算法练习三 优先级队列

在算法联系二写了一个堆排序，这次在堆排序的基础上写优先级队列。

这里先对上次的代码进行一下调整，可以避免一些重复工作。

调整一：形成独立的头文件 HeapHeader.h

#pragma once #include<iostream> #include<stdlib.h> #include<time.h> using namespace std; #define random(x) (rand()%x) #define LEFT(i) ( i << 1) #define RIGHT(i) ( ( i << 1 ) + 1 ) #define PARENT(i) ( i >> 1 ) /* 数组下标统一从1开始，第0位置不使用。 如果数组有10个元素从Ary[0] - Ary[9] 那么aryLen = 9 只使用 Ary[1] - Ary[9] */ void HeapSort(int ary[], int aryLen); void BuildMaxHeap(int ary[], int aryLen); void MaxHeapify(int ary[], int i,int heapSize); int ExtractMax(int ary[], int heapSize); void IncreaseKey(int ary[], int i, int key);  

调整二：独立的 构建堆、保持最大堆、堆排序 实现 HeapImp.cpp

#include "stdafx.h" #include "HeapHeader.h" void HeapSort(int ary[], int aryLen) { BuildMaxHeap( ary,aryLen ); cout << "after BuildMaxHeap" << endl; int j=0; for ( j=1; j<=aryLen; j++) { cout << ary[j] << "/t"; } int heapSize = aryLen; int i = aryLen; for( ; i>=2; i--) { int temp = ary[1]; ary[1] = ary[i]; ary[i] = temp; heapSize = heapSize - 1; MaxHeapify(ary,1,heapSize); } } /* 构造最大堆 子数组Ary[ (arylen >> 1 + 1)....arylen ] 中的元素都是树中的叶子，因此每个都可看作是只含一个元素的堆。 过程BuildMaxHeap对树中的每一个其他结点都调用一次MaxHeapify. */ void BuildMaxHeap(int ary[], int aryLen) { int i = aryLen; i = i >> 1; int heapSize = aryLen; for ( ; i>=1; i--) { MaxHeapify( ary, i, heapSize ); } } /* 保持最大堆性质 @i: 数组下标从1开始 */ void MaxHeapify( int ary[], int i,int heapSize) { int left = LEFT( i ); int right = RIGHT( i ); int largest = 0; if ( left <= heapSize && ary[left] > ary[i] ) { largest = left; } else { largest = i; } if ( right <= heapSize && ary[right] > ary[largest] ) { largest = right; } if ( largest != i ) { //cout << "ary[" <<i<< "]=" << ary[i] << "ary["<<largest<<"]=" <<ary[largest] << "/t"; int temp = ary[i]; ary[i] = ary[largest]; ary[largest] = temp; MaxHeapify( ary, largest, heapSize); } }

独立的 优先级队列 实现 PriorityQueue.cpp

#include "stdafx.h" #include "HeapHeader.h" int ExtractMax(int ary[], int heapSize) { if( heapSize < 1 ) { cout << "堆已空" << endl; return -1; } int max = ary[1]; ary[1] = ary[heapSize]; heapSize = heapSize - 1; MaxHeapify(ary,1,heapSize); return max; } void IncreaseKey(int ary[], int i, int key) { if ( key < ary[i]) { cout << "新值小于原先的值，输入无效" << endl; return ; } ary[i] = key; int parentIndex = PARENT(i); while( i > 1 && ary[parentIndex] < ary[i] ) { int temp = ary[parentIndex]; ary[parentIndex] = ary[i]; ary[i] = temp; i = parentIndex; parentIndex = PARENT(i); } }  

最后主函数，以及演示函数

// HeapSort.cpp : 定义控制台应用程序的入口点。 // #include "stdafx.h" #include "HeapHeader.h" int _tmain(int argc, _TCHAR* argv[]) { int num = 10; cout << "请输入需要排序数组的长度，数组将随机生成:" <<endl; cin >> num; int* arry = new int[num+1]; int AryLen = num; //srand( (int)time(0) ); for ( int x=1; x<num+1; x++ ) { arry[x] = random(10000); cout << arry[x] << endl; } //对数组采用最大堆排序 HeapSort( arry,AryLen ); cout << endl << "最大堆排序完成后，数组元素为升序 " << endl; for( int i=1; i<num+1; i++ ) { cout << arry[i] << "/t"; } //演示优先队列的操作 /* 1. 对数组构造一个最大堆 2. 演示 ExtractMax操作 3. 演示 IncreaseKey操作 */ //1. 对数组构造一个最大堆 BuildMaxHeap( arry,AryLen ); cout << "after BuildMaxHeap" << endl; for (int j=1; j<=AryLen; j++) { cout << arry[j] << "/t"; } cout << endl; ////2. 演示 Extract-Max操作 int heapSize = AryLen; int max = ExtractMax(arry,heapSize); cout << "The Max int in the heap:" << max << endl; //3. 演示 IncreaseKey操作 需要注释掉第2个演示 int index; cout << "请输入需要修改元素的下标，从1开始:" <<endl; cin >> index; int value; cout << "请输入需要修改元素后的值:" <<endl; cin >> value; IncreaseKey( arry, index, value ); for (int j=1; j<=AryLen; j++) { cout << arry[j] << "/t"; } cout << endl; delete[] arry; system("pause"); return 0; }