C++ Program to Create the Prufer Code for a Tree

Prufer code uniquely identifies a tree which is given by user as a graph representation with labels from 1 to p. This tree consist p(value is given by user) labels of node. It has sequence of p – 2 values.

Algorithm

Begin
   Declare i, j, ver, edg, minimum, p to the integer datatype.
   Print “Enter the number of vertexes: ”.
   Enter the value of ver.
   Initialize edg = ver-1.
   Declare EDG[edg][2], DG[ver+1] to the integer datatype.
      Initialize DG[ver+1] = {0}.
   Print “This tree has (value of edg) edges for (value of ver) vertexes”.
   Print “There are (value of edg) pairs of vertexes in the tree”.
   for(i = 0; i < edg; i++)
      Print "Enter the value of vertex pair for edge ".
      Print "Enter the value of V(1) vertex: ".
      Enter the value of EDG[i][0].
      Print "Enter the value of V(2) vertex: ".
      Enter the value of EDG[i][1].
      DG[EDG[i][0]]++.
      DG[EDG[i][1]]++.
   Print "The Prufer code for the tree is: { ".
      for(i = 0; i < ver-2; i++)
         minimum = 10000
         for(j = 0; j < edg; j++)
            if(DG[EDG[j][0]] == 1) then
               if(minimum > EDG[j][0]) then
                  minimum = EDG[j][0].
                  p = j.
            if(DG[EDG[j][1]] == 1) then
               if(minimum > EDG[j][1]) then
                  minimum = EDG[j][1].
                  p = j.
            DG[EDG[p][0]]--.
            DG[EDG[p][1]]--.
      if(DG[EDG[p][0]] == 0) then
         Print the value of EDG[p][1].
      else
         Print the value of EDG[p][0].
   Print "}".
End.

Example

 Live Demo

#include<iostream>
using namespace std;
int main() {
   int i, j, ver, edg, minimum, p;
   cout<<"Enter the number of vertexes: ";
   cin>>ver;
   cout<<endl;
   edg = ver-1;
   int EDG[edg][2], DG[ver+1] = {0};
   cout<<"This tree has "<<edg<<" edges for "<<ver<<"vertexes.\n";
   cout<<"There are "<<edg<<" pairs of vertexes in the three.\n";
   for(i = 0; i < edg; i++) {
      cout<<"Enter the value of vertex pair for edge "<<i+1<<":\n";
      cout<<"Enter the value of V(1) vertex: ";
      cin>>EDG[i][0];
      cout<<"Enter the value of V(2) vertex: ";
      cin>>EDG[i][1];
      DG[EDG[i][0]]++;
      DG[EDG[i][1]]++;
   }
   cout<<"\nThe Prufer code for the tree is: { "; // Print the prufer code of the given tree.
   for(i = 0; i < ver-2; i++) {
      minimum = 10000;
      for(j = 0; j < edg; j++) {
         if(DG[EDG[j][0]] == 1) {
            if(minimum > EDG[j][0]) {
               minimum = EDG[j][0];
               p = j;
            }
         }
         if(DG[EDG[j][1]] == 1) {
            if(minimum > EDG[j][1]) {
               minimum = EDG[j][1];
               p = j;
            }
         }
      }
      DG[EDG[p][0]]--; // Remove the selected vertex by decreasing its degree to 0.
      DG[EDG[p][1]]--; // Decrement the degree of other vertex, since we have removed the EDG.
      if(DG[EDG[p][0]] == 0)
         cout<<EDG[p][1]<<" ";
      else
         cout<<EDG[p][0]<<" ";
   }
   cout<<"}";
   return 0;
}

Output

Enter the number of vertexes: 5

This tree has 4 edges for 5vertexes.
There are 4 pairs of vertexes in the three.
Enter the value of vertex pair for edge 1:
Enter the value of V(1) vertex: 2
Enter the value of V(2) vertex: 3
Enter the value of vertex pair for edge 2:
Enter the value of V(1) vertex: 5
Enter the value of V(2) vertex: 6
Enter the value of vertex pair for edge 3:
Enter the value of V(1) vertex: 7
Enter the value of V(2) vertex: 8
Enter the value of vertex pair for edge 4:
Enter the value of V(1) vertex: 9
Enter the value of V(2) vertex: 10

The Prufer code for the tree is: { 4 8 4 }