Binary Min-Max Heap Implementation
A binary heap is a heap data structure created using a binary tree.
binary tree has two rules –
- Binary Heap has to be a complete binary tree at all levels except the last level. This is called a shape property.
- All nodes are either greater than equal to (Max-Heap) or less than equal to (Min-Heap) to each of its child nodes. This is called heap property.
Implementation:
- Use an array to store the data.
- Start storing from index 1, not 0.
- For any given node at position i:
- Its Left Child is at [2*i] if available.
- Its Right Child is at [2*i+1] if available.
- Its Parent Node is at [i/2]if available.
Heap Majorly has 3 operations –
- Insert Operation
- Delete Operation
- Extract-Min (OR Extract-Max)
Insert Operation:
- Add the element at the bottom leaf of the Heap.
- Perform the Bubble-Up operation.
- All Insert Operations must perform the bubble-up operation(it is also called as up-heap, percolate-up, sift-up, trickle-up, heapify-up, or cascade-up)
Extract-Min OR Extract-Max Operation:
- Take out the element from the root.( it will be minimum in case of Min-Heap and maximum in case of Max-Heap).
- Take out the last element from the last level from the heap and replace the root with the element.
- Perform Sink-Down
- All delete operations must perform Sink-Down Operation ( also known as bubble-down, percolate-down, sift-down, trickle-down, heapify-down, cascade-down).
Sink-Down Operation:
- If the replaced element is greater than any of its child node in case of Min-Heap OR smaller than any if its child node in case of Max-Heap, swap the element with its smallest child(Min-Heap) or with its greatest child(Max-Heap).
- Keep repeating the above step, if the node reaches its correct position, STOP.
Delete Operation:
- Find the index for the element to be deleted.
- Take out the last element from the last level from the heap and replace the index with this element .
- Perform Sink-Down
Time and Space Complexity:
| Space | O(n) |
| Search | O(n) |
| Insert | O(log n) |
| Delete | O(log n) |
Complete Code for Min-Heap:
Java
public class minHeap {
public int capacity;
public int [] mH;
public int currentSize;
public minHeap(int capacity){
this.capacity=capacity;
mH = new int [capacity+1];
currentSize =0;
}
public void createHeap(int [] arrA){
if(arrA.length>0){
for(int i=0;i<arrA.length;i++){
insert(arrA[i]);
}
}
}
public void display(){
for(int i=1;i<mH.length;i++){
System.out.print(" " + mH[i]);
}
System.out.println("");
}
public void insert(int x) {
if(currentSize==capacity){
System.out.println("heap is full");
return;
}
currentSize++;
int idx = currentSize;
mH[idx] = x;
bubbleUp(idx);
}
public void bubbleUp(int pos) {
int parentIdx = pos/2;
int currentIdx = pos;
while (currentIdx > 0 && mH[parentIdx] > mH[currentIdx]) {
swap(currentIdx,parentIdx);
currentIdx = parentIdx;
parentIdx = parentIdx/2;
}
}
public int extractMin() {
int min = mH[1];
mH[1] = mH[currentSize];
mH[currentSize] = 0;
sinkDown(1);
currentSize--;
return min;
}
public void sinkDown(int k) {
int smallest = k;
int leftChildIdx = 2 * k;
int rightChildIdx = 2 * k+1;
if (leftChildIdx < heapSize() && mH[smallest] > mH[leftChildIdx]) {
smallest = leftChildIdx;
}
if (rightChildIdx < heapSize() && mH[smallest] > mH[rightChildIdx]) {
smallest = rightChildIdx;
}
if (smallest != k) {
swap(k, smallest);
sinkDown(smallest);
}
}
public void swap(int a, int b) {
int temp = mH[a];
mH[a] = mH[b];
mH[b] = temp;
}
public boolean isEmpty() {
return currentSize == 0;
}
public int heapSize(){
return currentSize;
}
public static void main(String args[]){
int arrA [] = {3,2,1,7,8,4,10,16,12};
System.out.print("Original Array : ");
for(int i=0;i<arrA.length;i++){
System.out.print(" " + arrA[i]);
}
minHeap m = new minHeap(arrA.length);
System.out.print("\nMin-Heap : ");
m.createHeap(arrA);
m.display();
System.out.print("Extract Min :");
for(int i=0;i<arrA.length;i++){
System.out.print(" " + m.extractMin());
}
}
}Output:
Original Array : 3 2 1 7 8 4 10 16 12 Min-Heap : 1 3 2 7 8 4 10 16 12 Sorted: 1 3 2 12 8 4 10 16 0