本次項目的文件結構圖如下

在windows下的運行效果如圖

堆本質上就是平衡二叉樹，這里采用的是線段樹來實現的。比較簡單
但是在使用的QT自帶的QTTreeWidget來顯示的時候就實現了一個講線段樹還原成一般的平衡二叉樹的過程，這是很有趣的。

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mainwindow.h

#ifndef MAINWINDOW_H #define MAINWINDOW_H#include <QMainWindow> #include "minheap.h" namespace Ui { class MainWindow; }class MainWindow : public QMainWindow {Q_OBJECTpublic:explicit MainWindow(QWidget *parent = 0);~MainWindow();private slots:void on_pushButton_clicked();void on_pushButton_2_clicked();void on_pushButton_3_clicked();private:Ui::MainWindow *ui;MinHeap_ minheap;void buildTheTree(); };#endif // MAINWINDOW_H

minheap.h

#ifndef MINHEAP_H #define MINHEAP_H#ifndef DefaultSize #define DefaultSize 10 #endif // class MinHeap_ { public:MinHeap_(int sz = DefaultSize);MinHeap_(int arr[], int m);~MinHeap_() { delete[] heap; }bool Insert(const int& x);bool RemoveMin(int &x);bool IsEmpty()const {return currentsize == 0;}bool IsFull()const {return currentsize == maxHeapSize;}void makeEmpty(){currentsize = 0;}void ReSet(int arr[], int m);const int* getHeap();int getHeapSize(); private:int currentsize;int maxHeapSize;int * heap;void shiftDown(int start, int m);void shiftUp(int start); };#endif // MINHEAP_H

main.cpp

#include "mainwindow.h" #include <QApplication>int main(int argc, char *argv[]) {QApplication a(argc, argv);MainWindow w;w.setWindowTitle("MinHeap(最小堆)");w.show();return a.exec(); }

mainwindow.cpp

#include "mainwindow.h" #include "ui_mainwindow.h" #include <iostream> using namespace std; #include <queue> MainWindow::MainWindow(QWidget *parent) :QMainWindow(parent),ui(new Ui::MainWindow) {ui->setupUi(this);ui->treeWidget->setHeaderLabel("最小堆"); }MainWindow::~MainWindow() {delete ui; } void MainWindow::buildTheTree(){if (ui->treeWidget->topLevelItemCount() > 0) ui->treeWidget->clear();const int * heap = minheap.getHeap();int heapSize = minheap.getHeapSize();if (heap == NULL || heapSize <= 0){return;}QTreeWidgetItem * Top = new QTreeWidgetItem(QStringList(QString::number(heap[0])));ui->treeWidget->addTopLevelItem(Top);queue<QTreeWidgetItem*> q;q.push(Top);int pp = 1;while(!q.empty() && pp < heapSize) {QTreeWidgetItem* now = q.front();q.pop();for (int i = 0; i < 2 && pp < heapSize; ++i, ++pp) {QTreeWidgetItem* newI = new QTreeWidgetItem(QStringList(QString::number(heap[pp])));now->addChild(newI);q.push(newI);}} }void MainWindow::on_pushButton_clicked() {QString Ims = ui->lineEdit->text();ui->lineEdit->clear();if (Ims.isEmpty()) return;QStringList numStr = Ims.split(' ',QString::SkipEmptyParts);int *nums = new int [numStr.size()];for (int i = 0; i < numStr.size(); ++i) {nums[i] = numStr[i].toInt();}minheap.ReSet(nums, numStr.size());buildTheTree();delete[]nums; }void MainWindow::on_pushButton_2_clicked() {int text = 0;if (minheap.RemoveMin(text)) {buildTheTree();} }void MainWindow::on_pushButton_3_clicked() {QString ans;while (!minheap.IsEmpty()) {int text; minheap.RemoveMin(text);ans += QString::number(text) + " ";}ui->lineEdit->setText(ans); }

minheap.cpp

#include "minheap.h" #include <iostream> using namespace std;MinHeap_::MinHeap_(int sz) {currentsize = 0;maxHeapSize = (DefaultSize > sz)? DefaultSize : sz;heap = new int [maxHeapSize];if (!heap) {std::cout << "Memery build up error!\n";} } MinHeap_::MinHeap_(int arr[], int m){currentsize = (m > 0)? m : 0;maxHeapSize = (DefaultSize > m)? DefaultSize : m;heap = new int [maxHeapSize];if (arr && heap) {for (int i = 0; i < m; ++i) {heap[i] = arr[i];}int currentPos = currentsize / 2 - 1;while (currentPos >= 0) {shiftDown(currentPos, currentsize-1);currentPos--;}}else if (heap){for (int i = 0; i < m; ++i) heap[i] = 0;}else {std::cout << "Memery build up error!\n";} } bool MinHeap_::Insert(const int &x) {if(IsFull()) return false;heap[currentsize] = x;shiftUp(currentsize);currentsize++;return true; } bool MinHeap_::RemoveMin(int &x){if (currentsize <= 0) return false;x = heap[0]; heap[0] = heap[currentsize-1];currentsize --;shiftDown(0,currentsize-1);return true; } const int* MinHeap_:: getHeap(){return heap; }int MinHeap_::getHeapSize(){return currentsize; }void MinHeap_::ReSet(int arr[], int m){delete[] heap; heap = NULL;currentsize = (m > 0)? m : 0;maxHeapSize = (DefaultSize > m)? DefaultSize : m;heap = new int [maxHeapSize];if (arr && heap) {for (int i = 0; i < m; ++i) {heap[i] = arr[i];}int currentPos = currentsize / 2 - 1;while (currentPos >= 0) {shiftDown(currentPos, currentsize-1);currentPos--;}}else if (heap){for (int i = 0; i < m; ++i) heap[i] = 0;}else {std::cout << "Memery build up error!\n";} }void MinHeap_::shiftDown(int start, int m){if (start < 0 || m >= currentsize || start >= currentsize) return;int i = start, j = 2*i+1; // j point the left son of the heap[i];int temp = heap[start];while (j <= m) {if (j < m && heap[j] > heap[j+1]) j++; // make sure j point the smaller one in the two sonsif (temp <= heap[j]) break;else {heap[i] = heap[j]; i = j; j = 2*j+1;}}heap[i] = temp; } void MinHeap_::shiftUp(int start){if (start < 0 || start >= currentsize) return;int j = start, i = ( j - 1 ) / 2;int temp = heap[j];while (i >= 0) {if (heap[i] <= temp)break;else {heap[j] = heap[i];j = i;i = (j - 1) / 2;}}heap[j] = temp; }

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