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GH-117: Topological Sorting in C++ (#302)
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‎concepts/cpp/graph/notebook.ipynb

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"codemirror_mode": "text/x-c++src",
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"file_extension": ".cpp",
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"mimetype": "text/x-c++src",
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"name": "c++",
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"name": "C++17",
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"version": "17"
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},
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"orig_nbformat": 4

‎concepts/cpp/topological-sorting/README.md

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# Topological Sorting
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Topological sorting is a linear ordering of vertices in a directed acyclic graph (DAG) such that for every directed edge uv, vertex u comes before v in the ordering. Topological Sorting for a graph is not possible if the graph is not a DAG.
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## Topological Sorting in C++
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Example directed acyclic graph:
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```
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5 0
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^ / \
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| v v
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4 <- 2 <- 3
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^ |
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| v
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1 -> 6 -> 7
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```
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```cpp
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int n = 8;
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vector<vector<int>> adj(n);
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adj[0] = {2, 3};
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adj[1] = {4, 6};
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adj[2] = {4};
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adj[3] = {2, 7};
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adj[4] = {5};
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adj[5] = {};
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adj[6] = {7};
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adj[7] = {};
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```
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Use DFS to find the topological sort:
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```cpp
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void dfs(int i, vector<vector<int>> adj, vector<int> &visited, vector<int> &orders){
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visited[i] = true;
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for(auto j: adj[i]){
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if(!visited[j]){
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dfs(j, adj, visited, orders);
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}
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}
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orders.push_back(i);
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}
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vector<int> topological_sort(int n, vector<vector<int>> adj) {
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vector<int> visited(n, false);
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vector<int> orders;
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for(int i=0; i<n; i++){
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if(!visited[i]){
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dfs(i, adj, visited, orders);
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}
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}
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reverse(orders.begin(), orders.end());
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return orders;
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}
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```
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```cpp
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vector<int> orders = topological_sort(n, adj);
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for (auto i : orders) {
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cout << i << " ";
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}
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```
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Output
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```
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1 6 0 3 7 2 4 5
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```
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## References
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* [Topological Sort Algorithm | Graph Theory, WilliamFiset](https://www.youtube.com/watch?v=eL-KzMXSXXI&t=308s&ab_channel=WilliamFiset)
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* [Topological Sort | GeeksforGeeks](https://www.geeksforgeeks.org/topological-sorting/)
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* https://cp-algorithms.com/graph/topological-sort.html

‎concepts/cpp/topological-sorting/code.cpp

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#include <algorithm>
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#include <iostream>
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#include <vector>
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using namespace std;
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void dfs(int i, vector<vector<int>> adj, vector<int> &visited,
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vector<int> &orders) {
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visited[i] = true;
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for (auto j : adj[i]) {
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if (!visited[j]) {
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dfs(j, adj, visited, orders);
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}
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}
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orders.push_back(i);
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}
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vector<int> topological_sort(int n, vector<vector<int>> adj) {
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vector<int> visited(n, false);
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vector<int> orders;
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for (int i = 0; i < n; i++) {
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if (!visited[i]) {
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dfs(i, adj, visited, orders);
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}
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}
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reverse(orders.begin(), orders.end());
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return orders;
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}
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int main() {
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int n = 8;
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vector<vector<int>> adj(n);
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adj[0] = {2, 3};
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adj[1] = {4, 6};
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adj[2] = {4};
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adj[3] = {2, 7};
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adj[4] = {5};
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adj[5] = {};
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adj[6] = {7};
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adj[7] = {};
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vector<int> orders = topological_sort(n, adj);
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for (auto i : orders) {
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cout << i << " ";
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}
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cout << endl;
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return 0;
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}

‎concepts/cpp/topological-sorting/notebook.ipynb

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{
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"cells": [
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{
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"attachments": {},
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Topological Sorting\n",
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"\n",
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"Topological sorting is a linear ordering of vertices in a directed acyclic graph (DAG) such that for every directed edge uv, vertex u comes before v in the ordering. Topological Sorting for a graph is not possible if the graph is not a DAG."
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]
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},
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{
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"attachments": {},
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Topological Sorting in C++"
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]
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},
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{
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"attachments": {},
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Example directed acyclic graph:\n",
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"\n",
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"```\n",
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" 5 0\n",
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" ^ / \\\n",
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" | v v\n",
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" 4 <- 2 <- 3\n",
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" ^ |\n",
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" | v\n",
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" 1 -> 6 -> 7\n",
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"```"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"vscode": {
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"languageId": "cpp"
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}
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},
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"source": [
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"```cpp\n",
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"int n = 8;\n",
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"vector<vector<int>> adj(n);\n",
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"\n",
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"adj[0] = {2, 3};\n",
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"adj[1] = {4, 6};\n",
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"adj[2] = {4};\n",
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"adj[3] = {2, 7};\n",
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"adj[4] = {5};\n",
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"adj[5] = {};\n",
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"adj[6] = {7};\n",
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"adj[7] = {};\n",
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"```"
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]
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},
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{
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"attachments": {},
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"cell_type": "markdown",
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"metadata": {
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"vscode": {
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"languageId": "cpp"
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}
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},
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"source": [
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"Use DFS to find the topological sort:\n",
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"\n",
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"```cpp\n",
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"void dfs(int i, vector<vector<int>> adj, vector<int> &visited, vector<int> &orders){\n",
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" visited[i] = true;\n",
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" for(auto j: adj[i]){\n",
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" if(!visited[j]){\n",
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" dfs(j, adj, visited, orders);\n",
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" }\n",
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" }\n",
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" orders.push_back(i);\n",
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"}\n",
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"\n",
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"vector<int> topological_sort(int n, vector<vector<int>> adj) {\n",
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" vector<int> visited(n, false);\n",
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" vector<int> orders;\n",
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"\n",
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" for(int i=0; i<n; i++){\n",
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" if(!visited[i]){\n",
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" dfs(i, adj, visited, orders);\n",
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" }\n",
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" }\n",
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" reverse(orders.begin(), orders.end());\n",
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" return orders;\n",
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"}\n",
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"```\n",
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"\n",
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"```cpp\n",
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"vector<int> orders = topological_sort(n, adj);\n",
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"for (auto i : orders) {\n",
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" cout << i << \" \";\n",
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"}\n",
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"```\n",
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"\n",
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"Output\n",
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"\n",
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"```\n",
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"1 6 0 3 7 2 4 5\n",
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"```"
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]
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},
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{
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"attachments": {},
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## References\n",
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"\n",
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"* [Topological Sort Algorithm | Graph Theory, WilliamFiset](https://www.youtube.com/watch?v=eL-KzMXSXXI&t=308s&ab_channel=WilliamFiset)\n",
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"* [Topological Sort | GeeksforGeeks](https://www.geeksforgeeks.org/topological-sorting/)\n",
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"* https://cp-algorithms.com/graph/topological-sort.html"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "C++17",
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"language": "C++17",
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"name": "xcpp17"
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},
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"language_info": {
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"codemirror_mode": "text/x-c++src",
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"file_extension": ".cpp",
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"mimetype": "text/x-c++src",
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"name": "c++",
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"version": "17"
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},
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"orig_nbformat": 4
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},
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"nbformat": 4,
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"nbformat_minor": 2
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}

‎concepts/general/topological-sorting/README.md

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# Topological Sorting
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*See implementation in*
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C++,
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[C++](/concepts/cpp/topological-sorting/README.md),
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Java,
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Python,
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typescript
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## References
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* [Topological Sort Algorithm | Graph Theory, WilliamFiset](https://www.youtube.com/watch?v=eL-KzMXSXXI&t=308s&ab_channel=WilliamFiset)
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* [Topological Sort | GeeksforGeeks](https://www.geeksforgeeks.org/topological-sorting/)
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* [Topological Sort | GeeksforGeeks](https://www.geeksforgeeks.org/topological-sorting/)
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* https://cp-algorithms.com/graph/topological-sort.html

‎readme/cpp/README.md

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<code>A</code> Prim’s Algorithm
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</li>
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<li>
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<code>A</code> Topological Sorting
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<code>A</code>
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<a href="/concepts/cpp/topological-sorting/README.md">Topological Sorting</a>
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</li>
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<li>
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<code>A</code> Articulation Points

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