压缩矩阵

根据数据结构书本上敲打的，讲述内容较少，但是添加了一些注释。

//稀疏矩阵的压缩存储,最多存储10*10的矩阵#include<iostream>#include<iomanip>//use setwusing namespace std;typedef struct{int row;//非零元的行下标int column;//非零元的列下标int e;//非零元}Triple;typedef struct{Triple data[100];int mu;//矩阵的行数int nu;//矩阵的列数int tu;//非零元的个数}TSMatrix;/*1.输入矩阵，进行压缩*/void InitMatrix(TSMatrix &matrix){matrix.tu = 0;int a[100][100] = { 0 };cout << "请输入矩阵的行数和列数:\n";int rowNum, columnNum;//行数和列数cin >> rowNum >> columnNum;matrix.mu = rowNum;matrix.nu = columnNum;cout << "请输入矩阵\n";//矩阵的输入for (int i = 0; i < rowNum; i++)for (int j = 0; j < columnNum; j++)cin >> a[i][j];//进行压缩矩阵for (int i = 0; i < rowNum; i++){for (int j = 0; j < columnNum; j++){if (a[i][j] != 0){matrix.data[matrix.tu].e = a[i][j];//好好理解这个句子matrix.data[matrix.tu].row = i;matrix.data[matrix.tu++].column = j;}}}cout << "矩阵压缩成功\n";}/*2.矩阵转置*/void MatrixTransposition(const TSMatrix & tsmatrix, TSMatrix & tsmatrix1)//tsmatrix1是转置后的三元组表{/*在此预设num和cpot两个向量。num[col]表示矩阵tsmatrix中第col列中非零元的个数，cpot[col]指示tsmatrix中第col列的第一个非零元在tsmatrix1.data中的恰当位置*/tsmatrix1.mu = tsmatrix.nu;//转置后行列数要交换tsmatrix1.nu = tsmatrix.mu;tsmatrix1.tu = tsmatrix.tu;int num[100] = { 0 };int cpot[100] = { 0 };if (tsmatrix1.tu){for (int i = 0; i < tsmatrix.tu; i++)num[tsmatrix.data[i].column]++;//num[col]代表第col列中非零元的个数}for (int i = 1; i < tsmatrix.tu; i++)cpot[i] = cpot[i - 1] + num[i - 1];//cpot[col]代表第col列的第一个非零元在data数组中的位置for (int i = 0; i < tsmatrix.tu; i++){int col = tsmatrix.data[i].column;int p = cpot[col];tsmatrix1.data[p].row = tsmatrix.data[i].column;tsmatrix1.data[p].column = tsmatrix.data[i].row;tsmatrix1.data[p].e = tsmatrix.data[i].e;cpot[col]++;}}/*3.乘积矩阵*/void MatrixMult(const TSMatrix & M, const TSMatrix & N, TSMatrix & Q)//_____M*N=Q{int numM[100] = { 0 };//num[row]_____第row行的非零元个数int rposM[100] = { 0 };//rpos[row]____第row行中第一个非零元在data数组的位置int numN[100] = { 0 };int rposN[100] = { 0 };//preparation//for Mfor (int i = 0; i < M.tu; i++)numM[M.data[i].row]++;rposM[0] = 0;for (int i = 1; i < M.mu; i++)rposM[i] = rposM[i - 1] + numM[i - 1];//for Nfor (int i = 0; i < N.tu; i++)numN[N.data[i].row]++; rposN[0] = 0;for (int i = 1; i < N.mu; i++)rposN[i] = rposN[i - 1] + numN[i - 1];//matrix multif (M.nu != N.mu){cout << "矩阵无法运算\n";return;}//Q的初始化Q.mu = M.mu;Q.nu = N.nu;Q.tu = 0;//if (M.tu*N.tu != 0)//Q是非零矩阵{for (int i = 0; i < M.mu; i++)//对于M的每一行{int tp;int ctemp[10] = { 0 };//当前行各元素累加器清零//if (i < M.mu - 1)tp = rposM[i + 1];elsetp = M.tu;//for (int j = rposM[i]; j < tp; j++)//对于当前行的每一个非零元{int t;int brow = M.data[j].column;//由M中的列坐标找到对应的行坐标//if (brow < N.mu - 1)t = rposN[brow + 1];elset = N.tu;//for (int k = rposN[brow]; k < t; k++){ctemp[N.data[k].column] += M.data[j].e *N.data[k].e;}}//for (int p = 0; p < Q.nu; p++){if (ctemp[p])//如果不是非零元，则放入Q的data数组中{Q.data[Q.tu].e = ctemp[p];Q.data[Q.tu].column = p;Q.data[Q.tu++].row = i;}}}//for (int i = 0; i < M.mu; i++)______对于M的每一行}//if (M.tu*N.tu != 0)______Q是非零矩阵}/*4.打印矩阵*/void MatrixPrint(const TSMatrix & matrix){cout << "------------------------------------------" << endl;cout << "矩阵打印是:\n";int num = 0;for (int i = 0; i < matrix.mu; i++)//每一行{for (int j = 0; j < matrix.nu; j++)//当前行的每一列{if (num != matrix.tu){if (matrix.data[num].column == j&&matrix.data[num].row == i)cout << setw(3)<<matrix.data[num++].e << " ";elsecout << setw(3)<<0 << " ";}elsecout <<setw(3)<< 0 << " ";}cout << endl;}cout << "------------------------------------------" << endl;}int main(){TSMatrix matrixM,matrixN;TSMatrix temp;//矩阵初始化InitMatrix(matrixM);InitMatrix(matrixN);//矩阵转置，输出MatrixTransposition(matrixM, temp);cout << "\n\n转置后输出\n";MatrixPrint(temp);MatrixTransposition(matrixN, temp);cout << "\n\n转置后输出\n";MatrixPrint(temp);////矩阵乘积cout << "\n\n矩阵乘积输出\n";TSMatrix matrixQ;MatrixMult(matrixM, matrixN, matrixQ);MatrixPrint(matrixQ);return 0;}