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 1000using 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;
}