add function for estimating the optimal path

src/lib/estimateoptimalpath.ts

@@ -0,0 +1,67 @@
+import latlongdist from './latlongdist';
+
+export type Location = {
+	latitude: number;
+	longitude: number;
+};
+
+export type Path = {
+	from: Location;
+	to: Location;
+	waypoints: Location[];
+};
+
+function getDistance(...locations: Location[]): number {
+	let distance = 0;
+	for (let i = 0; i < locations.length - 1; i++) {
+		const from = locations[i];
+		const to = locations[i + 1];
+		distance += latlongdist(
+			from.latitude,
+			from.longitude,
+			to.latitude,
+			to.longitude
+		);
+	}
+	return distance;
+}
+
+export default function estimateOptimalPath(path: Path): {
+	path: Path;
+	distance: number;
+} {
+	const { from, to, waypoints } = path;
+	let sequence = [from, to];
+
+	// Calculates all possible paths from the start to the end of the given path
+	// and returns the one with the minimum distance
+	for (let waypoint of waypoints) {
+		// Iterate over all possible insertion points for the waypoint
+		let minDistance = Infinity;
+		let insertionPoint = 1;
+		for (let i = 0; i < sequence.length - 1; i++) {
+			const [start, end] = sequence.slice(i, i + 2);
+
+			const distance = getDistance(start, waypoint, end);
+			if (distance < minDistance) {
+				minDistance = distance;
+				insertionPoint = i;
+			}
+		}
+
+		sequence = sequence
+			.slice(0, insertionPoint)
+			.concat([waypoint])
+			.concat(sequence.slice(insertionPoint));
+	}
+
+	const newWaypoints = sequence.slice(1, sequence.length - 1);
+	return {
+		path: {
+			from,
+			to,
+			waypoints: newWaypoints,
+		},
+		distance: getDistance(from, ...sequence, to),
+	};
+}