c++ - 将图形表示为unordered_map >时，拓扑排序错误

Question

当我尝试使用代表图形的unordered_map<string, vector<string>>在C++中实现拓 flutter 排序时，遇到了无法解释的错误(就我而言)。具体而言，当正在访问的“当前节点”不作为unordered_map中的键存在(即，它没有传出边沿)时，仅在时才发生。它没有返回“正确”的顺序，而是完全终止了函数调用topSort，并且仅返回该顺序的一小部分。

代码返回:ML, AML, DL
相反，可能的正确解决方案可能是:LA, MT, MA, PT, ML, AML, DL
谁能解释为什么会这样？

下面是发生问题的一个小代码段:

// 0 -> white (node has not been visited)
// 1 -> grey (node is currently being visited)
// 2 -> black (node is completely explored)
bool topSortVisit(unordered_map<string, vector<string>>& graph,
 unordered_map<string, int>& visited, string node, vector<string>& result){

 if(visited[node] == 1) return false;
 if(visited[node] == 2) return true;

 // Mark current node as being visited.
 visited[node] = 1;
 // node might not have outgoing edges and therefore not in the
 // unordered_map (graph) as a key.
 for(auto neighbor : graph[node]){
 if(!topSortVisit(graph, visited, neighbor, result)) return false;
 }

 result.push_back(node);
 visited[node] = 2;
 return true;
}

vector<string> topSort(unordered_map<string, vector<string>>& graph){

 unordered_map<string, int> visited;
 vector<string> result;

 // Should visit all nodes with outgoing edges in the graph.
 for(auto elem : graph){
 string node = elem.first;
 bool acyclic = topSortVisit(graph, visited, node, result);
 if(!acyclic){
 cout << "cycle detected\n";
 return vector<string>{};
 }

 }

 reverse(result.begin(), result.end());
 return result;
}

这里是重现一切的代码:

#include<iostream>
#include<vector>
#include<unordered_map>
#include<algorithm>

using namespace std;

bool topSortVisit(unordered_map<string, vector<string>>& graph,
        unordered_map<string, int>& visited, string node, vector<string>& result){

    if(visited[node] == 1) return false;
    if(visited[node] == 2) return true;

    visited[node] = 1;
    for(auto neighbor : graph[node]){
        if(!topSortVisit(graph, visited, neighbor, result)) return false;
    }

    result.push_back(node);
    visited[node] = 2;
    return true;
}

vector<string> topSort(unordered_map<string, vector<string>>& graph){

    unordered_map<string, int> visited;
    vector<string> result;

    for(auto elem : graph){
        string node = elem.first;
        bool acyclic = topSortVisit(graph, visited, node, result);
        if(!acyclic){
            cout << "cycle detected\n";
            return vector<string>{};
        }

    }

    return result;
}


unordered_map<string, vector<string>> makeGraph(vector<pair<string, string>> courses){
    unordered_map<string, vector<string>> graph;

    for(auto p : courses){
        graph[p.first].push_back(p.second);
    }
    return graph;
}

int main(){

    vector<pair<string, string>> pairs;
    pairs.push_back(make_pair("LA", "ML"));
    pairs.push_back(make_pair("MT", "ML"));
    pairs.push_back(make_pair("MA", "PT"));
    pairs.push_back(make_pair("PT", "ML"));
    pairs.push_back(make_pair("ML", "DL"));
    pairs.push_back(make_pair("ML", "AML"));

    auto graph = makeGraph(pairs);
    vector<string> result = topSort(graph); // ML, AML, DL
    // A possible correct solution could be: LA, MT, MA, PT, ML, AML, DL


    for(string s : result){
        cout << s << " ";
    }
    cout << "\n";
}

Answer 1

在unordered_map中插入会使 map if it rehashes中的迭代器无效。这就破坏了您与auto elem : graph的循环(顺便说一句，它复制了vector<string>对象；改为使用auto &elem)。将您的图形作为const&传递，以避免这种恶作剧；然后，编译器会轻轻建议您使用at而不是operator[]。