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 = 0; 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] = 2;
    for (int there = 0; there < 26; ++there) {
        if ( find(vvmap.begin(),vvmap.end(),pair<int,int>(here,there)) != vvmap.end()
                    && seen[there] == 1 )
            dfs(there);
    }
    order.push_back(here);
}

vector<int> topologicalSort()
{
    seen = vector<int>(26, 0);
    for (int i = 0; i < vvmap.size(); i++) {
        //记录需要dfs的索引
        if (seen[vvmap[i].first] == 0)
            seen[vvmap[i].first] =1;
        if (seen[vvmap[i].second] == 0)
            seen[vvmap[i].second] = 1;
    }
    order.clear();
    for (int i = 0; i <  26; i++) {
        if (seen[i] == 1) 
            dfs(i);
    }

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

    for (int i = 0; i < order.size(); i++) {
        for (int j = i+1; 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 = 0; i < m; i++) {
            string s;
            cin >> s;
            vs.push_back(s);
        }

        for (int i = 0; i < vs.size()-1; i++) {
            Compare(vs[i], vs[i + 1]);
        }

        vector<int> ans = topologicalSort();
        if (ans.empty()) {
            cout << "INVALID HYPOTHESIS" << endl;
        }
        else {
            for (int i = 0; i < 26; i++) {
                if (find(ans.begin(), ans.end(), i) == ans.end()) {
                    ans.push_back(i);
                }
            }

            for (int i = 0; i < ans.size(); i++) {
                cout << (char)(ans[i] + 'a');
            }
            cout << endl;
        }
    }

}