稀疏矩阵

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该文章介绍稀疏矩阵的相关用法。

头文件：SMatrix.h

#include <iostream>const int MAXR = 20;//稀疏矩阵最大行数const int MAXC = 20;//稀疏矩阵最大列数const int MaxSize = 100;//三元组顺序表最大元素个数struct TupNode//单个三元组的类型{int r;//行号int c;//列号int d;//元素值};class SMatrixClass{int rows;//行数int cols;//列数int nums;//非零元素个数TupNode *data;//稀疏矩阵对应的三元组顺序表public:SMatrixClass();//构造函数~SMatrixClass();//析构函数void CreateTSMatrix(int A[][MAXC], int m, int n);//创建三元组bool Setvalue(int i, int j, int x);//三元组元素赋值A[i][j]=xbool GetValue(int i, int j, int &x);//将指定位置的元素值赋给变量x=A[i][j]void DispMat();//输出三元组void Transpose(SMatrixClass &tb);//矩阵转置//======稀疏矩阵的其他用法======friend bool MatAdd(SMatrixClass &a, SMatrixClass &b, SMatrixClass &c);//两个稀疏矩阵相加};

源文件：SMatrix.cpp

#include "SMatrix.h"//包括稀疏矩阵三元组表示的类声明using namespace std;SMatrixClass::SMatrixClass()//构造函数{data = new TupNode[MaxSize];}SMatrixClass::~SMatrixClass()//析构函数{delete[] data;}void SMatrixClass::CreateTSMatrix(int A[][MAXC], int m, int n)//创建三元组{int i, j;rows = m;cols = n; nums = 0;for (i = 0; i<m; i++){for (j = 0; j<n; j++)if (A[i][j] != 0){data[nums].r = i;data[nums].c = j;data[nums].d = A[i][j];nums++;}}}bool SMatrixClass::Setvalue(int i, int j, int x)//三元组元素赋值A[i][j]=x{int k = 0, k1;if (i<0 || i >= rows || j<0 || j >= cols)return false;while (k<nums && i>data[k].r)k++;while (k<nums && i == data[k].r && j>data[k].c)k++;if (data[k].r == i && data[k].c == j)data[k].d = x;else{for (k1 = nums - 1; k1 >= k; k1--){data[k1 + 1].r = data[k1].r;data[k1 + 1].c = data[k1].c;data[k1 + 1].d = data[k1].d;}data[k].r = i; data[k].c = j;data[k].d = x;nums++;}return true;}bool SMatrixClass::GetValue(int i, int j, int &x)//将指定位置的元素值赋给变量x=A[i][j]{int k = 0;if (i<0 || i >= rows || j<0 || j >= cols)return false;while (k<nums && data[k].r<i)k++;while (k<nums && data[k].r == i && data[k].c<j)k++;if (data[k].r == i && data[k].c == j)x = data[k].d;elsex = 0;return true;}void SMatrixClass::DispMat()//输出三元组{int i;if (nums <= 0) return;cout << "\t" << rows << "\t" << cols << "\t" << nums << endl;cout << "\t------------------\n";for (i = 0; i<nums; i++)cout << "\t" << data[i].r << "\t" << data[i].c << "\t" << data[i].d << endl;}void SMatrixClass::Transpose(SMatrixClass &tb)//矩阵转置{int p, q = 0, v;tb.rows = cols;tb.cols = rows;tb.nums = nums;if (nums != 0){for (v = 0; v<cols; v++)for (p = 0; p<nums; p++)if (data[p].c == v){tb.data[q].r = data[p].c;tb.data[q].c = data[p].r;tb.data[q].d = data[p].d;q++;}}}//=================稀疏矩阵的其他用法==============bool MatAdd(SMatrixClass &a, SMatrixClass &b, SMatrixClass &c)//两个稀疏矩阵相加{int i = 0, j = 0, k = 0;int v;if (a.rows != b.rows || a.cols != b.cols)return false;c.rows = a.rows;c.cols = a.cols;while (i<a.nums && j<b.nums){if (a.data[i].r == b.data[j].r){if (a.data[i].c<b.data[j].c){c.data[k].r = a.data[i].r;c.data[k].c = a.data[i].c;c.data[k].d = a.data[i].d;k++; i++;}else if (a.data[i].c>b.data[j].c) {c.data[k].r = b.data[j].r; c.data[k].c = b.data[j].c;c.data[k].d = b.data[j].d;k++; j++;}else//a元素的列号等于b元素的列号{v = a.data[i].d + b.data[j].d;if (v != 0)//只将不为0的结果添加到c中{c.data[k].r = a.data[i].r;c.data[k].c = a.data[i].c;c.data[k].d = v;k++;}i++; j++;}}else if (a.data[i].r<b.data[j].r)//a元素的行号小于b元素的行号{c.data[k].r = a.data[i].r;//将a元素添加到c中c.data[k].c = a.data[i].c;c.data[k].d = a.data[i].d;k++; i++;}else //a元素的行号大于b元素的行号{c.data[k].r = b.data[j].r;//将b元素添加到c中c.data[k].c = b.data[j].c;c.data[k].d = b.data[j].d;k++; j++;}c.nums = k;}return true;//成功时返回true}

主函数：main.cpp

#include "SMatrix.h"using namespace std;//==========稀疏矩阵基本用法==============void main1(){SMatrixClass t,tb;int x;int a[MAXR][MAXC]={{0,0,1,0,0,0,0},{0,2,0,0,0,0,0},{3,0,0,0,0,0,0},{0,0,0,5,0,0,0},{0,0,0,0,6,0,0},{0,0,0,0,0,7,4}};t.CreateTSMatrix(a,6,7);cout << "三元组t表示:\n"; t.DispMat();cout << "执行A[4][1]=8\n";t.Setvalue(4,1,8);cout << "三元组t表示:\n"; t.DispMat();cout << "求x=A[4][1]\n";t.GetValue(4,1,x);cout << "x=" << x << endl;cout << "t转置为tb\n";t.Transpose(tb);cout << "三元组tb表示:\n"; tb.DispMat();cout << "main函数结束,销毁所有的三元组对象" << endl;}//===========两个稀疏矩阵相加==============void main(){SMatrixClass a, b, c;int x;int A[MAXR][MAXC] = { { 0, 0, 1, 0, 0, 0, 0 }, { 0, 2, 0, 0, 0, 0, 0 }, { 3, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 5, 0, 0, 0 }, { 0, 0, 0, 0, 6, 0, 0 }, { 0, 0, 0, 0, 0, 7, 4 } };int B[MAXR][MAXC] = { { 0, 0, 1, 0, 0, 0, 0 }, { 0, 2, 0, 0, 0, 0, 0 }, { 3, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 5, 0, 0, 0 }, { 0, 0, 0, 0, 6, 0, 0 }, { 0, 0, 0, 0, 0, 7, 4 } };a.CreateTSMatrix(A, 6, 7);cout << "a三元组表示:\n"; a.DispMat();b.CreateTSMatrix(B, 6, 7);cout << "b三元组表示:\n"; b.DispMat();cout << "c=a+b\n";MatAdd(a, b, c);cout << "c三元组表示:\n"; c.DispMat();cout << "main函数结束,销毁所有的三元组对象" << endl;}

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