數(shù)據(jù)結(jié)構(gòu)課程設(shè)計數(shù)組的存儲格式轉(zhuǎn)換

1、數(shù)據(jù)結(jié)構(gòu)課 程 設(shè) 計 報 告 書題 目：數(shù)組的存儲格式轉(zhuǎn)換專 業(yè)： 計算機科學(xué)與技術(shù)班 級：計121學(xué) 號：完成時間：一、 問題描述1.1 問題描述根據(jù)數(shù)組的相關(guān)知識，以行列式的方式輸入矩陣，進行簡單的運算，轉(zhuǎn)置及求逆等過程，然后打印出該矩陣。1.2 基本要求需要按要求輸入矩陣，系統(tǒng)會自行運算，然后輸出矩陣。二、 概要設(shè)計進行運算開始進入程序提示輸入的矩陣類型輸入選擇提示輸入矩陣的方式輸入選擇輸出結(jié)果操作結(jié)束三、 詳細設(shè)計1.1 函數(shù)申明float MatDet(float *p, int n); /求矩陣的行列式float Creat_M(float *p, int m, int n, i

2、nt k); /求矩陣元素A(m, n)的代數(shù)余之式void print(float *p, int m,int n); /輸出矩陣n*nbool Gauss(float *pSrc, float *pDst, int iRow); /采用部分主元的高斯消去法求方陣A的逆矩陣Bbool Transepose(float *pSrc,float *pSdst, int iRow, int iCol); /求矩陣轉(zhuǎn)置bool MatMultiply(float *pSrc1, float *pSrc2,float *pDst,int iRow, int iCol);/矩陣相乘1.2 主函數(shù)floa

3、t *buffer, *p; /定義數(shù)組首地址指針變量int row, num; /定義矩陣的行數(shù)和矩陣元素個數(shù)int i, j;float determ; /定義矩陣的行列式float aNN, bNN;int n;cout << "采用逆矩陣的定義法求矩陣的逆矩陣!n"cout << "請輸入矩陣的行數(shù): "cin >> row;num = 2 * row * row;buffer = (float *)calloc(num, sizeof(float); /分配內(nèi)存單元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); /打印該矩

5、陣determ = MatDet(buffer, row); /求整個矩陣的行列式p = buffer + row * row;if (determ != 0)cout << "The determinant of the matrix is " << determ << endl;for (i = 0; i < row; i+) /求逆矩陣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); /打印該矩陣elsecout << "The determinant is 0, and there is no inverse matrix!n"free(buffer); /釋放內(nèi)存空間cout << "采用部分主元的高斯消去法求方陣的逆矩陣!n"cout << "請輸入方陣的階數(shù): "cin >> n;cout << "請輸入" <

7、;< n << "階方陣: n"/輸入一個n階方陣for (i = 0; i < n; i+)for (j = 0; j < n; j+)cin >> aij;/運用高斯消去法求該矩陣的逆矩陣并輸出if (Gauss(a, b, n)cout << "該方陣的逆矩陣為: 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 功能函數(shù)int i,m,n;cout << "請輸入方陣的行數(shù): "cin >> m;cout << "請輸入方陣的列數(shù): "cin >> n;float *a = new floatm*n;cout << "請輸入" << m << "*"<< n << "階方陣: n"/輸入一個n階方陣for (i = 0; i < m*n;

9、i+)cin >> ai;print(a,m,n);cout<<"轉(zhuǎn)置矩陣："<<endl;float *b = new floatn*m;Transepose(a,b,m,n);print(b,n,m);cout<<"矩陣乘積："<<endl;float *c = new floatm*m;MatMultiply(a,b,c,m,n);print(c,m,m);cout<<"矩陣的逆："<<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: 求矩陣(n*n)的行列式/入口參數(shù): 矩陣的首地址，矩陣的行數(shù)/返回值: 矩陣的行列式值/-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; /控制求和循環(huán)次數(shù),若為2階，則循環(huán)1次，否則為n次for (m = 0; m < l

11、op; m+)mid = 1; /順序求和, 主對角線元素相乘之和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; /逆序相減, 減去次對角線元素乘積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矩陣中元素A(m, n)的代數(shù)

12、余之式/入口參數(shù): k*k矩陣的首地址，矩陣元素A的下標m,n,矩陣行數(shù)k/返回值: k*k矩陣中元素A(m, n)的代數(shù)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階矩陣的代數(shù)余之式為k-1階矩陣p_creat = (float*)calloc(len, sizeof(float); /分配內(nèi)存單元p_mid = p_creat;for (i = 0;

13、 i < k; i+)for (j = 0; j < k; j+)if (i != m && j != n) /將除第i行和第j列外的所有元素存儲到以p_mid為首地址的內(nèi)存單元*p_mid+ = *(p+i*k+j);sign = (m+n)%2 = 0 ? 1 : -1; /代數(shù)余之式前面的正、負號mid_result = (float)sign*MatDet(p_creat, k-1);free(p_creat);return mid_result;/-/功能: 打印n*n矩陣/入口參數(shù): n*n矩陣的首地址,矩陣的行數(shù)n/返回值: 無返回值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陣A的逆矩陣B/入口參數(shù): 輸入方陣，輸出方陣，方陣階數(shù)/返回值: true or false/-四、 運行與測試1.1 進入提示畫面1.2 按提示輸入后1.3 輸出界面五

15、、 總結(jié)與體會通過這一次的課程設(shè)計，我掌握了另外的一種算法，對矩陣等復(fù)雜數(shù)據(jù)的輸入有了更深刻的理解，起初不知道應(yīng)該以怎樣的方式輸入矩陣，數(shù)據(jù)結(jié)構(gòu)這門課程在處理數(shù)據(jù)信息方面給了我很大的啟發(fā)，應(yīng)該以怎樣的方式輸入數(shù)據(jù)，處理數(shù)據(jù)，數(shù)據(jù)結(jié)構(gòu)都很系統(tǒng)的解釋了出來，對我的幫助很大，一開始也沒想到自己真的能做出來，后來通過網(wǎng)上的一些成功案例，一步一步的寫了出來，在經(jīng)過調(diào)試，驗證等一系列操作，終于解決了問題。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 /定義方陣的最大階數(shù)為10using namespace std;/函數(shù)的聲明部分float MatDet(float *p, int n); /求矩陣的行列式float Creat_M(float *p, int m, int n, int k); /求矩陣元素A(m, n)的代數(shù)余之式void print(float *p, int m,int n); /輸出矩陣n*nbool Gauss(float *pSrc, float *pDst, int iRow); /采用部分主元的高斯消去法求方陣A的逆矩陣Bbool Transepose(f

17、loat *pSrc,float *pSdst, int iRow, int iCol); /求矩陣轉(zhuǎn)置bool MatMultiply(float *pSrc1, float *pSrc2,float *pDst,int iRow, int iCol);/矩陣相乘int main()/*float *buffer, *p; /定義數(shù)組首地址指針變量int row, num; /定義矩陣的行數(shù)和矩陣元素個數(shù)int i, j;float determ; /定義矩陣的行列式float aNN, bNN;int n;cout << "采用逆矩陣的定義法求矩陣的逆矩陣!n&quo

18、t;cout << "請輸入矩陣的行數(shù): "cin >> row;num = 2 * row * row;buffer = (float *)calloc(num, sizeof(float); /分配內(nèi)存單元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); /打印該矩陣determ = MatDet(buffer, row); /求整個矩陣的行列式p = buffer + row * row;if (determ != 0)cout << "The determinant of the matrix is " << de

20、term << endl;for (i = 0; i < row; i+) /求逆矩陣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); /打印該矩陣elsecout << "The determinant is 0, and there is no inverse matrix!n"fre

21、e(buffer); /釋放內(nèi)存空間cout << "采用部分主元的高斯消去法求方陣的逆矩陣!n"cout << "請輸入方陣的階數(shù): "cin >> n;cout << "請輸入" << n << "階方陣: n"/輸入一個n階方陣for (i = 0; i < n; i+)for (j = 0; j < n; j+)cin >> aij;/運用高斯消去法求該矩陣的逆矩陣并輸出if (Gauss(a, b, n)cou

22、t << "該方陣的逆矩陣為: 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 << "請輸入方陣的行數(shù): "cin >> m;cout << "請輸入方陣的列數(shù): "cin >> n;float *a = new

23、floatm*n;cout << "請輸入" << m << "*"<< n << "階方陣: n"/輸入一個n階方陣for (i = 0; i < m*n; i+)cin >> ai;print(a,m,n);cout<<"轉(zhuǎn)置矩陣："<<endl;float *b = new floatn*m;Transepose(a,b,m,n);print(b,n,m);cout<<"矩陣乘積：&qu

24、ot;<<endl;float *c = new floatm*m;MatMultiply(a,b,c,m,n);print(c,m,m);cout<<"矩陣的逆："<<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: 求矩陣(n*n)的行列式/入口參數(shù): 矩陣的首地址，矩陣的行數(shù)/返回值: 矩陣的行列式值/-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; /控制求和循環(huán)次數(shù),若為2階，則循環(huán)1次，否則為n次for (m = 0; m < lop; m+)mid = 1; /順序求和, 主對角線元素相乘之和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; /逆序相減, 減去次對角

26、線元素乘積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矩陣中元素A(m, n)的代數(shù)余之式/入口參數(shù): k*k矩陣的首地址，矩陣元素A的下標m,n,矩陣行數(shù)k/返回值: k*k矩陣中元素A(m, n)的代數(shù)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階矩陣的代數(shù)余之式為k-1階矩陣p_creat = (float*)calloc(len, sizeof(float); /分配內(nèi)存單元p_mid = p_creat;for (i = 0; i < k; i+)for (j = 0; j < k; j+)if (i != m && j != n) /將除第i行和第j列外的所有元素存儲到以p_mid為首地址的內(nèi)存單元*p_mid+ = *(p+i*k+j);sign = (m+n)%2 = 0 ? 1 : -1; /代數(shù)余

28、之式前面的正、負號mid_result = (float)sign*MatDet(p_creat, k-1);free(p_creat);return mid_result;/-/功能: 打印n*n矩陣/入口參數(shù): n*n矩陣的首地址,矩陣的行數(shù)n/返回值: 無返回值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陣A的逆矩陣B/入口參數(shù): 輸入方陣，輸出方陣，方陣階數(shù)/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; /臨時矩陣/將A矩陣存放在臨時矩陣tnn中for (i = 0; i < n; i+) for (j = 0; j < n; j+)tij = pSrci*iRow+j;/初始化B

30、矩陣為單位陣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+)/尋找主元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，進行行交換if (k != i)for (j = 0; j < n; j+)temp = tij;tij = tkj;tkj = temp;/B伴隨交換temp = pDsti*iRow+j;pDsti*iRow+j = pDstk