Prroblem: write an algorithm to calculate the minimum cost to add new roads between the cities such that all the cities are accessible from each other
int numTotalAvailableCities = 6;
int numTotalAvailableRoads = 3;
int[,] roadsAvailable = { { 1, 4 }, { 4, 5 }, { 2, 3 } };
int[,] costNewRoadsToConstruct = { { 1, 2,5 }, { 1,3,10 }, {1,6,2} ,{ 5, 6, 5 } };
int numNewRoadsConstruct = 4;
public class MinimumCostToConstructNewRoad
{
public static int getMinimumCostToConstruct(int numTotalAvailableCities,
int numTotalAvailableRoads,
int[,] roadsAvailable,
int numNewRoadsConstruct,
int[,] costNewRoadsConstruct)
{
int totalCost = 0;
bool[] Visited = new bool[numTotalAvailableCities];
int[] Keys = new int[numTotalAvailableCities];
int[] Parent = new int[numTotalAvailableCities];
int[,] AdjMatrix = GetAdjecencyMatrix(roadsAvailable, costNewRoadsConstruct, numTotalAvailableCities);
for (int i=0;i< numTotalAvailableCities;i++)
{
Keys[i] = Int32.MaxValue;
}
Keys[0] = 0;
Parent[0] = -1;
for(int i=0;i< numTotalAvailableCities-1;i++)
{
var u = FindMin(Visited, Keys);
Visited[u] = true;
for(int v=0;v< numTotalAvailableCities;v++)
{
if(Visited[v]==false && AdjMatrix[u, v]!=Int32.MaxValue && AdjMatrix[u,v]<Keys[v])
{
Parent[v] = u;
Keys[v] = AdjMatrix[u, v];
}
}
}
for(int i=1;i< numTotalAvailableCities;i++)
{
totalCost = totalCost + AdjMatrix[Parent[i], i];
}
return totalCost;
}
private static int FindMin(bool[] Visited, int[] Keys)
{
int min = Int32.MaxValue; int index = -1;
for (int i = 0; i < Keys.Length; i++)
{
if (Visited[i] == false && Keys[i] < min)
{
min = Keys[i];
index = i;
}
}
return index;
}
private static int[,] GetAdjecencyMatrix(int[,] roadsAvailable, int[,] costNewRoadsConstruct,int numTotalAvailableCities)
{
int[,] AdjMatrix = new int[numTotalAvailableCities, numTotalAvailableCities];
for (int i = 0; i < numTotalAvailableCities; i++)
{
for (int j = 0; j < numTotalAvailableCities; j++)
{
AdjMatrix[i, j] = Int32.MaxValue;
}
}
int count = 0;
for (int i = 0; i < roadsAvailable.GetLength(0); i++)
{
int start = roadsAvailable[i, count]-1;
int end = roadsAvailable[i,count+1]-1;
AdjMatrix[start, end] = 0;
}
for (int i = 0; i < costNewRoadsConstruct.GetLength(0); i++)
{
int start = costNewRoadsConstruct[i, count]-1;
int end = costNewRoadsConstruct[i, count+1]-1;
int cost= costNewRoadsConstruct[i, count + 2];
AdjMatrix[start, end] = cost;
}
return AdjMatrix;
}
}
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