ftr[x] = y;
62 if (rnk[x] == rnk[y])
63 {
64 ++rnk[y];
65 }
66 }
67 }
68
69 // Tree
70 struct Tree
71 {
72 Tree *next[26];
73 bool flag;
74 int num;
75 Tree()
76 {
77 flag = false;
78 memset(next, NULL, sizeof(next));
79 }
80 };
81
82 Tree *Root = new Tree;
83
84 int insertNode(string str, int num)
85 {
86 Tree *p = Root;
87 for (int i = 0; i < str.size(); ++i)
88 {
89 int pos = str[i] - 'a';
90 if (!(p->next[pos]))
91 {
92 p->next[pos] = new Tree;
93 }
94 p = p->next[pos];
95 }
96 if (!(p->flag))
97 {
98 p->flag = true;
99 p->num = num;
100 }
101 return p->num;
102 }
103
104 void destroyTree(Tree *root)
105 {
106 for (int i = 0; i < 26; ++i)
107 {
108 if (root->next[i])
109 {
110 destroyTree(root->next[i]);
111 }
112 }
113 delete[] root;
114 }
115
116
117 int main()
118 {
119 #ifdef HOME
120 freopen("in", "r", stdin);
121 //freopen("out", "w", stdout);
122 #endif
123
124 char str1[11], str2[11];
125 int num = 0;
126 fill(degree, degree + MaxN, 0);
127 ufsIni();
128 while (~scanf("%s %s", str1, str2))
129 {
130 int numTmp1 = insertNode(str1, num);
131 if (numTmp1 == num)
132 {
133 ++num;
134 }
135 int numTmp2 = insertNode(str2, num);
136 if (numTmp2 == num)
137 {
138 ++num;
139 }
140
141 ++degree[numTmp1];
142 ++degree[numTmp2];
143 ufsUnite(numTmp1, numTmp2);
144 }
145 destroyTree(Root);
146 for (int i = 1; i < num; ++i)
147 {
148 if (ftr[i] != ftr[0])
149 {
150 printf("Impossible\n");
151 return 0;
152 }
153 }
154 int oddCnt = 0;
155 for (int i = 0; i < num; ++i)
156 {
157 if (degree[i] & 1)
158 {
159 ++oddCnt;
160 if (oddCnt >= 3)
161 {
162 break;
163 }
164 }
165 }
166 if (oddCnt == 0 || oddCnt == 2)
167 {
168 printf("Possible\n");
169 }
170 else
171 {
172 printf("Impossible\n");
173 }
174
175
176 #ifdef HOME
177 cerr << "Time elapsed: " << clock() / CLOCKS_PER_SEC << " ms" << endl;
178 _CrtDumpMemoryLeaks();
179 #endif
180 return 0;
181 }
