Java에서 힙은 루트 노드 또는 상위 노드를 왼쪽 및 오른쪽 하위 노드와 비교하여 순서에 따라 배열하는 특수한 유형의 데이터 구조입니다. x가 루트 노드이고 y가 하위 노드, 속성이라고 가정합니다. 키(x)<= key(y)< strong>최소 힙을 생성하고 해당 관계를 다음과 같이 참조합니다. '힙 속성' .
Heap은 부모 노드와 자식 노드의 순서에 따라 Min heap과 Max heap의 두 가지 형태로 분류할 수 있습니다. 두 가지를 하나씩 이해하고 코드를 Java로 구현해 보겠습니다.
최소 힙
최소 힙은 그 자체로 완전한 이진 트리인 특별한 유형의 힙 데이터 구조입니다. 최소 힙에는 다음과 같은 속성이 있습니다.
- 루트 노드 값은 힙의 다른 노드에 비해 항상 작습니다.
- 각 내부 노드에는 항상 하위 노드보다 작거나 같은 키 값이 있습니다.
최소 힙에서는 다음 세 가지 작업을 수행할 수 있습니다.
삽입노드()
트리 끝에 새 키를 추가하여 Min 힙에 삽입을 수행할 수 있습니다. 삽입된 키의 값이 상위 노드보다 작으면 힙 속성을 충족하기 위해 키를 위쪽으로 탐색해야 합니다. 삽입 과정에는 O(log n) 시간이 걸립니다.
추출최소()
이는 최소값 노드, 즉 힙의 루트 노드를 제거하기 위해 수행하는 가장 중요한 작업 중 하나입니다. 루트 노드를 제거한 후에는 힙 속성이 유지되는지 확인해야 합니다. extractMin() 작업은 힙에서 최소 요소를 제거하는 데 O(Logn) 시간이 걸립니다.
Java에서 문자열을 문자로 변환
getMin()
그만큼 getMin() 작업은 힙의 루트 노드, 즉 O(1) 시간의 최소 요소를 가져오는 데 사용됩니다.
예:
최소 힙 알고리즘
proceduredesign_min_heap Array arr: of size n => array of elements // call min_heapify procedure for each element of the array to form min heap repeat for (k = n/2 ; k >= 1 ; k--) call procedure min_heapify (arr, k); proceduremin_heapify (vararr[ ] , var k, varn) { varleft_child = 2*k; varright_child = 2*k+1; var smallest; if(left_child<= n and arr[left_child ] <arr[ k ) smallest="left_child;" else if(right_child<="n" arr[right_child <arr[smallest] if(smallest !="k)" { swaparr[ arr[ ]); callmin_heapify (arr, smallest, n); } < pre> <p> <strong>MinHeapJavaImplementation.java</strong> </p> <pre> // import required classes and packages packagejavaTpoint.javacodes; importjava.util.Scanner; // create class MinHeap to construct Min heap in Java classMinHeap { // declare array and variables privateint[] heapData; privateintsizeOfHeap; privateintheapMaxSize; private static final int FRONT = 1; //use constructor to initialize heapData array publicMinHeap(intheapMaxSize) { this.heapMaxSize = heapMaxSize; this.sizeOfHeap = 0; heapData = new int[this.heapMaxSize + 1]; heapData[0] = Integer.MIN_VALUE; } // create getParentPos() method that returns parent position for the node privateintgetParentPosition(int position) { return position / 2; } // create getLeftChildPosition() method that returns the position of left child privateintgetLeftChildPosition(int position) { return (2 * position); } // create getRightChildPosition() method that returns the position of right child privateintgetRightChildPosition(int position) { return (2 * position) + 1; } // checks whether the given node is leaf or not privatebooleancheckLeaf(int position) { if (position >= (sizeOfHeap / 2) && position heapData[getLeftChildPosition(position)] || heapData[position] >heapData[getRightChildPosition(position)]) { // swap with left child and then heapify the left child if (heapData[getLeftChildPosition(position)] = heapMaxSize) { return; } heapData[++sizeOfHeap] = data; int current = sizeOfHeap; while (heapData[current] <heapdata[getparentposition(current)]) { swap(current, getparentposition(current)); current="getParentPosition(current);" } crreatedisplayheap() method to print the data of heap public void displayheap() system.out.println('parent node' + ' ' 'left child 'right node'); for (int k="1;" position--) minheapify(position); create removeroot() removing minimum element from publicintremoveroot() intpopelement="heapData[FRONT];" heapdata[front]="heapData[sizeOfHeap--];" minheapify(front); returnpopelement; minheapjavaimplementation class in java classminheapjavaimplementation{ main() start static main(string[] arg) declare variable intheapsize; scanner object sc="new" scanner(system.in); system.out.println('enter size min heap'); heapsize="sc.nextInt();" minheapheapobj="new" minheap(heapsize); for(inti="1;" i<="heapSize;" i++) system.out.print('enter '+i+' element: '); int heapobj.insertnode(data); close obj sc.close(); construct a given heapobj.designminheap(); display system.out.println('the is heapobj.displayheap(); root node system.out.println('after element(root node) '+heapobj.removeroot()+', is:'); < pre> <p> <strong>Output:</strong> </p> <img src="//techcodeview.com/img/java-tutorial/97/heap-implementation-java-2.webp" alt="Heap implementation in Java"> <h2>Max heap</h2> <p>Max heap is another special type of heap data structure that is also a complete binary tree in itself in Java. Max heap has the following properties:</p> <ol class="points"> <li>Root node value is always greater in comparison to the other nodes of the heap.</li> <li>Each internal node has a key value that is always greater or equal to its children.</li> </ol> <p>We can perform the following three operations in Max heap:</p> <h3>insertNode()</h3> <p>We can perform insertion in the Max heap by adding a new key at the end of the tree. If the value of the inserted key is greater than its parent node, we have to traverse the key upwards for fulfilling the heap property. The insertion process takes O(log n) time.</p> <h3>extractMax()</h3> <p>It is one of the most important operations which we perform to remove the maximum value node, i.e., the root node of the heap. After removing the root node, we have to make sure that heap property should be maintained. The extractMax() operation takes O(Log n) time to remove the maximum element from the heap.</p> <h3>getMax()</h3> <p>The <strong>getMax()</strong> operation is used to get the root node of the heap, i.e., maximum element in O(1) time.</p> <p> <strong>Example:</strong> </p> <img src="//techcodeview.com/img/java-tutorial/97/heap-implementation-java-3.webp" alt="Heap implementation in Java"> <p> <strong>Min heap Algorithm</strong> </p> <pre> proceduredesign_max_heap Array arr: of size n => array of elements // call min_heapify procedure for each element of the array to form max heap repeat for (k = n/2 ; k >= 1 ; k--) call procedure max_heapify (arr, k); proceduremin_heapify (vararr[ ] , var k, varn) { varleft_child = 2*k + 1; varright_child = 2*k+ 2; if(left_childarr[ largest ] ) largest = left_child; else largest = k; if(right_childarr[largest] ) largest = right_child; if(largest != k) { swaparr[ k ] and arr[ largest ]); callmax_heapify (arr, largest, n); } } </pre> <p> <strong>MaxHeapJavaImplementation.java</strong> </p> <pre> //import required classes and packages packagejavaTpoint.javacodes; importjava.util.Scanner; //create class MinHeap to construct Min heap in Java classMaxHeap { // declare array and variables privateint[] heapData; privateintsizeOfHeap; privateintheapMaxSize; private static final int FRONT = 1; //use constructor to initialize heapData array publicMaxHeap(intheapMaxSize) { this.heapMaxSize = heapMaxSize; this.sizeOfHeap = 0; heapData = new int[this.heapMaxSize]; } // create getParentPos() method that returns parent position for the node privateintgetParentPosition(int position) { return (position - 1) / 2; } // create getLeftChildPosition() method that returns the position of left child privateintgetLeftChildPosition(int position) { return (2 * position); } // create getRightChildPosition() method that returns the position of right child privateintgetRightChildPosition(int position) { return (2 * position) + 1; } // checks whether the given node is leaf or not privatebooleancheckLeaf(int position) { if (position > (sizeOfHeap / 2) && position <= sizeofheap) { return true; } false; create swapnodes() method that perform swapping of the given nodes heap firstnode and secondnode are positions private void swap(intfirstnode, intsecondnode) int temp; temp="heapData[firstNode];" heapdata[firstnode]="heapData[secondNode];" heapdata[secondnode]="temp;" maxheapify() to heapify node for maintaining property maxheapify(int position) check whether is non-leaf greater than its right left child if (!checkleaf(position)) (heapdata[position] <heapdata[getleftchildposition(position)] || heapdata[position] heapdata[getrightchildposition(position)]) swap(position, getleftchildposition(position)); maxheapify(getleftchildposition(position)); swap with else getrightchildposition(position)); maxheapify(getrightchildposition(position)); insertnode() insert element in public insertnode(int data) heapdata[sizeofheap]="data;" current="sizeOfHeap;" while (heapdata[current]>heapData[getParentPosition(current)]) { swap(current, getParentPosition(current)); current = getParentPosition(current); } sizeOfHeap++; } // create displayHeap() method to print the data of the heap public void displayHeap() { System.out.println('PARENT NODE' + ' ' + 'LEFT CHILD NODE' + ' ' + 'RIGHT CHILD NODE'); for (int k = 0; k <sizeofheap 2; k++) { system.out.print(' ' + heapdata[k] ' ' heapdata[2 * k 1] 2]); system.out.println(); } create designmaxheap() method to construct min heap public void for (int position="0;" < (sizeofheap 2); position++) maxheapify(position); removeroot() removing maximum element from the publicintremoveroot() intpopelement="heapData[FRONT];" heapdata[front]="heapData[sizeOfHeap--];" maxheapify(front); returnpopelement; minheapjavaimplementation class in java classmaxheapjavaimplementation{ main() start static main(string[] arg) declare variable intheapsize; scanner object sc="new" scanner(system.in); system.out.println('enter size of max heap'); heapsize="sc.nextInt();" maxheapheapobj="new" maxheap(50); for(inti="1;" i<="heapSize;" i++) system.out.print('enter '+i+' element: '); int data="sc.nextInt();" heapobj.insertnode(data); close obj sc.close(); a given heapobj.designmaxheap(); display system.out.println('the is heapobj.displayheap(); root node system.out.println('after element(root node) '+heapobj.removeroot()+', is:'); pre> <p> <strong>Output:</strong> </p> <img src="//techcodeview.com/img/java-tutorial/97/heap-implementation-java-4.webp" alt="Heap implementation in Java"> <hr></sizeofheap></=></pre></heapdata[getparentposition(current)])></pre></=> MaxHeapJavaImplementation.java
//import required classes and packages packagejavaTpoint.javacodes; importjava.util.Scanner; //create class MinHeap to construct Min heap in Java classMaxHeap { // declare array and variables privateint[] heapData; privateintsizeOfHeap; privateintheapMaxSize; private static final int FRONT = 1; //use constructor to initialize heapData array publicMaxHeap(intheapMaxSize) { this.heapMaxSize = heapMaxSize; this.sizeOfHeap = 0; heapData = new int[this.heapMaxSize]; } // create getParentPos() method that returns parent position for the node privateintgetParentPosition(int position) { return (position - 1) / 2; } // create getLeftChildPosition() method that returns the position of left child privateintgetLeftChildPosition(int position) { return (2 * position); } // create getRightChildPosition() method that returns the position of right child privateintgetRightChildPosition(int position) { return (2 * position) + 1; } // checks whether the given node is leaf or not privatebooleancheckLeaf(int position) { if (position > (sizeOfHeap / 2) && position <= sizeofheap) { return true; } false; create swapnodes() method that perform swapping of the given nodes heap firstnode and secondnode are positions private void swap(intfirstnode, intsecondnode) int temp; temp="heapData[firstNode];" heapdata[firstnode]="heapData[secondNode];" heapdata[secondnode]="temp;" maxheapify() to heapify node for maintaining property maxheapify(int position) check whether is non-leaf greater than its right left child if (!checkleaf(position)) (heapdata[position] <heapdata[getleftchildposition(position)] || heapdata[position] heapdata[getrightchildposition(position)]) swap(position, getleftchildposition(position)); maxheapify(getleftchildposition(position)); swap with else getrightchildposition(position)); maxheapify(getrightchildposition(position)); insertnode() insert element in public insertnode(int data) heapdata[sizeofheap]="data;" current="sizeOfHeap;" while (heapdata[current]>heapData[getParentPosition(current)]) { swap(current, getParentPosition(current)); current = getParentPosition(current); } sizeOfHeap++; } // create displayHeap() method to print the data of the heap public void displayHeap() { System.out.println('PARENT NODE' + ' ' + 'LEFT CHILD NODE' + ' ' + 'RIGHT CHILD NODE'); for (int k = 0; k <sizeofheap 2; k++) { system.out.print(\' \' + heapdata[k] \' \' heapdata[2 * k 1] 2]); system.out.println(); } create designmaxheap() method to construct min heap public void for (int position="0;" < (sizeofheap 2); position++) maxheapify(position); removeroot() removing maximum element from the publicintremoveroot() intpopelement="heapData[FRONT];" heapdata[front]="heapData[sizeOfHeap--];" maxheapify(front); returnpopelement; minheapjavaimplementation class in java classmaxheapjavaimplementation{ main() start static main(string[] arg) declare variable intheapsize; scanner object sc="new" scanner(system.in); system.out.println(\'enter size of max heap\'); heapsize="sc.nextInt();" maxheapheapobj="new" maxheap(50); for(inti="1;" i<="heapSize;" i++) system.out.print(\'enter \'+i+\' element: \'); int data="sc.nextInt();" heapobj.insertnode(data); close obj sc.close(); a given heapobj.designmaxheap(); display system.out.println(\'the is heapobj.displayheap(); root node system.out.println(\'after element(root node) \'+heapobj.removeroot()+\', is:\'); pre> <p> <strong>Output:</strong> </p> <img src="//techcodeview.com/img/java-tutorial/97/heap-implementation-java-4.webp" alt="Heap implementation in Java"> <hr></sizeofheap></=>