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三元组（（x，y），z）其中（x，y）表示非零元位置，z表示该坐标的值
由于实际操作时，我们所用的矩阵0非常多，所以一个一个输入值很浪费时间，也浪费空间，所以用一些三元组表示非零元即能表示一个矩阵
三元组稀疏矩阵表示一些图也是很不错的选择
这样就很浪费空间，三元组直接
((0,1),1)
((1,2),1)
((3,4),1)
((5,6),1)
((7,8),1)
下面是稀疏矩阵代码：
#include <iostream>
#include<malloc.h>
#include<stdio.h>
#define SMAX 1000
using namespace std;
typedef struct
{
int i,j; //储存非零元素的行和列信息
int v; //非零元素的值
} SPNode; //定义三元组类型
typedef struct
{
int row,col,notZero; //矩阵的行、列和非零元素的个数
SPNode data[SMAX]; //三元组表
} SPMatrix;
void printMatrix(SPMatrix m);
SPMatrix createMatrix()
{
cout<<"enter row and col and notZero"<<endl;
int row,col, notZero;
cin>>row >>col >>notZero;
SPMatrix matrix;
matrix.row = row;
matrix.col = col;
matrix.notZero = notZero;
for(int k = 1; k <= notZero; k++)
{
cout <<"enter each row and col and value"<<endl;
cin >> matrix.data[k].i >>matrix.data[k].j>>matrix.data[k].v;
}
cout <<"三元组："<<endl;
for(int k = 1; k <= notZero; k++)
{
cout <<"(("<<matrix.data[k].i<<"," << matrix.data[k].j<<")"<<matrix.data[k].v<<"))"<<endl;
}
// printMatrix(matrix);
return matrix;
}
void printMatrix(SPMatrix m)
{
int row = m.row;
int col = m.col;
int show[row][col]= {0};
//初始化矩阵
for(int i=0; i<row; i++)
{
for(int j=0; j<col; j++)
{
show[i][j]=0;
}
}
for(int k=1; k<=m.notZero; k++)
{
show[m.data[k].i-1][m.data[k].j-1] = m.data[k].v;
}
for(int i=0; i<row; i++)
{
for(int j=0; j<col; j++)
{
cout<<show[i][j]<<" ";
}
cout<<endl;
}
}
SPMatrix add(SPMatrix m1,SPMatrix m2)
{
if(m1.row!=m2.row || m1.col!=m2.col)
{
cout<<"wrong"<<endl;
return m1;
}
int flag = 0;
int num = m1.notZero;
int m;
for(int k = 1; k <= num; k++)
{
for(m = 1; m <= m2.notZero; m++)
{
if(m1.data[k].i == m2.data[m].i && m1.data[k].j == m2.data[m].j)
{
m2.data[k].v += m1.data[m].v;
flag = 1;
break;
}
}
if(flag ==0) //当前位置m2和m1未重合
{
m2.notZero++;
m2.data[m2.notZero] = m1.data[k];
}
flag = 0;
}
return m2;
}
SPMatrix sub(SPMatrix m1,SPMatrix m2)
{
if(m1.row!=m2.row || m1.col!=m2.col)
{
cout<<"wrong"<<endl;
return m1;
}
int flag = 0;
int num = m1.notZero;
int m;
for(int k = 1; k <= num; k++)
{
for(m = 1; m <= m2.notZero; m++)
{
if(m1.data[k].i == m2.data[m].i && m1.data[k].j == m2.data[m].j)
{
m2.data[k].v -= m1.data[m].v;
flag = 1;
break;
}
}
if(flag ==0) //当前位置m2和m1未重合
{
m2.notZero++;
m2.data[m2.notZero] = m1.data[k];
m2.data[m2.notZero].v = -m1.data[k].v;
}
flag = 0;
}
return m2;
}
SPMatrix numMul(SPMatrix m)
{
int num ;
cout <<"输入数乘的数："<<endl;
cin >> num;
for(int k = 1; k <= num; k++)
{
m.data[k].v *= num;
}
return m;
}
int isExist(SPMatrix m,SPNode a){
for(int i=1;i<=m.notZero;i++)
if(m.data[i].i == a.i &&m.data[i].j == a.j)
return i;
return 0;
}
SPMatrix Mul(SPMatrix m1,SPMatrix m2)
{
if(m1.col != m2.row)
{
cout<<"wrong"<<endl;
return m1;
}
SPMatrix result;
result.row = m1.row;
result.col = m2.col;
result.notZero = 0;//初始化
SPNode data[m1.notZero+m2.notZero];
int n = 0;
for(int k = 1; k <= m1.notZero; k++)
{
for(int m = 1; m <= m2.notZero; m++)
{
if(m1.data[k].j == m2.data[m].i)
{
data[n].v = m1.data[k].v*m2.data[m].v;
data[n].i = m1.data[k].i;
data[n].j = m2.data[m].j;
n++;
continue;
}
}
}
int flag = 0;
for(int k =0;k<n;k++){
flag = isExist(result,data[k]);
if(flag>0){
result.data[flag].v+=data[k].v;
}
else{
result.notZero++;
result.data[result.notZero] = data[k];
}
}
return result;
}
int main()
{
int num = 0;
do
{
cout<<"***********************************\n";
cout<<"* 菜单 *\n";
cout<<"* 1.矩阵相加 *\n";
cout<<"* 2.矩阵相减 *\n";
cout<<"* 3.矩阵相乘 *\n";
cout<<"* 4.矩阵数乘 *\n";
cout<<"* 6.退出 *\n";
cout<<"***********************************\n";
cin>>num;
if(1 == num|| 2 == num || 3 == num)
{
SPMatrix m1 = createMatrix();
SPMatrix m2 = createMatrix();
cout<<"两矩阵为"<<endl;
printMatrix(m1);
cout<<endl;
printMatrix(m2);
switch(num)
{
case 1:
{
if(m1.col!=m2.col || m1.row!=m2.row)
{
cout<<"行列不同"<<endl;
}
else{
cout<<"结果为："<<endl;
printMatrix(add(m1,m2));
}
break;
}
case 2:
{
if(m1.col!=m2.col || m1.row!=m2.row)
{
cout<<"参数错误"<<endl;
}
else{
cout<<"结果为："<<endl;
printMatrix(sub(m1,m2));
}
break;
}
case 3:
{
if(m1.col!=m2.row)
{
cout<<"参数错误"<<endl;
}
else{
cout<<"结果为："<<endl;
printMatrix(Mul(m1,m2));
}
break;
}
default:
break;
}
}
else if(4 == num)
{
int number = 1;
cout<<"请输入矩阵"<<endl;
SPMatrix m = createMatrix();
cout<<"请输入数值"<<endl;
cin>>number;
cout<<"矩阵为："<<endl;
printMatrix(m);
printMatrix(numMul(m));
}
cout<<"按回车继续....";
getchar();
getchar();
system("cls");
}
while(1 == num|| 2 == num || 3 == num ||4 == num);
return 0;
}