Topological sorting is a typical algorithm in graph theory. The hierarchical structure of the graph can be sorted through topological sorting. Graph theory tasks such as the completion of a period of time are typical applications. The second application is to determine whether there is a loop problem in the graph.
The way to build a graph in the program is in the form of adjacency list, the code is as follows:
vector<vector<int> > graph(n, vector<int>{
});
The following is a template for topological sorting:
vector<vector<int> > graph(n, vector<int>{
});
根据所给有向图的指向关系，完成graph图的建立
// 统计初始入度为0的
vector<int> indegree(n, 0);
for (int i=0; i<n; i++) {
for (int j=0; j<graph[i].size(); j++) {
indegree[graph[i][j]]++;
}
}
queue<int> que; // 队列存储，其实如果对于顺序没有要求栈也行
for (int i=0; i<n; i++) {
if (indegree[i] == 0)
que.push(i);
}
while (!que.empty()) {
int a = que.front();
cout << a + 1 << " ";
que.pop();
for (int i=0; i<graph[a].size(); i++) {
indegree[graph[a][i]]--;
if (indegree[graph[a][i]] == 0)
que.push(graph[a][i]);
}
}
/*
如果要判断是否存在环路，可以在最后判断一下indegree数组，如果全为0说明无环，否则说明有环。
*/
Let's practice with two questions! (The topic was found by someone else’s blog, not from the website. I didn’t go to OJ to verify the AC, but just passed the sample test. The output format is not adjusted, just barely pass it!)
Topic 1: Determine the ranking of the competition
code show as below:
#include<bits/stdc++.h>
using namespace std;
int main(void) {
int n, m;
cin >> n >> m;
vector<vector<int>> graph(n, vector<int>{
});
for (int i=0; i<m; i++) {
int u, v;
cin >> u >> v;
graph[u-1].push_back(v-1);
}
vector<int> indegree(n, 0);
for (int i=0; i<graph.size(); i++) {
for (int j=0; j<graph[i].size(); j++) {
indegree[graph[i][j]]++;
}
}
priority_queue<int> que; // 题目对顺序有要求，这里用了优先队列
for (int i=0; i<n; i++) {
if (indegree[i] == 0)
que.push(-i);
}
while (!que.empty()) {
int num = -que.top();
cout << num + 1 << " ";
que.pop();
for (int i=0; i<graph[num].size(); i++) {
indegree[graph[num][i]]--;
if (indegree[graph[num][i]] == 0)
que.push(-graph[num][i]);
}
}
return 0;
}
Topic 2: POJ 2367: Genealogical tree
#include<bits/stdc++.h>
using namespace std;
int main(void) {
int n;
cin >> n;
vector<vector<int> > graph(n, vector<int>{
});
int i;
for (int j=0; j<n; j++) {
while (1) {
cin >> i;
if (i != 0)
graph[j].push_back(i-1);
else
break;
}
}
vector<int> indegree(n, 0);
for (int i=0; i<n; i++) {
for (int j=0; j<graph[i].size(); j++) {
indegree[graph[i][j]]++;
}
}
queue<int> que;
for (int i=0; i<n; i++) {
if (indegree[i] == 0)
que.push(i);
}
while (!que.empty()) {
int a = que.front();
cout << a + 1 << " ";
que.pop();
for (int i=0; i<graph[a].size(); i++) {
indegree[graph[a][i]]--;
if (indegree[graph[a][i]] == 0)
que.push(graph[a][i]);
}
}
return 0;
}
Reference materials: https://blog.csdn.net/wang_123_zy/article/details/81411683