堆实现最优队列

来源：互联网发布：淘宝网长袖女t恤编辑：程序博客网时间：2024/06/03 16:44

最优队列就是靠堆实现的，普通的队列是一种先进先出的数据结构，元素在队列尾追加，而从队列头删除。在优先队列中，元素被赋予优先级。当访问元素时，具有最高优先级的元素最先删除。优先队列具有最高级先出（largest-in，first-out）的行为特征。也就最优队列可以保证队头一定是有限度最大的元素。一个优先队列一般满足以下几个操作：

INSERT(S,x)：把元素x插入集合S中

MAXIMUM(S)：返回S中具有最大关键字的元素

EXTRACT-MAX(S)：去掉并返回S中具有最大关键字的元素

INCREASE-KEY(S,x,k)：将元素x的关键字增加到k，这里假设k的值不小于x的关键字值

#include<iostream>#include<algorithm>#define maxsize 5000using namespace std;int heapsize;int HeapMaximum(int a[])//返回优先队列中关键字最大的元素{return a[1];}void MaxHeapify(int a[], int i)//维护最大堆{int left = 2 * i;int right = 2 * i + 1;int largest;if (left<=heapsize&&a[i] < a[left])largest = left;elselargest = i;if (right<=heapsize&&a[largest] < a[right])largest = right;if (largest != i){swap(a[i], a[largest]);MaxHeapify(a,largest);}}int HeapExtractMax(int a[])//去掉并返回关键字最大的元素{if (heapsize < 1)cout << "error:heap underflow" << endl;int max = a[1];a[1] = a[heapsize];heapsize--;MaxHeapify(a, 1);return max;}void HeapIncreaseKey(int a[], int i, int key)//将元素x的关键字增加为key，这里假设key的值不小于原值{if (key < a[i])cout << "error:new key is smaller than current key" << endl;a[i] = key;while (i > 1 && a[i / 2] < a[i]){swap(a[i], a[i / 2]);i = i / 2;}}void MaxHeapInsert(int a[], int key)//往优先队列中插入一个关键字为key的元素{heapsize++;a[heapsize] = -0xfffffff;//先增加一个关键字为负无穷的叶节点HeapIncreaseKey(a, heapsize, key);}int main(){int n;int key[maxsize],heap[maxsize];cin >> n;heapsize = 0;for (int i = 1; i <= n; i++){cin >> key[i];MaxHeapInsert(heap, key[i]);}cout << "max is : " << HeapMaximum(heap) << endl;cout << "heapsize is : " << heapsize << endl;cout << "drop an item and then the max is : " << HeapExtractMax(heap) << endl;cout << "heapsize is : " << heapsize << endl;for (int i = 1; i <= heapsize; i++)cout << heap[i] << " ";cout << endl;cout << "change the third item's key" << endl;HeapIncreaseKey(heap, 3, 100);for (int i = 1; i <= heapsize; i++)cout << heap[i] << " ";cout << endl;cout << "max is : " << HeapMaximum(heap) << endl;return 0;}

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