added several grid-walks

added new helper methods/classes (e.g. for heading)
new test cases
optimize the dijkstra
cleanups/refactoring
added timed-benchmarks to the log
many more...

math/DrawList.h

@@ -0,0 +1,82 @@
+#ifndef DRAWLIST_H
+#define DRAWLIST_H
+
+#include <vector>
+#include <random>
+
+/**
+ * add elements of a certain probability
+ * and randomly draw from them
+ */
+template <typename T> class DrawList {
+
+	/** one entry */
+	struct Entry {
+
+		/** the user element */
+		T element;
+
+		/** the cumulative probability up to this element */
+		double cumProbability;
+
+		/** ctor */
+		Entry(T element, const double cumProbability) : element(element), cumProbability(cumProbability) {;}
+
+		/** compare for searches */
+		bool operator < (const double val) const {return cumProbability < val;}
+
+	};
+
+private:
+
+	/** current cumulative probability */
+	double cumProbability;
+
+	/** all contained elements */
+	std::vector<Entry> elements;
+
+	/** random number generator */
+	std::minstd_rand gen;
+
+public:
+
+	/** ctor */
+	DrawList() : cumProbability(0) {
+		;
+	}
+
+	/** reset */
+	void reset() {
+		cumProbability = 0;
+		elements.clear();
+	}
+
+	/** add a new user-element and its probability */
+	void add(T element, const double probability) {
+		cumProbability += probability;
+		elements.push_back(Entry(element, cumProbability));
+	}
+
+	/** get a random element based on its probability */
+	T get() {
+
+		// generate random number between [0:cumProbability]
+		std::uniform_real_distribution<> dist(0, cumProbability);
+
+		// get a random value
+		const double rndVal = dist(gen);
+
+		// binary search for the matching entry O(log(n))
+		const auto tmp = std::lower_bound(elements.begin(), elements.end(), rndVal);
+		return (*tmp).element;
+
+	}
+
+	/** get the current, cumulative probability */
+	double getCumProbability() const {
+		return cumProbability;
+	}
+
+};
+
+#endif // DRAWLIST_H