数据结构课程设计数组的存储格式转换

1、数据结构课 程 设 计 报 告 书题 目：数组的存储格式转换专 业： 计算机科学与技术班 级：计121学 号：完成时间：一、 问题描述1.1 问题描述根据数组的相关知识，以行列式的方式输入矩阵，进行简单的运算，转置及求逆等过程，然后打印出该矩阵。1.2 基本要求需要按要求输入矩阵，系统会自行运算，然后输出矩阵。二、 概要设计进行运算开始进入程序提示输入的矩阵类型输入选择提示输入矩阵的方式输入选择输出结果操作结束三、 详细设计1.1 函数申明float MatDet(float *p, int n); /求矩阵的行列式float Creat_M(float *p, int m, int n, i

2、nt k); /求矩阵元素A(m, n)的代数余之式void print(float *p, int m,int n); /输出矩阵n*nbool Gauss(float *pSrc, float *pDst, int iRow); /采用部分主元的高斯消去法求方阵A的逆矩阵Bbool Transepose(float *pSrc,float *pSdst, int iRow, int iCol); /求矩阵转置bool MatMultiply(float *pSrc1, float *pSrc2,float *pDst,int iRow, int iCol);/矩阵相乘1.2 主函数floa

3、t *buffer, *p; /定义数组首地址指针变量int row, num; /定义矩阵的行数和矩阵元素个数int i, j;float determ; /定义矩阵的行列式float aNN, bNN;int n;cout << "采用逆矩阵的定义法求矩阵的逆矩阵!n"cout << "请输入矩阵的行数: "cin >> row;num = 2 * row * row;buffer = (float *)calloc(num, sizeof(float); /分配内存单元p = buffer;if (NULL !=

4、 p)for (i = 0; i < row; i+)cout << "Please input the number of " << i+1 << " row: "for (j = 0; j < row; j+)cin >> *p+;elsecout << "Can't distribute memoryn"cout << "The original matrix : n"print(buffer, row); /打印该矩

5、阵determ = MatDet(buffer, row); /求整个矩阵的行列式p = buffer + row * row;if (determ != 0)cout << "The determinant of the matrix is " << determ << endl;for (i = 0; i < row; i+) /求逆矩阵for (j = 0; j < row; j+)*(p+j*row+i) = Creat_M(buffer, i, j, row)/determ;cout << "T

6、he inverse matrix is: " << endl;print(p, row); /打印该矩阵elsecout << "The determinant is 0, and there is no inverse matrix!n"free(buffer); /释放内存空间cout << "采用部分主元的高斯消去法求方阵的逆矩阵!n"cout << "请输入方阵的阶数: "cin >> n;cout << "请输入" <

7、;< n << "阶方阵: n"/输入一个n阶方阵for (i = 0; i < n; i+)for (j = 0; j < n; j+)cin >> aij;/运用高斯消去法求该矩阵的逆矩阵并输出if (Gauss(a, b, n)cout << "该方阵的逆矩阵为: n"for (i = 0; i < n; i+)cout << setw(4);for (j = 0; j < n; j+)cout << bij << setw(10);cout &l

8、t;< endl; return 0;1.3 功能函数int i,m,n;cout << "请输入方阵的行数: "cin >> m;cout << "请输入方阵的列数: "cin >> n;float *a = new floatm*n;cout << "请输入" << m << "*"<< n << "阶方阵: n"/输入一个n阶方阵for (i = 0; i < m*n;

9、i+)cin >> ai;print(a,m,n);cout<<"转置矩阵："<<endl;float *b = new floatn*m;Transepose(a,b,m,n);print(b,n,m);cout<<"矩阵乘积："<<endl;float *c = new floatm*m;MatMultiply(a,b,c,m,n);print(c,m,m);cout<<"矩阵的逆："<<endl;float *d = new floatm*m;G

10、auss(c,d,m);print(d,m,m);cin>>m;delete a;delete b;delete c;delete d;return 0;/-/功能: 求矩阵(n*n)的行列式/入口参数: 矩阵的首地址，矩阵的行数/返回值: 矩阵的行列式值/-float MatDet(float *p, int n)int r, c, m;int lop = 0;float result = 0;float mid = 1;if (n != 1)lop = (n = 2) ? 1 : n; /控制求和循环次数,若为2阶，则循环1次，否则为n次for (m = 0; m < l

11、op; m+)mid = 1; /顺序求和, 主对角线元素相乘之和for (r = 0, c = m; r < n; r+, c+)mid = mid * (*(p+r*n+c%n);result += mid;for (m = 0; m < lop; m+)mid = 1; /逆序相减, 减去次对角线元素乘积for (r = 0, c = n-1-m+n; r < n; r+, c-)mid = mid * (*(p+r*n+c%n);result -= mid;elseresult = *p;return result;/-/功能: 求k*k矩阵中元素A(m, n)的代数

12、余之式/入口参数: k*k矩阵的首地址，矩阵元素A的下标m,n,矩阵行数k/返回值: k*k矩阵中元素A(m, n)的代数余之式/-float Creat_M(float *p, int m, int n, int k)int len;int i, j;float mid_result = 0;int sign = 1;float *p_creat, *p_mid;len = (k-1)*(k-1); /k阶矩阵的代数余之式为k-1阶矩阵p_creat = (float*)calloc(len, sizeof(float); /分配内存单元p_mid = p_creat;for (i = 0;

13、 i < k; i+)for (j = 0; j < k; j+)if (i != m && j != n) /将除第i行和第j列外的所有元素存储到以p_mid为首地址的内存单元*p_mid+ = *(p+i*k+j);sign = (m+n)%2 = 0 ? 1 : -1; /代数余之式前面的正、负号mid_result = (float)sign*MatDet(p_creat, k-1);free(p_creat);return mid_result;/-/功能: 打印n*n矩阵/入口参数: n*n矩阵的首地址,矩阵的行数n/返回值: 无返回值void prin

14、t(float *p, int m, int n)int i, j;for (i = 0; i < m; i+)cout << setw(4);for (j = 0; j < n; j+)cout << setiosflags(ios:right) << *p+ << setw(10);cout << endl;/-/功能: 采用部分主元的高斯消去法求方阵A的逆矩阵B/入口参数: 输入方阵，输出方阵，方阵阶数/返回值: true or false/-四、 运行与测试1.1 进入提示画面1.2 按提示输入后1.3 输出界面五

15、、 总结与体会通过这一次的课程设计，我掌握了另外的一种算法，对矩阵等复杂数据的输入有了更深刻的理解，起初不知道应该以怎样的方式输入矩阵，数据结构这门课程在处理数据信息方面给了我很大的启发，应该以怎样的方式输入数据，处理数据，数据结构都很系统的解释了出来，对我的帮助很大，一开始也没想到自己真的能做出来，后来通过网上的一些成功案例，一步一步的写了出来，在经过调试，验证等一系列操作，终于解决了问题。也增加了自己的信心。六、 附源程序#include <math.h>#include <malloc.h>#include <iomanip>#include <

16、iostream>#define N 10 /定义方阵的最大阶数为10using namespace std;/函数的声明部分float MatDet(float *p, int n); /求矩阵的行列式float Creat_M(float *p, int m, int n, int k); /求矩阵元素A(m, n)的代数余之式void print(float *p, int m,int n); /输出矩阵n*nbool Gauss(float *pSrc, float *pDst, int iRow); /采用部分主元的高斯消去法求方阵A的逆矩阵Bbool Transepose(f

17、loat *pSrc,float *pSdst, int iRow, int iCol); /求矩阵转置bool MatMultiply(float *pSrc1, float *pSrc2,float *pDst,int iRow, int iCol);/矩阵相乘int main()/*float *buffer, *p; /定义数组首地址指针变量int row, num; /定义矩阵的行数和矩阵元素个数int i, j;float determ; /定义矩阵的行列式float aNN, bNN;int n;cout << "采用逆矩阵的定义法求矩阵的逆矩阵!n&quo

18、t;cout << "请输入矩阵的行数: "cin >> row;num = 2 * row * row;buffer = (float *)calloc(num, sizeof(float); /分配内存单元p = buffer;if (NULL != p)for (i = 0; i < row; i+)cout << "Please input the number of " << i+1 << " row: "for (j = 0; j < row; j+)

19、cin >> *p+;elsecout << "Can't distribute memoryn"cout << "The original matrix : n"print(buffer, row); /打印该矩阵determ = MatDet(buffer, row); /求整个矩阵的行列式p = buffer + row * row;if (determ != 0)cout << "The determinant of the matrix is " << de

20、term << endl;for (i = 0; i < row; i+) /求逆矩阵for (j = 0; j < row; j+)*(p+j*row+i) = Creat_M(buffer, i, j, row)/determ;cout << "The inverse matrix is: " << endl;print(p, row); /打印该矩阵elsecout << "The determinant is 0, and there is no inverse matrix!n"fre

21、e(buffer); /释放内存空间cout << "采用部分主元的高斯消去法求方阵的逆矩阵!n"cout << "请输入方阵的阶数: "cin >> n;cout << "请输入" << n << "阶方阵: n"/输入一个n阶方阵for (i = 0; i < n; i+)for (j = 0; j < n; j+)cin >> aij;/运用高斯消去法求该矩阵的逆矩阵并输出if (Gauss(a, b, n)cou

22、t << "该方阵的逆矩阵为: n"for (i = 0; i < n; i+)cout << setw(4);for (j = 0; j < n; j+)cout << bij << setw(10);cout << endl; return 0;*/int i,m,n;cout << "请输入方阵的行数: "cin >> m;cout << "请输入方阵的列数: "cin >> n;float *a = new

23、floatm*n;cout << "请输入" << m << "*"<< n << "阶方阵: n"/输入一个n阶方阵for (i = 0; i < m*n; i+)cin >> ai;print(a,m,n);cout<<"转置矩阵："<<endl;float *b = new floatn*m;Transepose(a,b,m,n);print(b,n,m);cout<<"矩阵乘积：&qu

24、ot;<<endl;float *c = new floatm*m;MatMultiply(a,b,c,m,n);print(c,m,m);cout<<"矩阵的逆："<<endl;float *d = new floatm*m;Gauss(c,d,m);print(d,m,m);cin>>m;delete a;delete b;delete c;delete d;return 0;/-/功能: 求矩阵(n*n)的行列式/入口参数: 矩阵的首地址，矩阵的行数/返回值: 矩阵的行列式值/-float MatDet(float *p

25、, int n)int r, c, m;int lop = 0;float result = 0;float mid = 1;if (n != 1)lop = (n = 2) ? 1 : n; /控制求和循环次数,若为2阶，则循环1次，否则为n次for (m = 0; m < lop; m+)mid = 1; /顺序求和, 主对角线元素相乘之和for (r = 0, c = m; r < n; r+, c+)mid = mid * (*(p+r*n+c%n);result += mid;for (m = 0; m < lop; m+)mid = 1; /逆序相减, 减去次对角

26、线元素乘积for (r = 0, c = n-1-m+n; r < n; r+, c-)mid = mid * (*(p+r*n+c%n);result -= mid;elseresult = *p;return result;/-/功能: 求k*k矩阵中元素A(m, n)的代数余之式/入口参数: k*k矩阵的首地址，矩阵元素A的下标m,n,矩阵行数k/返回值: k*k矩阵中元素A(m, n)的代数余之式/-float Creat_M(float *p, int m, int n, int k)int len;int i, j;float mid_result = 0;int sign

27、= 1;float *p_creat, *p_mid;len = (k-1)*(k-1); /k阶矩阵的代数余之式为k-1阶矩阵p_creat = (float*)calloc(len, sizeof(float); /分配内存单元p_mid = p_creat;for (i = 0; i < k; i+)for (j = 0; j < k; j+)if (i != m && j != n) /将除第i行和第j列外的所有元素存储到以p_mid为首地址的内存单元*p_mid+ = *(p+i*k+j);sign = (m+n)%2 = 0 ? 1 : -1; /代数余

28、之式前面的正、负号mid_result = (float)sign*MatDet(p_creat, k-1);free(p_creat);return mid_result;/-/功能: 打印n*n矩阵/入口参数: n*n矩阵的首地址,矩阵的行数n/返回值: 无返回值void print(float *p, int m, int n)int i, j;for (i = 0; i < m; i+)cout << setw(4);for (j = 0; j < n; j+)cout << setiosflags(ios:right) << *p+ &

29、lt;< setw(10);cout << endl;/-/功能: 采用部分主元的高斯消去法求方阵A的逆矩阵B/入口参数: 输入方阵，输出方阵，方阵阶数/返回值: true or false/-bool Gauss(float *pSrc, float *pDst, int iRow)int i, j, k;int n = iRow;float max, temp;float tNN; /临时矩阵/将A矩阵存放在临时矩阵tnn中for (i = 0; i < n; i+) for (j = 0; j < n; j+)tij = pSrci*iRow+j;/初始化B

30、矩阵为单位阵for (i = 0; i < n; i+) for (j = 0; j < n; j+)pDsti*iRow+j = (i = j) ? (float)1 : 0;for (i = 0; i < n; i+)/寻找主元max = tii;k = i;for (j = i+1; j < n; j+)if (fabs(tji) > fabs(max)max = tji;k = j;/如果主元所在行不是第i行，进行行交换if (k != i)for (j = 0; j < n; j+)temp = tij;tij = tkj;tkj = temp;/B伴随交换temp = pDsti*iRow+j;pDsti*iRow+j = pDstk