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C++ Implementation of Graph Algorithms


1 Task Description

You are asked to use C++ to solve the following puzzle.

Hint: All it takes is an algorithm mentioned in this course (with a slight twist).

The graph is undirected!

2 Submission Guideline

You must follow this guideline! Your submission will be marked automatically. Failure to

follow this guideline will result in 0.

Your submission should contain exactly one  file: main.cpp.

You do not need to submit a design.

3 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 Ci and Ci+1.

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.


• Sample input 1: 000,000,000 ABD,BAC,DCA ABD,BAC,DCA

Note: 000,000,000 describes the two-dimensional array country. ABD,BAC,DCA describes the two- dimensional array build. ABD,BAC,DCA describes the two-dimensional array destroy. The input format is: three strings separated by spaces; each string contains N parts separated by commas; each part contains N characters.

Sample output 1: 3

Comment: There are three cities, totally disconnected.

• Sample input 2: 011,101,110 ABD,BAC,DCA ABD,BAC,DCA

Sample output 2: 1

Comment: Now the three cities form a connected triangle and we need to destroy one road. Optimal solution is to destroy the road between the cities 0-1 (cost 1).

• Sample input 3: (note: all inputs are on the same line. I just couldn't _t them in one line in this pdf.)




Sample output 3: 7

Comment: We have six cities forming two separate triangles. Destroy one road in each triangle (costs 1 for each road) and then join the triangles by a new road (costs 5).

• Sample input 4: 0 A A

Sample output 4: 0

Comment: One city is okay just as it is.

• Sample input 5: 0001,0001,0001,1110 AfOj,fAcC,OcAP,jCPA AWFH,WAxU,FxAV,HUVA

Sample output 5: 0

Comment: We have four cities, which are connected in such a way that there is exactly one path between each two cities.

Thus there is nothing to reconstruct.


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C++Implementation of Graph Algorithms

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