C++ Programming Code Examples
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C++ Program to Create the Prufer Code for a Tree
/* C++ Program to Create the Prufer Code for a Tree
- This algorithm generates a prufer code for the given tree.
- For a given tree of v vertexes, a prufer code is a unique sequence of v-2 vertex indexes.
- The time complexity to generate this code is O(v*e).
- This algorithm takes the input of the number of vertexes for the tree.
- Then it takes the input if vertex pairs which have an edge between them.
- To generate prufer code it removes the leaf vertex which has lowest index value.
- It simultaneously adds the other vertex to the prufer code from which this leaf vertex was connected.
- This process is done till two vertex remains in the tree.
- Exit. */
#include<iostream>
using namespace std;
int main()
{
int i, j, v, e, min, x;
// Take the input of the number of vertexes of the tree.
cout<<"Enter the number of vertexes of the tree: ";
cin>>v;
// Calculate the number of edges in the tree as 'v-1'.
e = v-1;
int edge[e][2], deg[v+1] = {0};
cout<<"\nFor "<<v<<" vertexes this connected tree must have exactly "<<e<<" edges.\n";
// Enter the vertex pairs which have an edge between them.
cout<<"\nEnter "<<e<<" pair of vertexes for the tree.\n";
for(i = 0; i < e; i++)
{
cout<<"Enter the vertex pair for edge "<<i+1<<":";
cout<<"\nV(1): ";
cin>>edge[i][0];
cout<<"V(2): ";
cin>>edge[i][1];
deg[edge[i][0]]++;
deg[edge[i][1]]++;
}
// Print the prufer code of the given tree.
cout<<"\nThe Prufer code for the given tree is: { ";
for(i = 0; i < v-2; i++)
{
min = 10000;
// Select the vertex which have lowest index and degree as 1.
for(j = 0; j < e; j++)
{
if(deg[edge[j][0]] == 1)
{
if(min > edge[j][0])
{
min = edge[j][0];
x = j;
}
}
if(deg[edge[j][1]] == 1)
{
if(min > edge[j][1])
{
min = edge[j][1];
x = j;
}
}
}
// Remove the selected vertex by decreasing its degree to 0.
deg[edge[x][0]]--;
// Decrement the degree of other vertex, since we have removed the edge.
deg[edge[x][1]]--;
// Print the vertex from which leaf vertex is removed.
if(deg[edge[x][0]] == 0)
cout<<edge[x][1]<<" ";
else
cout<<edge[x][0]<<" ";
}
cout<<"}";
return 0;
}
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