堆排序基本概念
堆是一种数据结构，它是将一些数据放在物理数据结构：数组或者vector中；逻辑数据结构是完全二叉树。
如果根节点的值大于两个子节点值，就是大根堆；
如果根节点的值小于两个子节点值，就是小根堆。
用堆这种数据结构来实现排序，就是堆排序。
该算法的操作主要有
minheapify：最小堆处理，复杂度是O(logN)
find_min：找到最小值，复杂度是O(1)
delete_min：删除最小值节点，及根节点，复杂度是O(logN)
build_minheap：建立最小堆，复杂度是O(N)
minheap_sort：最小堆排序，复杂度是O(NlogN)
算法导论中该算法在minheapify时用的是递归，如下程序用的是迭代处理，效率会更高一些；
如下程序实现的是小根堆
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 | #include<iostream>#include<cstdio>#include<stdlib.h>#include<assert.h> #include<map>#include<vector>using namespace std;void minheapify(vector<double>& minheap,int pos){ while(1) { double temp=minheap[pos]; int loc=pos; if((pos*2 <= minheap.size()-1) && minheap[pos]>minheap[pos*2]){ loc=pos*2; temp=minheap[pos*2]; } if((pos*2+1 <= minheap.size()-1) && temp>minheap[pos*2+1]){ loc=pos*2+1; temp=minheap[pos*2+1]; } if(loc!=pos){ minheap[loc]=minheap[pos]; minheap[pos]=temp; pos=loc; continue; } else if(loc==pos) break; }}void build_minheap(vector<double>& minheap, double* a, int n){ for(int i=0;i<n;i++) minheap.push_back(a[i]); for(int i=(minheap.size()-1)/2;i>=1;i--) minheapify(minheap,i);}double find_min(vector<double>& minheap){ return minheap[1];}void delete_min(vector<double>& minheap){ minheap[1]=minheap[minheap.size()-1]; minheap.erase(minheap.end()-1); minheapify(minheap,1);}vector<double> minheap_sort(vector<double>& minheap){ vector<double> result; while(minheap.size()>1){ result.push_back(find_min(minheap)); delete_min(minheap); } return result;}int main(){ vector<double> minheap; minheap.push_back(-1); int n=5; double a[5]={100.1,20,3,5,2}; build_minheap(minheap,a,n); for(int i=0;i<minheap.size();i++) cout<<minheap[i]<<" "; cout<<endl<<"build complete"<<endl; vector<double> result; result=minheap_sort(minheap); for(int i=0;i<result.size();i++) cout<<result[i]<<" "; getchar(); return 0; } |