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【算法导论】--分治策略Strassen算法（运用下标…

2019-08-16 07:57:54来源：博客园阅读 ()

【算法导论】--分治策略Strassen算法（运用下标运算）【c++】

由于偷懒不想用泛型，所以直接用了整型来写了一份

①首先你得有一个矩阵的class Matrix

②Matrix为了方便用下标进行运算，

Matrix的结构如图：(我知道我的字丑。。。)

Matrix.h代码如下：(个人并不喜欢把代码全写在一块，对于阅读者是相当巨大的负担，其实自己受不了（逃）)

 1 #pragma once
 2 #include<vector>
 3 using namespace std;
 4 class Matrix
 5 {
 6 public:
 7     vector<vector<int>> nums;
 8     int x0, y0;
 9 
10     int size;
11     Matrix();
12     ~Matrix();
13     Matrix(int size, int x0, int y0);
14     Matrix(Matrix input, int x0, int y0, int size);
15     Matrix(vector<vector<int>>input);
16     void Display();
17     static void MatrixMultiInit(Matrix &A, Matrix &B);
18     static Matrix MatrixMulti(Matrix A, Matrix B);
19     static Matrix MatrixAdd(Matrix A, Matrix B);
20     static Matrix MatrixSub(Matrix A, Matrix B);
21 };

Matrix.cpp对类的实现

一，构造，析构函数

 1 Matrix::Matrix()
 2 {
 3 }
 4 
 5 
 6 Matrix::~Matrix()
 7 {
 8 }
 9 
10 Matrix::Matrix(int size, int x0, int y0)
11 {
12     vector<vector<int>> temp(size, *new vector<int>(size));
13     for (int i = 0; i < size; i++)
14         for (int j = 0; j < size; j++)
15             temp[i][j] = 0;
16     this->nums = temp;
17     this->x0 = x0;
18     this->y0 = y0;
19     this->size = size;
20 
21 }
22 
23 Matrix::Matrix(Matrix input, int x0, int y0, int size)
24 {
25     this->nums = input.nums;
26     this->x0 = x0;
27     this->y0 = y0;
28     this->size = size;
29 }
30 
31 Matrix::Matrix(vector<vector<int>> input)
32 {
33     this->nums = input;
34     this->x0 = 0;
35     this->y0 = 0;
36     this->size = input.size();
37 }

二，A+B，A-B实现

 1 Matrix Matrix::MatrixAdd(Matrix A, Matrix B)
 2 {
 3     Matrix result(A.size, 0, 0);
 4     for (int i = 0; i < result.nums.size(); i++)
 5         for (int j = 0; j < result.nums.size(); j++)
 6             result.nums[i][j] = A.nums[A.x0 + i][A.y0 + j] + B.nums[B.x0 + i][B.y0 + j];
 7     return result;
 8 }
 9 
10 Matrix Matrix::MatrixSub(Matrix A, Matrix B)
11 {
12 
13     Matrix result(A.size, 0, 0);
14     for (int i = 0; i < result.nums.size(); i++)
15         for (int j = 0; j < result.nums.size(); j++)
16             result.nums[i][j] = A.nums[A.x0 + i][A.y0 + j] - B.nums[B.x0 + i][B.y0 + j];
17     return result;
18 }

三，A*B的实现

 1 Matrix Matrix::MatrixMulti(Matrix A, Matrix B)
 2 {
 3     int n = A.size;
 4     int halfsize =n / 2;
 5     Matrix result(n, 0, 0);
 6     if (n == 1)
 7         result.nums[0][0] = A.nums[A.x0][A.y0] * B.nums[B.x0][B.y0];
 8     else
 9     {
10         Matrix tempS[10];
11         for (int i = 0; i < 10; i++)
12         {
13             tempS[i] = *new Matrix(halfsize, 0, 0);
14         }
15 
16         //00--  A.x0,A.y0,halfsize
17         //01-- A.x0,A.y0+halfsize,halfsize
18         //10--  A.x0+halfsize,A.y0,halfsize
19         //11--    A.x0+halfsize,A.y0+halfsize,halfsize
20                 
21         //00-- B.x0,B.y0,halfsize
22         //01-- B.x0,B.y0+halfsize,halfsize
23         //10-- B.x0+halfsize,B.y0,halfsize
24         //11--    B.x0+halfsize,B.y0+halfsize,halfsize
25         tempS[0] = tempS[0].MatrixSub(*new Matrix(B, B.x0, B.y0 + halfsize, halfsize), *new Matrix(B, B.x0 + halfsize, B.y0 + halfsize, halfsize));//01-11 B
26         tempS[1] = tempS[1].MatrixAdd(*new Matrix(A, A.x0, A.y0, halfsize), *new Matrix(A, A.x0, A.y0 + halfsize, halfsize));//00+01 A
27         tempS[2] = tempS[2].MatrixAdd(*new Matrix(A, A.x0 + halfsize, A.y0, halfsize), *new Matrix(A, A.x0 + halfsize, A.y0 + halfsize, halfsize));//10+11 A
28         tempS[3] = tempS[3].MatrixSub(*new Matrix(B, B.x0 + halfsize, B.y0, halfsize), *new Matrix(B, B.x0, B.y0, halfsize));//10-00 B
29         tempS[4] = tempS[4].MatrixAdd(*new Matrix(A, A.x0, A.y0, halfsize), *new Matrix(A, A.x0 + halfsize, A.y0 + halfsize, halfsize));//00+11 A
30         tempS[5] = tempS[5].MatrixAdd(*new Matrix(B, B.x0, B.y0, halfsize), *new Matrix(B, B.x0 + halfsize, B.y0 + halfsize, halfsize));//00+11 B
31         tempS[6] = tempS[6].MatrixSub(*new Matrix(A, A.x0, A.y0 + halfsize, halfsize), *new Matrix(A, A.x0 + halfsize, A.y0 + halfsize, halfsize));//01-11 A
32         tempS[7] = tempS[7].MatrixAdd(*new Matrix(B, B.x0 + halfsize, B.y0, halfsize), *new Matrix(B, B.x0 + halfsize, B.y0 + halfsize, halfsize));//10+11 B
33         tempS[8] = tempS[8].MatrixSub(*new Matrix(A, A.x0, A.y0, halfsize), *new Matrix(A, A.x0 + halfsize, A.y0, halfsize));//00-10 A
34         tempS[9] = tempS[9].MatrixAdd(*new Matrix(B, B.x0, B.y0, halfsize), *new Matrix(B, B.x0, B.y0 + halfsize, halfsize));//00+01 B
35 
36 
37         Matrix tempP[7];
38         for (int i = 0; i < 7; i++)
39         {
40             tempP[i] = *new Matrix(n / 2, 0, 0);
41         }
42         tempP[0] = tempP[0].MatrixMulti(*new Matrix(A, A.x0, A.y0, halfsize), *new Matrix(tempS[0], 0, 0, halfsize));
43         tempP[1] = tempP[1].MatrixMulti(*new Matrix(tempS[1], 0, 0,halfsize), *new Matrix(B, B.x0 + halfsize, B.y0 + halfsize, halfsize));
44         tempP[2] = tempP[2].MatrixMulti(*new Matrix(tempS[2], 0, 0, halfsize), *new Matrix(B, B.x0, B.y0, halfsize));
45         tempP[3] = tempP[3].MatrixMulti(*new Matrix(A, A.x0 + halfsize, A.y0 + halfsize, halfsize), *new Matrix(tempS[3], 0, 0, halfsize));
46         tempP[4] = tempP[4].MatrixMulti(*new Matrix(tempS[4], 0, 0, halfsize), *new Matrix(tempS[5], 0, 0, halfsize));
47         tempP[5] = tempP[5].MatrixMulti(*new Matrix(tempS[6], 0, 0, halfsize), *new Matrix(tempS[7], 0, 0, halfsize));
48         tempP[6] = tempP[6].MatrixMulti(*new Matrix(tempS[8], 0, 0, halfsize), *new Matrix(tempS[9], 0, 0, halfsize));
49 
50 
51 
52         Matrix result00 = result00.MatrixAdd(tempP[4], tempP[3]);
53         result00 = result00.MatrixSub(result00, tempP[1]);
54         result00 = result00.MatrixAdd(result00, tempP[5]);
55         Matrix result01 = result01.MatrixAdd(tempP[0], tempP[1]);
56         Matrix result10 = result10.MatrixAdd(tempP[2], tempP[3]);
57         Matrix result11 = result11.MatrixAdd(tempP[4], tempP[0]);
58         result11 = result11.MatrixSub(result11, tempP[2]);
59         result11 = result11.MatrixSub(result11, tempP[6]);
60 
61         if (n == 3) {
62         for(int i=0;i<n/2+1;i++)
63             for (int j = 0; j < n / 2 + 1; j++) {
64             
65             result.nums[i][j]= result00.nums[i][j];
66             result.nums[i][j+n/2+1] = result01.nums[i][j];
67             result.nums[i+n/2+1][j] = result10.nums[i][j];
68             result.nums[i+n/2+1][j+n/2+1] = result11.nums[i][j];
69             }
70         }
71 
72         for(int i=0;i<n/2;i++)
73             for (int j = 0; j < n / 2; j++) {
74             
75             result.nums[i][j]= result00.nums[i][j];
76             result.nums[i][j+n/2] = result01.nums[i][j];
77             result.nums[i+n/2][j] = result10.nums[i][j];
78             result.nums[i+n/2][j+n/2] = result11.nums[i][j];
79             }
80 
81     }
82     return result;
83 }

四，防止size%2！=0的处理函数（即矩阵的行列数为奇数）

 1 void Matrix::MatrixMultiInit(Matrix &A, Matrix &B) {
 2 
 3     if (A.nums.size() % 2 != 0)
 4     {
 5         for (int i = 0; i < A.nums.size(); i++)
 6             A.nums[i].push_back(0);
 7         for (int i = 0; i < B.nums.size(); i++)
 8             B.nums[i].push_back(0);
 9         A.nums.push_back(*new vector<int>(A.nums[0].size(), 0));
10         B.nums.push_back(*new vector<int>(B.nums[0].size(), 0));
11         A.size++;
12         B.size++;
13     }
14 }

五，输出函数（这个读者随意）

 1 void Matrix::Display()
 2 {
 3     for (int i = 0; i < this->nums.size(); i++) {
 4 
 5         cout << "||";
 6         for (int j = 0; j < this->nums[i].size(); j++) {
 7             cout << this->nums[i][j] << " ";
 8         }
 9         cout << "||" << endl;
10 
11     }
12 }

六，测试函数

 1 #include <iostream>
 2 #include"Matrix.h"
 3 int main()
 4 {
 5     vector<vector<int>> input = { 
 6         {1,2,3},
 7         {1,2,3},
 8         {1,1,1},
 9     };
10     Matrix test0 = * new Matrix(input);
11     Matrix test1 = * new Matrix(input);
12     Matrix test2;
13     test2.MatrixMultiInit(test0, test1);
14     test2= test2.MatrixMulti(test0, test1);
15     test2.Display();
16 
17 }