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- Design and Analysis of Algorithms
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Extracting Root Element From Heap
Extract method is used to extract the root element of a Heap. Following is the algorithm.
Pseudocode
Heap-Extract-Max (numbers[]) max = numbers[1] numbers[1] = numbers[heapsize] heapsize = heapsize – 1 Max-Heapify (numbers[], 1) return max
Example
Let us consider the same example discussed previously. Now we want to extract an element. This method will return the root element of the heap.
![Method](/design_and_analysis_of_algorithms/images/method.jpg)
After deletion of the root element, the last element will be moved to the root position.
![Root Element](/design_and_analysis_of_algorithms/images/root_element.jpg)
Now, Heapify function will be called. After Heapify, the following heap is generated.
![Heapify](/design_and_analysis_of_algorithms/images/heapify.jpg)
Implementation
Following are the implementations of this operation in various programming languages −
#include <stdio.h> void swap(int arr[], int i, int j) { int temp = arr[i]; arr[i] = arr[j]; arr[j] = temp; } void maxHeapify(int arr[], int size, int i) { int leftChild = 2 * i + 1; int rightChild = 2 * i + 2; int largest = i; if (leftChild < size && arr[leftChild] > arr[largest]) largest = leftChild; if (rightChild < size && arr[rightChild] > arr[largest]) largest = rightChild; if (largest != i) { swap(arr, i, largest); maxHeapify(arr, size, largest); // Recursive call to continue heapifying } } int extractMax(int arr[], int *heapSize) { if (*heapSize < 1) { printf("Heap underflow!\n"); return -1; } int max = arr[0]; arr[0] = arr[*heapSize - 1]; (*heapSize)--; maxHeapify(arr, *heapSize, 0); // Heapify the updated heap return max; } int main() { int arr[] = { 55, 50, 30, 40, 20, 15, 10 }; // Max-Heap int heapSize = sizeof(arr) / sizeof(arr[0]); int max = extractMax(arr, &heapSize); // Extract the max element from the heap printf("Extracted Max Element: %d\n", max); // Print the updated Max-Heap printf("Updated Max-Heap: "); for (int i = 0; i < heapSize; i++) printf("%d ", arr[i]); printf("\n"); return 0; }
Output
Extracted Max Element: 55 Updated Max-Heap: 50 40 30 10 20 15
#include <iostream> #include <vector> void swap(std::vector<int>& arr, int i, int j) { int temp = arr[i]; arr[i] = arr[j]; arr[j] = temp; } void maxHeapify(std::vector<int>& arr, int size, int i) { int leftChild = 2 * i + 1; int rightChild = 2 * i + 2; int largest = i; if (leftChild < size && arr[leftChild] > arr[largest]) largest = leftChild; if (rightChild < size && arr[rightChild] > arr[largest]) largest = rightChild; if (largest != i) { swap(arr, i, largest); maxHeapify(arr, size, largest); // Recursive call to continue heapifying } } int extractMax(std::vector<int>& arr, int& heapSize) { if (heapSize < 1) { std::cout << "Heap underflow!" << std::endl; return -1; } int max = arr[0]; arr[0] = arr[heapSize - 1]; heapSize--; maxHeapify(arr, heapSize, 0); // Heapify the updated heap return max; } int main() { std::vector<int> arr = { 55, 50, 30, 40, 20, 15, 10 }; // Max-Heap int heapSize = arr.size(); int max = extractMax(arr, heapSize); // Extract the max element from the heap std::cout << "Extracted Max Element: " << max << std::endl; // Print the updated Max-Heap std::cout << "Updated Max-Heap: "; for (int i = 0; i < heapSize; i++) std::cout << arr[i] << " "; std::cout << std::endl; return 0; }
Output
Extracted Max Element: 55 Updated Max-Heap: 50 40 30 10 20 15
import java.util.Arrays; public class MaxHeap { public static void swap(int arr[], int i, int j) { int temp = arr[i]; arr[i] = arr[j]; arr[j] = temp; } public static void maxHeapify(int arr[], int size, int i) { int leftChild = 2 * i + 1; int rightChild = 2 * i + 2; int largest = i; if (leftChild < size && arr[leftChild] > arr[largest]) largest = leftChild; if (rightChild < size && arr[rightChild] > arr[largest]) largest = rightChild; if (largest != i) { swap(arr, i, largest); maxHeapify(arr, size, largest); // Recursive call to continue heapifying } } public static int extractMax(int arr[], int heapSize) { if (heapSize < 1) { System.out.println("Heap underflow!"); return -1; } int max = arr[0]; arr[0] = arr[heapSize - 1]; heapSize--; maxHeapify(arr, heapSize, 0); // Heapify the updated heap return max; } public static void main(String args[]) { int arr[] = { 55, 50, 30, 40, 20, 15, 10 }; // Max-Heap int heapSize = arr.length; int max = extractMax(arr, heapSize); // Extract the max element from the heap System.out.println("Extracted Max Element: " + max); // Print the updated Max-Heap System.out.print("Updated Max-Heap: "); for (int i = 0; i < heapSize; i++) System.out.print(arr[i] + " "); System.out.println(); } }
Output
Extracted Max Element: 55 Updated Max-Heap: 50 40 30 10 20 15 10
def swap(arr, i, j): arr[i], arr[j] = arr[j], arr[i] def max_heapify(arr, size, i): left_child = 2 * i + 1 right_child = 2 * i + 2 largest = i if left_child < size and arr[left_child] > arr[largest]: largest = left_child if right_child < size and arr[right_child] > arr[largest]: largest = right_child if largest != i: swap(arr, i, largest) max_heapify(arr, size, largest) # Recursive call to continue heapifying def extract_max(arr, heap_size): if heap_size < 1: print("Heap underflow!") return -1 max_element = arr[0] arr[0] = arr[heap_size - 1] heap_size -= 1 max_heapify(arr, heap_size, 0) # Heapify the updated heap return max_element arr = [55, 50, 30, 40, 20, 15, 10] # Max-Heap heap_size = len(arr) max_element = extract_max(arr, heap_size) # Extract the max element from the heap print("Extracted Max Element:", max_element) # Print the updated Max-Heap print("Updated Max-Heap:", arr)
Output
Extracted Max Element: 55 Updated Max-Heap: [50, 40, 30, 10, 20, 15, 10]
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