Redesign the Road System of An Imaginary Country - Computer Science Assignment Help

Assignment Task
 

Puzzle 
 

You need to redesign the road system of an imaginary country. The country is composed of N cities (for simplicity numbered from 0 to N — 1). Some pairs of cities are connected by bidirectional roads. We say that there is a path between different cities A and B if there exists a sequence of unique cities C1, C2, ... , CM, such that C1 = A and CM = B and for each index i < M, there is a road between cities CZ and Ci±i. The current state of the road network is miserable. Some pairs of cities are not connected by any path. On the other hand, other pairs of cities are connected by multiple different paths, and that leads to complicated traffic routing. You want to build some new roads and destroy some of the already existing roads in the country so that after the reconstruction there will exist exactly one path between every pair of distinct cities. As building new roads and destroying old ones costs a lot of money, you want to minimize the total cost spent on the reconstruction.

You are given three two-dimensional arrays: 
 

• country [i] [ j ] =1 or 0: there is an existing road between city i and j if and only if country [i] [j ] =1.

• build [i] [j] : the cost for building a road between i and j. The values of build [i] [j] are represented using English letters. A, B,...,Z represent 0, 1, ... , 25 and a, b,...,z represent 26, 27, ... , 51. For example, if build [2] [4] =b, then that means the cost for building a road between city 2 and city 4 is 
27. 

• destroy [i] [j] : the cost for destroying a road between i and j. Again, the values are represented using English letters like the above. 

Your task is to find and print the minimal cost needed for the road network reconstruction. You don't need to worry about invalid inputs.

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