/*
拓扑序列变形 之 poj 1094 Sorting It All Out
变形：
在每消去唯一一个入度为0的点后，只剩下唯一一个入度为0的点。
这样获得的n个点才是排序好的。
*/
1 #include <iostream>
2 #include <cstdlib>
3 #include <cstdio>
4 #include <cstddef>
5 #include <iterator>
6 #include <algorithm>
7 #include <string>
8 #include <locale>
9 #include <cmath>
10 #include <vector>
11 #include <cstring>
12 #include <map>
13 #include <utility>
14 #include <queue>
15 #include <stack>
16 #include <set>
17 #include <functional>
18 using namespace std;
19 typedef pair<int, int> PII;
20 typedef long long int64;
21 const int INF = 0x3f3f3f3f;
22 const int modPrime = 3046721;
23 const double eps = 1e-9;
24 const int MaxN = 30;
25 const int MaxM = 10010;
26
27 int n, m;
28 bool G[MaxN][MaxN];
29 int ndCnt[MaxN];
30 char chList[MaxN];
31
32 enum emFlag
33 {
34 fgSUCCESS, fgFAIL, fgWAIT
35 };
36
37
38 emFlag Solve()
39 {
40 stack<int> stk;
41
42 int ndCntTmp[MaxN];
43 for (int i = 0; i < n; ++i)
44 {
45 ndCntTmp[i] = ndCnt[i];
46 if (0 == ndCnt[i])
47 {
48 stk.push(i);
49 }
50 }
51
52 bool sign = true;
53 int chLen = 0;
54
55 while (!stk.empty())
56 {
57 // 下面的if语句，就是需要注意的地方
58 if (stk.size() > 1)
59 {
60 sign = false;
61 }
62 int nd = stk.top();
63 stk.pop();
64 chList[chLen++] = static_cast<char> ('A' + nd);
65 for (int i = 0; i < n; ++i)
66 {
67 if (G[nd][i])
68 {
69 --ndCntTmp[i];
70 if (0 == ndCntTmp[i])
71 {
72 stk.push(i);
73 }
74 }
75 }
76 }
77
78 if (n == chLen)
79 {
80 if (sign)
81 {
82 return fgSUCCESS;
83 }
84 else
85 {
86 return fgWAIT;
87 }
88 }
89 else
90 {
91 return fgFAIL;
92 }
93 }
94
95 void ini()
96 {
97 for (int i = 0; i < n; ++i)
98 {
99 ndCnt[i] = 0;
100 for (int j = 0; j < n; ++j)
101 {
102 G[i][j] = false;
103 }
104 }
105 }
106
107 int main()
108 {
109 #ifdef HOME
110 freopen("in", "r", stdin);
111 //freopen("out", "w", stdout);
112 #endif
113 string str;
114 while ((cin >> n >> m) && (n || m))
115 {
116 ini();
117
118 bool sign = false;
119 int pos;
120 emFlag fg = fgWAIT;
121 for (int i = 1; i <= m; ++i)
122 {
123 cin >> str;
124 if (!sign)
125 {
126 int a = str[0] - 'A', b = str[2] - 'A';
127 if (!G[a][b])
128 {
129 G[a][b] = true;
130 ++ndCnt[b];
131 fg = Solve();
132 if (fg != fgWAIT)
133 {
134 pos = i;
135 sign = true;
136 }
137 }
138 }
139 }
140 if (sign)
141 {
142 if (fgSUCCESS == fg)
143 {
144 cout << "Sorted sequence determined after " << pos << " relations: ";
145 for (int j = 0; j < n; ++j)
146 {
147 cout << chList[j];
148 }
149 cout << "." << endl;
150 }
151 else
152 {
153 cout << "Inconsistency found after " << pos << " relations." << endl;
154 }
155 }
156 else
157 {
158 cout << "Sorted sequence cannot be determined." << endl;
159 }
160 }
161
162 #ifdef HOME
163 cerr << "Time elapsed: " << clock() / CLOCKS_PER_SEC << " ms" << endl;
164 _CrtDumpMemoryLeaks();
165 #endif
166 return 0;
167 }