Prufer 코드는 1에서 p까지 레이블이 있는 그래프 표현으로 사용자가 제공한 트리를 고유하게 식별합니다. 이 트리는 노드의 p(값은 사용자가 제공함) 레이블로 구성됩니다. p – 2 값의 시퀀스를 가집니다.
알고리즘
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.
예시
#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; }
출력
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 }