算法问题实战策略 DICTIONARY

地址 https://algospot.com/judge/problem/read/DICTIONARY

解法构造一个26字母的有向图判断无回路后就可以输出判断出来的字符序了

比较各个字母的先后次序不必用一个单词分别同其他单词比较只需要将临近的两个单词一一比较即可

证明如下

算法1 中判断有无回路采取的是DFS方法

代码

  1 #include <iostream>
  2 #include <string>
  3 #include <vector>
  4 #include <algorithm>
  5 #include <memory.h>
  6 
  7 using namespace std;
  8 
  9 /*
 10 3
 11 3
 12 ba
 13 aa
 14 ab
 15 5
 16 gg
 17 kia
 18 lotte
 19 lg
 20 hanhwa
 21 6
 22 dictionary
 23 english
 24 is
 25 ordered
 26 ordinary
 27 this
 28 ======================================================
 29 INVALID HYPOTHESIS
 30 ogklhabcdefijmnpqrstuvwxyz
 31 abcdefghijklmnopqrstuvwxyz
 32 */
 33 
 34 int n;
 35 
 36 vector<pair<int, int>> vvmap;
 37 
 38 void Compare(string s1, string s2)
 39 {
 40     int len = min(s1.size(),s2.size());
 41 
 42     for (int i = 0; i < len; i++) {
 43         if (s1[i] == s2[i]) continue;
 44         int a = s1[i] - 'a';
 45         int b = s2[i] - 'a';
 46         vvmap.push_back({a,b});
 47         break;
 48     }
 49 }
 50 
 51 
 52 vector<int>  seen, order;
 53 
 54 void dfs(int here) {
 55     seen[here] = 2;
 56     for (int there = 0; there < 26; ++there) {
 57         if ( find(vvmap.begin(),vvmap.end(),pair<int,int>(here,there)) != vvmap.end()
 58                     && seen[there] == 1 )
 59             dfs(there);
 60     }
 61     order.push_back(here);
 62 }
 63 
 64 vector<int> topologicalSort()
 65 {
 66     seen = vector<int>(26, 0);
 67     for (int i = 0; i < vvmap.size(); i++) {
 68         //记录需要dfs的索引
 69         if (seen[vvmap[i].first] == 0)
 70             seen[vvmap[i].first] =1;
 71         if (seen[vvmap[i].second] == 0)
 72             seen[vvmap[i].second] = 1;
 73     }
 74     order.clear();
 75     for (int i = 0; i <  26; i++) {
 76         if (seen[i] == 1) 
 77             dfs(i);
 78     }
 79 
 80     reverse(order.begin(), order.end());
 81 
 82     for (int i = 0; i < order.size(); i++) {
 83         for (int j = i+1; j < order.size(); j++) {
 84             if (find(vvmap.begin(), vvmap.end(), pair<int, int>(order[j], order[i])) != vvmap.end())
 85             {
 86                 return vector<int>();
 87             }
 88         }
 89     }
 90     return order;
 91 }
 92 
 93 
 94 int main()
 95 {
 96     cin >> n;
 97 
 98     while (n--) {
 99         int m;
100         vvmap.clear();
101         cin >> m;
102         vector<string> vs;
103         for (int i = 0; i < m; i++) {
104             string s;
105             cin >> s;
106             vs.push_back(s);
107         }
108 
109         for (int i = 0; i < vs.size()-1; i++) {
110             Compare(vs[i], vs[i + 1]);
111         }
112 
113         vector<int> ans = topologicalSort();
114         if (ans.empty()) {
115             cout << "INVALID HYPOTHESIS" << endl;
116         }
117         else {
118             for (int i = 0; i < 26; i++) {
119                 if (find(ans.begin(), ans.end(), i) == ans.end()) {
120                     ans.push_back(i);
121                 }
122             }
123 
124             for (int i = 0; i < ans.size(); i++) {
125                 cout << (char)(ans[i] + 'a');
126             }
127             cout << endl;
128         }
129     }
130 
131 }