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

 #include <iostream>
 #include <string>
 #include <vector>
 #include <algorithm>
 #include <memory.h>

 using namespace std;

 /*
 3
 3
 ba
 aa
 ab
 5
 gg
 kia
 lotte
 lg
 hanhwa
 6
 dictionary
 english
 is
 ordered
 ordinary
 this
 ======================================================
 INVALID HYPOTHESIS
 ogklhabcdefijmnpqrstuvwxyz
 abcdefghijklmnopqrstuvwxyz
 */

 int n;

 vector<pair<int, int>> vvmap;

 void Compare(string s1, string s2)
 {
     int len = min(s1.size(),s2.size());

     for (int i = ; i < len; i++) {
         if (s1[i] == s2[i]) continue;
         int a = s1[i] - 'a';
         int b = s2[i] - 'a';
         vvmap.push_back({a,b});
         break;
     }
 }

 vector<int>  seen, order;

 void dfs(int here) {
     seen[here] = ;
     for (int there = ; there < ; ++there) {
         if ( find(vvmap.begin(),vvmap.end(),pair<int,int>(here,there)) != vvmap.end()
                     && seen[there] ==  )
             dfs(there);
     }
     order.push_back(here);
 }

 vector<int> topologicalSort()
 {
     seen = vector<int>(, );
     for (int i = ; i < vvmap.size(); i++) {
         //记录需要dfs的索引
         if (seen[vvmap[i].first] == )
             seen[vvmap[i].first] =;
         if (seen[vvmap[i].second] == )
             seen[vvmap[i].second] = ;
     }
     order.clear();
     for (int i = ; i <  ; i++) {
         if (seen[i] == )
             dfs(i);
     }

     reverse(order.begin(), order.end());

     for (int i = ; i < order.size(); i++) {
         for (int j = i+; j < order.size(); j++) {
             if (find(vvmap.begin(), vvmap.end(), pair<int, int>(order[j], order[i])) != vvmap.end())
             {
                 return vector<int>();
             }
         }
     }
     return order;
 }

 int main()
 {
     cin >> n;

     while (n--) {
         int m;
         vvmap.clear();
         cin >> m;
         vector<string> vs;
         for (int i = ; i < m; i++) {
             string s;
             cin >> s;
             vs.push_back(s);
         }

         for (int i = ; i < vs.size()-; i++) {
             Compare(vs[i], vs[i + ]);
         }

         vector<int> ans = topologicalSort();
         if (ans.empty()) {
             cout << "INVALID HYPOTHESIS" << endl;
         }
         else {
             for (int i = ; i < ; i++) {
                 if (find(ans.begin(), ans.end(), i) == ans.end()) {
                     ans.push_back(i);
                 }
             }

             for (int i = ; i < ans.size(); i++) {
                 cout << (char)(ans[i] + 'a');
             }
             cout << endl;
         }
     }

 }