分支限界法之单源最短路径问题

#include <iostream>
#include <vector>
#include <queue>
#include <limits>
using namespace std;

struct node_info
{
public:
    node_info (int i,int w)
        : index (i), weight (w) {}
    node_info ()
        : index(0),weight(0) {}
    node_info (const node_info & ni)
        : index (ni.index), weight (ni.weight) {}

    friend
    bool operator < (const node_info& lth,const node_info& rth) {
        return lth.weight > rth.weight ; // 为了实现从小到大的顺序
    }

public:
    int index; // 结点位置
    int weight; // 权值
};

struct path_info
{
public:
    path_info ()
        : front_index(0), weight (numeric_limits<int>::max()) {}

public:
    int front_index;
    int weight;
};

// single source shortest paths
class ss_shortest_paths
{

public:
    ss_shortest_paths (const vector<vector<int> >& g,int end_location)
        :no_edge (-1), end_node (end_location), node_count (g.size()) , graph (g)
    {}

    // 打印最短路径
    void print_spaths () const {
        cout << "min weight : " << shortest_path << endl;
        cout << "path: " ;
        copy (s_path_index.rbegin(),s_path_index.rend(),
            ostream_iterator<int> (cout, " "));
        cout << endl;
    }

    // 求最短路径
    void shortest_paths () {
        vector<path_info> path(node_count);
        priority_queue<node_info,vector<node_info> > min_heap;
        min_heap.push (node_info(0,0));    // 将起始结点入队

        while (true) {
            node_info top = min_heap.top ();    // 取出最大值
            min_heap.pop ();

            // 已到达目的结点
            if (top.index == end_node) {
                break ;
            }
            // 未到达则遍历
            for (int i = 0; i < node_count; ++ i) {
                // 顶点top.index和i间有边，且此路径长小于原先从原点到i的路径长
                if (graph[top.index][i] != no_edge &&
                    (top.weight + graph[top.index][i]) < path[i].weight) {
                    min_heap.push (node_info (i,top.weight + graph[top.index][i]));
                    path[i].front_index = top.index;
                    path[i].weight = top.weight + graph[top.index][i];
                }
            }
            if (min_heap.empty()) {
                break ;
            }
        }

        shortest_path = path[end_node].weight;
        int index = end_node;
        s_path_index.push_back(index) ;
        while (true) {
            index = path[index].front_index ;
            s_path_index.push_back(index);
            if (index == 0) {
                break;
            }
        }
    }

private:
    vector<vector<int> >    graph ;            // 图的数组表示
    int                        node_count;        // 结点个数
    const int                no_edge;        // 无通路
    const int                end_node;        // 目的结点
    vector<int>                s_path_index;    // 最短路径
    int                        shortest_path;    // 最短路径
};

int main()
{
    const int size = 11;
    vector<vector<int> > graph (size);
    for (int i = 0;i < size; ++ i) {
        graph[i].resize (size);
    }
    for (int i = 0;i < size; ++ i) {
        for (int j = 0;j < size; ++ j) {
            graph[i][j] = -1;
        }
    }
    graph[0][1] = 2;
    graph[0][2] = 3;
    graph[0][3] = 4;
    graph[1][2] = 3;
    graph[1][5] = 2;
    graph[1][4] = 7;
    graph[2][5] = 9;
    graph[2][6] = 2;
    graph[3][6] = 2;
    graph[4][7] = 3;
    graph[4][8] = 3;
    graph[5][6] = 1;
    graph[5][8] = 3;
    graph[6][9] = 1;
    graph[6][8] = 5;
    graph[7][10] = 3;
    graph[8][10] = 2;
    graph[9][8] = 2;
    graph[9][10] = 2;

    ss_shortest_paths ssp (graph, 10);
    ssp.shortest_paths ();
    ssp.print_spaths ();
    return 0;
}