Minimum travel path for a pen-plotter to draw given strokes

Problem: Minimum travel path for a pen-plotter to draw given strokes You are implementing a pen-plotter robot that moves a pen on paper to draw a figure. You are given n strokes, each stroke being a straight line segment with two endpoints. The robot must draw every stroke. The pen has two movement modes: Pen-down (drawing): movement along a stroke leaves ink and contributes distance. Pen-up (travel): movement without drawing still costs distance. You may choose: The order in which strokes are drawn. The direction of each stroke (you may draw a stroke from either endpoint). Your goal is to minimize the total traveled distance (pen-down drawing distance + pen-up travel distance). Input Integer n (number of strokes) Next n lines: x1 y1 x2 y2 describing the endpoints of each stroke The robot starts at (0,0) with pen up. Output Output the minimum possible total travel distance. Constraints 1 <= n <= 15 Coordinates are integers, assume range [-1e4, 1e4] Use Euclidean distance. Example Input: 2 0 0 1 0 2 0 3 0 Output: 3.0 Example Input 1 0 0 3 4 Output 5.0000000000