快速排序
排序的分类
1.快速排序详解
1.1 快速排序
基础版本:
/** * ----------------------------------------------------------------- * Copyright (c) 2013 crazyacking.All rights reserved. * ----------------------------------------------------------------- * Author: crazyacking */ #include <queue> #include <cstdio> #include <set> #include <string> #include <stack> #include <cmath> #include <climits> #include <map> #include <cstdlib> #include <iostream> #include <vector> #include <algorithm> #include <cstring> using namespace std; typedef long long(LL); typedef unsigned long long(ULL); const double eps(1e-8); class Solution { public: void QuickSort(vector<int>& ve) // 第一层函数:外包函数 { QSort(ve,0,ve.size()-1); } void QSort(vector<int>& ve,int low,int high) //第二层函数:递归函数(实现分割数组的作用) { if(low<high) { int pos=partition(ve,low,high); QSort(ve,low,pos-1); QSort(ve,pos+1,high); } } int partition(vector<int>& ve,int low,int high) // 第三层函数:有序函数(交换数据,使ve[low~high]有序,并返回中间位置) { int val=ve[low]; while(low<high) { while(low<high && ve[high]>=val) --high; swap(ve[low],ve[high]); while(low<high && ve[low]<=val) ++low; swap(ve[low],ve[high]); } return low; } }; int main() { int n; while(cin>>n) { vector<int> ve(n); for(int i=0;i<n;++i) cin>>ve[i]; Solution solution; solution.QuickSort(ve); for(auto ptr:ve) cout<<ptr<<" "; cout<<endl; } return 0; } /* */
优化1:三数取中法(尽量使选取的基准数的值位于中间,减少交换次数)
/** * ----------------------------------------------------------------- * Copyright (c) 2013 crazyacking.All rights reserved. * ----------------------------------------------------------------- * Author: crazyacking */ #include <queue> #include <cstdio> #include <set> #include <string> #include <stack> #include <cmath> #include <climits> #include <map> #include <cstdlib> #include <iostream> #include <vector> #include <algorithm> #include <cstring> using namespace std; typedef long long(LL); typedef unsigned long long(ULL); const double eps(1e-8); class Solution { public: void QuickSort(vector<int>& ve) // 第一层函数:外包函数 { QSort(ve,0,ve.size()-1); } void QSort(vector<int>& ve,int low,int high) //第二层函数:递归函数(实现分割数组的作用) { if(low<high) { int pos=partition(ve,low,high); QSort(ve,low,pos-1); QSort(ve,pos+1,high); } } int partition(vector<int>& ve,int low,int high) // 第三层函数:有序函数(交换数据,使ve[low~high]有序,并返回中间位置) { //****** // 优化1:三数取中法: // 选择ve[0],ve[middle],ve[end]三个位置的数,取大小在中间的数来作为val int mid=(low+high)>>1; if(ve[high]<ve[low]) swap(ve[high],ve[low]); if(ve[high]<ve[mid]) swap(ve[high],ve[mid]); if(ve[low]<ve[mid]) swap(ve[low],ve[mid]); int val=ve[low]; while(low<high) { while(low<high && ve[high]>=val) --high; swap(ve[low],ve[high]); while(low<high && ve[low]<=val) ++low; swap(ve[low],ve[high]); } return low; } }; int main() { int n; while(cin>>n) { vector<int> ve(n); for(int i=0;i<n;++i) cin>>ve[i]; Solution solution; solution.QuickSort(ve); for(auto ptr:ve) cout<<ptr<<" "; cout<<endl; } return 0; } /* */
优化2:在排序函数中,直接改变比较的基数,减少交换次数
/** * ----------------------------------------------------------------- * Copyright (c) 2013 crazyacking.All rights reserved. * ----------------------------------------------------------------- * Author: crazyacking */ #include <queue> #include <cstdio> #include <set> #include <string> #include <stack> #include <cmath> #include <climits> #include <map> #include <cstdlib> #include <iostream> #include <vector> #include <algorithm> #include <cstring> using namespace std; typedef long long(LL); typedef unsigned long long(ULL); const double eps(1e-8); class Solution { public: void QuickSort(vector<int>& ve) // 第一层函数:外包函数 { QSort(ve,0,ve.size()-1); } void QSort(vector<int>& ve,int low,int high) //第二层函数:递归函数(实现分割数组的作用) { if(low<high) { int pos=partition(ve,low,high); QSort(ve,low,pos-1); QSort(ve,pos+1,high); } } int partition(vector<int>& ve,int low,int high) // 第三层函数:有序函数(交换数据,使ve[low~high]有序,并返回中间位置) { //****** // 优化2:直接改变ve[low]的中间运行值,减少交换次数: int mid=(low+high)>>1; if(ve[high]<ve[low]) swap(ve[high],ve[low]); if(ve[high]<ve[mid]) swap(ve[high],ve[mid]); if(ve[low]<ve[mid]) swap(ve[low],ve[mid]); int val=ve[low]; while(low<high) { while(low<high && ve[high]>=val) --high; ve[low]=ve[high]; swap(ve[low],ve[high]); while(low<high && ve[low]<=val) ++low; ve[high]=ve[low]; } //*** 还原 ve[low]=val; return low; } }; int main() { int n; while(cin>>n) { vector<int> ve(n); for(int i=0;i<n;++i) cin>>ve[i]; Solution solution; solution.QuickSort(ve); for(auto ptr:ve) cout<<ptr<<" "; cout<<endl; } return 0; } /* */
其他优化方法:
1.数组长度小时,使用插入排序.因为对于小数据而言,插入排序的性能更好.
2.将递归写成尾递归的形式,节约栈空间.
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