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import java.util.NoSuchElementException;

public class MinHeap {

private int size;

private int capacity;

private int[] arr;

public MinHeap(int capacity) {

this.size = 0;

this.capacity = capacity;

this.arr = new int[capacity];

}

public int getMin() {

if (this.size == 0) throw new NoSuchElementException();

return this.arr[0];

}

public int extractMin() {

if (this.size == 0) throw new NoSuchElementException();

if (this.size == 1) {

this.size--;

return this.arr[0];

}

int minVal = this.arr[0];

this.arr[0] = this.arr[this.size - 1];

this.size--;

heapify(0);

return minVal;

}

private void heapify(int idx) {

heapify(this.arr, this.size, idx);

}

private void heapify(int[] A, int size, int idx) {

int l = left(idx);

int r = right(idx);

int minIdx = idx;

if (l < size && A[l] < A[minIdx]) minIdx = l;

if (r < size && A[r] < A[minIdx]) minIdx = r;

if (minIdx != idx) {

swap(A, minIdx, idx);

heapify(minIdx);

}

}

private void swap(int[] A, int i, int j) {

int temp = A[i];

A[i] = A[j];

A[j] = temp;

}

public void decreaseKey(int idx, int x) {

if (this.size <= idx) throw new NoSuchElementException();

this.arr[idx] = x;

popUp(idx);

}

public void insert(int x) {

if (this.size >= this.capacity) throw new StackOverflowError();

this.arr[this.size++] = x;

popUp(this.size - 1);

}

private void popUp(int idx) {

int i = idx;

while (i > 0 && this.arr[i] < this.arr[parent(i)]) {

swap(this.arr, i, parent(i));

i = parent(i);

}

}

public int delete(int idx) {

decreaseKey(idx, Integer.MIN_VALUE);

return extractMin();

}

public void buildHeap(int[] A) {

for (int i = parent(A.length-1); i >= 0; i--) {

heapify(A, A.length, i);

}

}

// Heap Sort in Descending Order

public void sort(int[] A) {

buildHeap(A);

for (int i = 0; i < A.length; i++) {

swap(A, i, A.length - 1);

heapify(A, A.length - i - 1, 0);

}

}

private int parent(int i) {

return (i - 1) / 2;

}

private int left(int i) {

return i * 2 + 1;

}

private int right(int i) {

return i * 2 + 2;

}

}