A police department is facing severe budget cuts. Until recently, the streets have been patrolled overnight by 15 patrol cars, one in each sector. The police department has divided the city into 15 patrol sectors (as shown in the map) so that the officers can respond quickly to service calls. The chief of police has mandated that each sector should be covered by at least one unit located within the sector or in an adjacent sector. In the map given below, two sectors are said to be adjacent if they share a common boundary. Thus sectors 1 and 2, and sectors 1 and 11 are adjacent, while sectors 9 and 6 are not adjacent. There are two exceptions to this. Sectors 7 and 14 are not accessible from each other because their boundary is the site of a duck pond, while Sectors 9 and 13 are not mutually accessible due to a Mountain, which is located at their boundary. Help the police chief to find the minimum number of patrol cars required to service the city’s 15 sectors. Hint: First create the adjacency matrix of the map
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