이진 힙은 최소 힙 또는 최대 힙인 완전한 이진 트리입니다. Max Binary Heap에서 루트의 키는 Binary Heap에 있는 모든 키 중 최대값이어야 합니다. 이 속성은 해당 이진 트리의 모든 노드에 대해 재귀적으로 true여야 합니다. Min Binary Heap은 MinHeap과 유사합니다.
기능 설명:
void BHeap::Insert(int ele) :힙에 요소를 삽입하기 위해 삽입 연산을 수행합니다.
BHeap::DeleteMin() 무효 :삭제 연산을 수행하여 힙에서 최소값을 삭제합니다.
int BHeap::ExtractMin() :heap에서 최소값을 추출하는 연산을 수행합니다.
무효 BHeap::showHeap() :힙의 요소를 표시합니다.
무효 BHeap::heapifyup(int in) :힙 구조를 상향식으로 유지합니다.
void BHeap::heapifydown(int in) :힙 구조를 하향식으로 유지합니다.
예시
#include <iostream>
#include <cstdlib>
#include <vector>
#include <iterator>
using namespace std;
class BHeap {
private:
vector <int> heap;
int l(int parent);
int r(int parent);
int par(int child);
void heapifyup(int index);
void heapifydown(int index);
public:
BHeap() {}
void Insert(int element);
void DeleteMin();
int ExtractMin();
void showHeap();
int Size();
};
int main() {
BHeap h;
while (1) {
cout<<"1.Insert Element"<<endl;
cout<<"2.Delete Minimum Element"<<endl;
cout<<"3.Extract Minimum Element"<<endl;
cout<<"4.Show Heap"<<endl;
cout<<"5.Exit"<<endl;
int c, e;
cout<<"Enter your choice: ";
cin>>c;
switch(c) {
case 1:
cout<<"Enter the element to be inserted: ";
cin>>e;
h.Insert(e);
break;
case 2:
h.DeleteMin();
break;
case 3:
if (h.ExtractMin() == -1) {
cout<<"Heap is Empty"<<endl;
}
else
cout<<"Minimum Element: "<<h.ExtractMin()<<endl;
break;
case 4:
cout<<"Displaying elements of Hwap: ";
h.showHeap();
break;
case 5:
exit(1);
default:
cout<<"Enter Correct Choice"<<endl;
}
}
return 0;
}
int BHeap::Size() {
return heap.size();
}
void BHeap::Insert(int ele) {
heap.push_back(ele);
heapifyup(heap.size() -1);
}
void BHeap::DeleteMin() {
if (heap.size() == 0) {
cout<<"Heap is Empty"<<endl;
return;
}
heap[0] = heap.at(heap.size() - 1);
heap.pop_back();
heapifydown(0);
cout<<"Element Deleted"<<endl;
}
int BHeap::ExtractMin() {
if (heap.size() == 0) {
return -1;
}
else
return heap.front();
}
void BHeap::showHeap() {
vector <int>::iterator pos = heap.begin();
cout<<"Heap --> ";
while (pos != heap.end()) {
cout<<*pos<<" ";
pos++;
}
cout<<endl;
}
int BHeap::l(int parent) {
int l = 2 * parent + 1;
if (l < heap.size())
return l;
else
return -1;
}
int BHeap::r(int parent) {
int r = 2 * parent + 2;
if (r < heap.size())
return r;
else
return -1;
}
int BHeap::par(int child) {
int p = (child - 1)/2;
if (child == 0)
return -1;
else
return p;
}
void BHeap::heapifyup(int in) {
if (in >= 0 && par(in) >= 0 && heap[par(in)] > heap[in]) {
int temp = heap[in];
heap[in] = heap[par(in)];
heap[par(in)] = temp;
heapifyup(par(in));
}
}
void BHeap::heapifydown(int in) {
int child = l(in);
int child1 = r(in);
if (child >= 0 && child1 >= 0 && heap[child] > heap[child1]) {
child = child1;
}
if (child > 0 && heap[in] > heap[child]) {
int t = heap[in];
heap[in] = heap[child];
heap[child] = t;
heapifydown(child);
}
} 출력
1.Insert Element 2.Delete Minimum Element 3.Extract Minimum Element 4.Show Heap 5.Exit Enter your choice: 1 Enter the element to be inserted: 2 1.Insert Element 2.Delete Minimum Element 3.Extract Minimum Element 4.Show Heap 5.Exit Enter your choice: 1 Enter the element to be inserted: 3 1.Insert Element 2.Delete Minimum Element 3.Extract Minimum Element 4.Show Heap 5.Exit Enter your choice: 1 Enter the element to be inserted: 7 1.Insert Element 2.Delete Minimum Element 3.Extract Minimum Element 4.Show Heap 5.Exit Enter your choice: 1 Enter the element to be inserted: 6 1.Insert Element 2.Delete Minimum Element 3.Extract Minimum Element 4.Show Heap 5.Exit Enter your choice: 4 Displaying elements of Hwap: Heap --> 2 3 7 6 1.Insert Element 2.Delete Minimum Element 3.Extract Minimum Element 4.Show Heap 5.Exit Enter your choice: 3 Minimum Element: 2 1.Insert Element 2.Delete Minimum Element 3.Extract Minimum Element 4.Show Heap 5.Exit Enter your choice: 3 Minimum Element: 2 1.Insert Element 2.Delete Minimum Element 3.Extract Minimum Element 4.Show Heap 5.Exit Enter your choice: 2 Element Deleted 1.Insert Element 2.Delete Minimum Element 3.Extract Minimum Element 4.Show Heap 5.Exit Enter your choice: 4 Displaying elements of Hwap: Heap --> 3 6 7 1.Insert Element 2.Delete Minimum Element 3.Extract Minimum Element 4.Show Heap 5.Exit Enter your choice: 5