Weighted Circle Coverage
Place up to 20 circles. Weighted score with covered cities.
Given 500 fixed cities, choose up to 20 circles (radius between minR and maxR from the instance: 100–200). A circle center must not lie inside another circle. Score: cities inside an odd number of circles give +1 (boundary excluded), but if the city id is divisible by 10 they give -10 instead when odd-covered.
Instance: N=500 cities. The first line is "N minR maxR", then N lines "id x y".
Solution format: First line: k (0..20). Then k lines: x y R (radius within [100,200] from the instance header). Circle centers cannot be inside another circle. Boundary does not count as inside.
Scoring: Weighted: +1 for cities in an odd number of circles, but -10 instead if the city id is divisible by 10. Larger is better.
Solution example: Download example