Fill out Using Algorithms quick-start document (#210)

docs/docs/quickstart/basics/using-algorithms.md

@@ -2,4 +2,78 @@
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-# Using Algorithms
+# Using Algorithms
+
+1. In your `main.cpp` import Graaf and algorithm of choice:
+
+```c++
+#include <graaflib/graph.h>
+#include <graaflib/algorithm/cycle_detection/dfs_cycle_detection.h>
+```
+
+2. Build your graph:
+
+```c++
+graaf::directed_graph<const char, int> g;
+
+const auto a = g.add_vertex('a');
+const auto b = g.add_vertex('b');
+const auto c = g.add_vertex('c');
+
+g.add_edge(a, b, 1);
+g.add_edge(c, a, 1);
+```
+
+3. Run the algorithm:
+
+```c++
+std::cout << "Has cycles: " << graaf::algorithm::dfs_cycle_detection(g) << "\n";
+```
+
+4. Visualize the graph:
+
+```c++
+#include <graaflib/io/dot.h>
+...
+graaf::io::to_dot(g, "./Cycles.dot");
+```
+
+5. Putting it all together:
+
+```c++
+#include <graaflib/graph.h>
+#include <graaflib/io/dot.h>
+#include <graaflib/algorithm/cycle_detection/dfs_cycle_detection.h>
+
+#include <iostream>
+
+int main(int argc, char** argv)
+{
+    graaf::directed_graph<const char, int> g;
+
+    const auto a = g.add_vertex('a');
+    const auto b = g.add_vertex('b');
+    const auto c = g.add_vertex('c');
+
+    g.add_edge(a, b, 1);
+    g.add_edge(c, a, 1);
+
+    std::cout << "Vertices: " << g.vertex_count() << "\n";
+    std::cout << "Edges: " << g.edge_count() << "\n";
+
+    std::cout << "Has cycles: " << graaf::algorithm::dfs_cycle_detection(g) << "\n";
+
+    g.add_edge(b, c, 1);
+    std::cout << "Has cycles: " << graaf::algorithm::dfs_cycle_detection(g) << "\n";
+
+    graaf::io::to_dot(g, "./Cycles.dot");
+    std::cout << "Run: dot -Tpng -o Cycles.png Cycles.dot\n";
+    
+    return 0;
+}
+
+```
+
+### Congratulations! You just detected if there are cycles in the following graph
+
+![Cycle detection example](../../../static/img/quickstart/Cycles.png)