算法分治策略

1、實(shí)驗(yàn)報(bào)告（2016/2017學(xué)年第二學(xué)期）課程名稱(chēng)算法分析與設(shè)計(jì)實(shí)驗(yàn)名稱(chēng)分治策略實(shí)驗(yàn)時(shí)間2017年3月30日指導(dǎo)單位計(jì)算機(jī)學(xué)院軟件工程系指導(dǎo)教師張怡婷學(xué)生姓名霍淇濱班級(jí)學(xué)號(hào)學(xué)院（系）計(jì)算機(jī)學(xué)院專(zhuān) 業(yè)軟件工程實(shí)驗(yàn)報(bào)告實(shí)驗(yàn)名稱(chēng)分治策略指導(dǎo)教師張怡婷實(shí)驗(yàn)類(lèi)型驗(yàn)證型（第4個(gè)實(shí)驗(yàn)密 碼算法是“設(shè)計(jì)型”）實(shí)驗(yàn)學(xué)時(shí)2實(shí)驗(yàn)時(shí)間2017-3-30一、實(shí)驗(yàn)?zāi)康暮腿蝿?wù)理解分治法的算法思想，閱讀實(shí)現(xiàn)書(shū)上已有的部分程序代碼弁完善程序，加深對(duì)分治法的算法原理及實(shí)現(xiàn)過(guò)程的理解二、實(shí)驗(yàn)環(huán)境（實(shí)驗(yàn)設(shè)備）Visual Studio 2015三、實(shí)驗(yàn)原理及內(nèi)容（包括操作過(guò)程、結(jié)果分析等）一、用分治法實(shí)現(xiàn)一組無(wú)序序列的兩路合并排序和

2、快速排序。要求清楚合并排序及快速排序的基本原理，編程實(shí)現(xiàn)分別用這兩種方法將輸入的一組無(wú)序序列排序?yàn)橛行蛐蛄泻筝敵?。?biāo)頭.h#include<iostream> using namespace std;class SortableList public:SortableList(int mSize);SortableList();void Input();/ 輸入數(shù)組void Output。;/輸出數(shù)組void MergeSort();/兩路合并排序void QuickSort();/快速排序private:int *l;/數(shù)組指針int maxSize;/ 數(shù)組最大長(zhǎng)度int n;

3、/ 數(shù)組已有元素個(gè)數(shù)void MergeSort(int left, int right);void Merge(int left, int mid, int right);void Swap(int i, int j);/交換函數(shù)void QuickSort(int left, int right);int Parition(int left, int right);/分割函數(shù);SortableList:SortableList(int mSize) maxSize = mSize;l = new intmaxSize;n = 0;SortableList:SortableList() de

4、lete口l; void SortableList:Input() cout << "請(qǐng)輸入待排序的數(shù)組n"for (int i = 0; i < maxSize; i+) cin >> li;if (li = -1)break;n+;void SortableList:Output()for (int i = 0; i < n; i+) cout << li << ""void SortableList:MergeSort() MergeSort(0, n - 1); void Sortabl

5、eList:QuickSort() QuickSort(0, n - 1); void SortableList:MergeSort(int left, int right)if (left < right)int mid = (left + right) / 2;MergeSort(left, mid);MergeSort(mid + 1, right);Merge(left, mid, right);void SortableList:Merge(int left, int mid, int right)int *temp = new intright - left + 1;int

6、i = left, j = mid + 1, k = 0;while (i <= mid) && (j <= right)if (li <=加 tempk+ = li+;else tempk+ = lj+;while (i <= mid) tempk+ = li+;while (j <= right) tempk+ = lj+;for (i = 0, k = left; k <= right;)lk+ = tempi+; void SortableList:Swap(int i, int j)int c = li;li = lj;lj = c

7、;void SortableList:QuickSort(int left, int right)if (left < right)int j = Parition(left, right);QuickSort(left, j - 1);QuickSort(j + 1, right);int SortableList:Parition(int left, int right)int i = left, j = right + 1;dodo i+; while (li < lleft);do j-; while (lj > lleft);if (i < j) Swap(i

8、, j); while (i < j);Swap(left, j);return j;源.app#include<iostream>#include"標(biāo)頭.h"using namespace std;void main()int n = 10;SortableList my1(n);SortableList my2(n);my1.Input();my2.Input();my1.MergeSort();my2.QuickSort();my1.Output();my2.Output();二、采用基于“五元中值組取中值分割法” (median-of-median

9、-of-fivepartitioning )的線性時(shí)間選擇算法，找出N個(gè)元素集合S中的第k個(gè)最小的元素，使其在線性時(shí)間內(nèi)解決。標(biāo)頭.h#include<iostream>using namespace std;enum ResultCode OutOfBounds,Success;class SortableListpublic:SortableList(int mSize);SortableList();void Input();void Output。；ResultCode Select(int &x, int k); private:int *l;int maxSiz

10、e;int n;void Swap(int i, int j);void InsertSort(int left, int right);int Partition(int left, int right);int Select(int k,int left,int right,int r);SortableList:SortableList(int mSize)maxSize = mSize;l = new intmaxSize;n = 0;SortableList:SortableList() deletel; void SortableList:Input()cout <<

11、"請(qǐng)輸入帶排序的數(shù)組n"for (int i = 0; i < maxSize; i+)cin >> li;if (li = -1) break;n+;void SortableList:Output()for (int i = 0; i < n; i+) cout << li << ""void SortableList:Swap(int i, int j)int c = li;li=皿；皿=c;int SortableList:Partition(int left, int right)int i =

12、left, j = right + 1;dodo i+; while (li < lleft);do j-; while (lj > lleft);if (i < j) Swap(i, j)； while (i < j);Swap(left, j);return j;ResultCode SortableList:Select(int &x, int k) if (n <= 0 | k > n | k <= 0)return OutOfBounds;int j = Select(k, 0,n - 1,5);x =皿；return Success

13、;int SortableList:Select(int k, int left, int right, int r) int n = right - left + 1;if (n <= r)/若問(wèn)題足夠小，使用直接插入排序InsertSort(left, right);return left + k - 1; / 取其中的第k小元素，其下標(biāo)為left+k-1for (int i = 1; i <= n / r; i+)InsertSort(left + (i - 1)*r, left + i*r - 1); /二次取中規(guī)則求每組的中間值Swap(left + i - 1, lef

14、t + (i - 1)*r + (int)ceil(double)r / 2) - 1); /將每組的中間值交換到子表前部集中存放 /求二次中間值，其下標(biāo)為j int j = Select(int)ceil(double)n / r / 2), left, left + (n / r) - 1, r);Swap(left, j);/二次中間值為樞紐元，并換至left處j = Partition(left, right); /對(duì)表(子表)進(jìn)行分劃操作if (k = j - left + 1)return j; / 返回第k小元素下標(biāo)else if (k<j - left + 1)return Select(k, left, j - 1, r);/在左子表求第 k小元素else return Select(k - (j - left + 1), j + 1, right, r); /在右子表求第 k-(j-left+1) 小元素void SortableList:InsertSort(int left, int right) for (int i = left+1; i <= right; i+) int j = i;int temp = li;while (j > left && temp < lj - 1)lj = lj - 1;