advent_or_day6.mzn

advent_or_day6.mzn

include "globals.mzn";

int: NUM_SEGMENTS;
int: NUM_SUBSETS;

set of int: SUBSETS = 1..NUM_SUBSETS;
set of int: SEGMENTS = 1..NUM_SEGMENTS;


array[SUBSETS] of set of int: combinations;
array[SUBSETS] of int: costs;

array[SUBSETS] of var bool: selected;

var min(costs)..sum(costs): total_cost;

constraint total_cost = 
  sum(c in SUBSETS)(selected[c] * costs[c]);

constraint forall(s in SEGMENTS)(
  sum(c in SUBSETS where s in combinations[c])(selected[c]) >=1
);

constraint forall(c in SUBSETS)(
  sum(combinations[c]) > 0 <- selected[c]
);

solve minimize total_cost; 

Best solution: total_cost = 169 (CBC-COIN)

List of subsets:

[246, 248, 352, 568, 611, 1393, 2010, 2064, 2441, 2850, 2949, 3042, 3115, 3155,

 3173, 3259, 3307, 3458, 4667, 5235, 5891, 6230, 6860, 6883, 7179, 7280, 9029,

 9188, 9261, 9262, 9342, 9964, 10374, 10684, 11016, 11397, 11595, 11812, 11969,

 12130, 12322, 12392, 12487, 12646, 12875, 13103, 13298, 14452, 15763, 18529,

 18538, 19940, 20647, 20668, 20669, 22386, 23622, 23901, 25974, 27080, 27849,

 30827, 33131, 33190, 36507, 37778, 38063, 38217, 38382, 39017, 39077, 39119,

 39663, 39709, 40633, 40833, 41165, 41196, 41385, 41744, 42315, 42658, 42833,

 43829, 44804, 44977, 45717, 47877, 48923, 49228, 52110, 53276, 55671, 55675,

 55760, 55810, 56144, 56642, 56704, 56893, 56922, 56965, 57150, 57906, 57922,

 60233, 60594, 61650, 62336, 62363]