[算法与数据结构][图算法][拓扑排序]尝试3

Posted 2021-05-23 xcy6666

#include<cassert>

#include<vector>
#include<queue>
#include<iostream>
/*
e.g.1   1

e.g.2   2 -> 1

e.g.3
     /- 6
   4 -- 3 -- 1
   5 -- 2 -/
e.g.4
   2 -> 1 -> 3 -> 2

*/
using namespace std;
vector<vector<int>> adj_list(7);
vector<int> in_d(7, 0); // in degree of id

void construct(){
        //e.g.3
        adj_list[4].push_back(6);
        adj_list[4].push_back(3);
        adj_list[3].push_back(1);
        adj_list[5].push_back(2);
        adj_list[2].push_back(1);
        //time: O(E), space O(E)

        //look up; remove; insert
        in_d[6]++;
        in_d[3]++;
        in_d[1]++;
        in_d[2]++;
        in_d[1]++;
        //time:  O(V) + O(E*log_deg*1)
        //space: O(V+V+deg)
}

bool topo_sort(){
        vector<int> res;
        queue<int> next;
        //priority_queue<int> next;
        for(int i=1; i < in_d.size(); i++){
                if(in_d[i] == 0) next.push(i);
        }

        while(next.size() > 0){
                int id = next.front(); next.pop();
                //int id = next.top(); next.pop();
                res.push_back(id);
                for(auto nbr : adj_list[id]){
                        in_d[nbr]--;
                        if(in_d[nbr] == 0) next.push(nbr);
                }
        }
        //time: O(V*log_deg)
        if(res.size()+1 != in_d.size())
                return false;
        for(auto e : res) cout << e << " ";
        cout << endl;

        return true;
}

int main(){
    construct();
//    print_deg_ids();
    topo_sort();
}

/*
 * fail to construct a data structure that can:
 *      store {id, degree}
 *      quick find minimal degree
 *      quick update degree
 *
 *      deg_ids: store degree : set<id>, sorted on degree
 *      vector<int> degree
 *
 * reflection:
 *      deg_ids is a global structure to maintain all nodes degree info and updated all nodes order info
 *      on graph structure:
 *              bfs pattern or dfs pattern is common
 *              for the next degree 0 nodes, a bfs pattern can be used to simplify
 *
 * */