## K-4 City Program in JavaThe K4 City program uses a method called the The program uses the k-means clustering algorithm to find k cities that will act as centers or representatives for the other cities. The value of k is input by the user. The code works by iteratively selecting the city with the maximum distance to its closest center. The center is then added to the list of centers and the distances of all cities to the new center are updated. The process is repeated until k centers have been selected. The output of the code is a list of the k cities that have been selected as centers. The cities are listed in the order in which they were selected.
Consider the following four cities, 0, 1, 2, and 3, and the distances between them, how to place 2 ATMs among these 4 cities so that the maximum distance of a city to an ATM is minimized. ## ImplementationThe provided Java code implements a The code takes two inputs, a list of n cities and a distance matrix. The distance matrix provides the distances between each pair of cities. The information is used to calculate the similarity or dissimilarity between cities. The output of the code is a list of k cities that have been selected as centers. These cities are considered to be representative of the other cities in the list and are used for further analysis or processing.
- The
**main()**function reads the number of cities n and the 2D array weights representing the distances between cities. It also reads the number of centers k to be selected. - The selectKcenters() function is called to select k centers from the cities.
- The selectKcenters() function initializes an array dist to store the minimum distance of each city to its closest center. Initially, all distances are set to Integer.MAX_VALUE.
- In each iteration, it finds the city max with the maximum distance to its closest center.
- It adds max to the list of centers centers.
- It updates the dist[] array for all cities, considering the newly added center max.
Finally, the function returns the list of selected centers. The main() function prints the list of k selected centers.
The 2 cities selected as centers are: 0 2
The method in the above code selectKcenters() takes O(n^2k) times to execute, and the method findMaxDistance() and updateDistance() takes O(n) times to execute the code. So, the over all,
Space complexity depends on how the distance matrix is implemented. In this code, the space complexity is O(n + k). Where n is the number of cities and k is the number of centers to be selected. |

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