c++ - Dijkstra 算法 - 邻接矩阵和列表

Question

我的 Dijkstra 实现有一个奇怪的问题...我有 2 种算法，一种用于邻接矩阵，另一种用于邻接列表。它们几乎相同，唯一的区别在于这些结构中传递的数字。

我将矩阵中的数字保存在称为 weightmat 的简单二维矩阵中。列表中的数字保存在称为 nbhlist 的列表数组中。列表由称为 ListNode 的结构组成。

struct ListNode{    
        int number;             
        int weight;         
        ListNode* next;             
        ListNode(){                         
            number = weight = 0;
            next = 0;
        }
    };

还有几个通用变量:vertex(顶点数)、edge(边数)、vstart(起始顶点数)。

Dijkstra矩阵算法代码:

typedef vector<vector<pair<int, float> > > Graph;
struct Compare{
    int operator() (const pair<int,float>& p1, const pair<int,float>& p2)
    {
        return p1.second > p2.second;
    }
};

vector<float> d(vertex);
vector<int> parent(vertex);

for (int i = 0; i < vertex; i++){
    d[i] = numeric_limits<float>::max();
    parent[i] = -1;
}

priority_queue<pair<int, float>, vector<pair<int, float> >, Compare> MatQueue;

d[vstart] = 0;
MatQueue.push(make_pair(vstart, d[vstart]));
while (!MatQueue.empty()){
    int u = MatQueue.top().first;
    if (u == vertex - 1) break;
    MatQueue.pop();
    for (int i = 0; i < vertex; i++){
        if (weightmat[u][i] != 0){
            int v = i;
            float w = weightmat[u][i];
            //cout << "U " << u << "Number " << i << " Weight " << weightmat[u][i] << endl;
            if (d[v]> d[u] + w){
                d[v] = d[u] + w;
                parent[v] = u;
                MatQueue.push(make_pair(v, d[v]));
            }
        }
    }
}

vector<int> path;
path.clear();
int p = vertex - 1;
path.push_back(vertex - 1);
while (p != vstart)
{
    p = parent[p];
    path.push_back(p);
}
for (int i = path.size()-1; i >=0; i--){
    cout << path[i] << "->";
}

这是我的列表的 Dijkstra 算法代码:

typedef vector<vector<pair<int, float> > > Graph;

    struct Compare{
        int operator() (const pair<int, float>& p1, const pair<int, float>& p2)
        {
            return p1.second > p2.second;
        }
    };

    vector<float> d(vertex);
    vector<int> parent(vertex);

    for (int i = 0; i < vertex; i++){
        d[i] = numeric_limits<float>::max();
        parent[i] = -1;
    }

    priority_queue<pair<int, float>, vector<pair<int, float> >, Compare> MatQueue;

    d[vstart] = 0;
    MatQueue.push(make_pair(vstart, d[vstart]));

    ListNode* hand = new ListNode;

    while (!MatQueue.empty()){
        int u = MatQueue.top().first;
        if (u == vertex - 1) break;
        MatQueue.pop();
        hand = NbhList[u];
        while (hand){
            int v = hand->number;
            float w = hand->weight;
            //cout << "U " << u << "Number " << v << " Weight " << w << endl;
            hand = hand->next;
            if (d[v] > d[u] + w){
                d[v] = d[u] + w;
                parent[v] = u;
                MatQueue.push(make_pair(v, d[v]));
            }
        }
    }


    vector<int> path;
    path.clear();
    int p = (vertex-1);
    path.push_back(p);
    while (p != vstart)
    {
        p = parent[p];
        path.push_back(p);
    }
    cout << endl << endl;
    for (int i = path.size() - 1; i >= 0; i--){
        cout << path[i] << "->";
    }

正如我所说，它们几乎相同。唯一区别:

MatQueue.pop();
        hand = NbhList[u];
        while (hand){
            int v = hand->number;
            float w = hand->weight;
            //cout << "U " << u << "Number " << v << " Weight " << w << endl;
            hand = hand->next;
            if (d[v] > d[u] + w){
                d[v] = d[u] + w;
                parent[v] = u;
                MatQueue.push(make_pair(v, d[v]));
            }
        }

和:

MatQueue.pop();
        for (int i = 0; i < vertex; i++){
            if (weightmat[u][i] != 0){
                int v = i;
                float w = weightmat[u][i];
                //cout << "U " << u << "Number " << i << " Weight " << weightmat[u][i] << endl;
                if (d[v]> d[u] + w){
                    d[v] = d[u] + w;
                    parent[v] = u;
                    MatQueue.push(make_pair(v, d[v]));
                }
            }
        }

我的问题是 - 他们有时会给我不同的输出，我不知道为什么。你能帮我找到我的问题吗？

Answer 1

一个可能的错误是在您的 ListNode 结构中:

struct ListNode{    
        int number;             
        int weight;         
        ListNode* next;             
        ListNode(){                         
            number = weight = 0;
            next = 0;
        }
    };

weight 是一个 int，但根据您的其余代码，您的权重是 float，这可能会导致不需要的截断。