怎么用c语言实现一下稀疏矩阵操作?

Question

要求用C语言编写
实现三元组，十字链表下的稀疏矩阵的加、转、乘的实现。
（1）稀疏矩阵的存储
（2）稀疏矩阵加法
（3）矩阵乘法
（4）矩阵转置

求各位大神指点！！！求源代码，最好有注释

 

Answer 1

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#include<iostream>
using namespace std;
typedef  int  ElemType ;
#define M 4  //稀疏矩阵行数
#define N 4  //稀疏矩阵列数
#define MaxSize  6  //非零元素最多个数
//三元组类型定义
typedef struct
{
	int r;         //行号  
	int c;          //列号  
	ElemType d;     //元素值  
} TupNode;         //三元组定义  
typedef struct
{
	int rows;      //行数  
	int cols;     //列数  
	int nums;       //非零元素个数  
	TupNode data[MaxSize];
} TSMatrix;    //三元组顺序表定义  
//十字链表类型定义
typedef struct mtxn
{
	int row;   //行号
	int col;    //列号
	struct mtxn *right, *down;  //向右和向下的指针
	union
	{
		ElemType value;   //非零元素值
		struct mtxn *link;  //指向下一个头结点
	}tag;
}MatNode;


//三元组创建
void Create_1(TSMatrix &t, ElemType A[M][N])
{
	int i, j;
	t.rows = M;
	t.cols = N;
	t.nums = 0;
	for (i = 0; i < M; i++)
	{
		for (j = 0; j < N; j++)
		{
			if (A[i][j] != 0)    //元素值不为零，建立三元组
			{
				t.data[t.nums].r = i;
				t.data[t.nums].c = j;
				t.data[t.nums].d = A[i][j];
				t.nums++;
			}
		}
	}
}
//十字链表创建
void Create_2(MatNode *&mh, ElemType a[M][N])
{
	int i, j;
	MatNode *h[MaxSize], *p, *q, *r;
	mh = (MatNode *)malloc(sizeof(MatNode));   //创建十字链表的头节点
	mh->row = M;
	mh->col = N;
	r = mh;   //r指向尾节点
	for (i = 0; i < MaxSize; i++)   //采用尾插法创建循环表
	{
		h[i] = (MatNode *)malloc(sizeof(MatNode));
		h[i]->down = h[i]->right = h[i];	//将down和right方向量置为循环的
		r->tag.link = h[i];  //将h[i]加到链表中
		r = h[i];
	}
	r->tag.link = mh;   //置为循环链表


	for (i = 0; i < M; i++)    //处理每一行
	{
		for (j = 0; j < N; j++)    //处理每一列
		{
			if (a[i][j] != 0)   //处理非零元素
			{
				p = (MatNode *)malloc(sizeof(MatNode));	  //创建一个新节点
				p->row = i;
				p->col = j;
				p->tag.value = a[i][j];
				q = h[i];   //查找在行表中插入位置
				while (q->right != h[i] && q->right->col < j)
				{
					q = q->right;
				}
				p->right = q->right;
				q->right = p;			//完成行表的操作
				q = h[j];      //查找在链表中插入的位置

				while (q->down != h[j] && q->down->row < i)
				{
					q = q->down;
				}
				p->down = q->down;
				q->down = p;			//完成列表的插入
			}
		}

	}
}


//输出三元组矩阵 
void  DispMat_1(TSMatrix t)
{
	int k;
	if (t.nums <= 0)
	{
		return ;
	}
	cout << t.rows << "\t" << t.cols << "\t" << t.nums << endl;
	cout << "=====================" << endl;
	cout << "行数" << " " << " 列数" << " " << "非零元素" << endl;
	for (k = 0; k < t.nums; k++)
	{
		cout << t.data[k].r << '\t' << t.data[k].c << '\t' << t.data[k].d << endl;
	}
}
//输出十字链表矩阵
void DispMat_2(MatNode *mh)
{
	MatNode *p, *q;
	cout << "行=" << mh->row << "列=" << mh->col << endl;
	p = mh->tag.link;
	while (p != mh)
	{
		q = p->right;
		while (p != q)				//输出一行非零元素
		{
			cout << q->row << '\t' << q->col << '\t' << q->tag.value << endl;
			q = q->right;
		}
		p = p->tag.link;
	}

}


//三元组元素赋值  
bool Value(TSMatrix &t, ElemType x, int i, int j)
{
	int k = 0, k1;
	if (i >= t.rows || j >= t.cols)
		return false;
	while (k<t.nums && i>t.data[k].r)
		k++;      //查找行  
	while (k<t.nums && i == t.data[k].r && j>t.data[k].c)
		k++;     //查找列  
	if (t.data[k].r == i && t.data[k].c == j)   //存在这样的元素  
		t.data[k].d = x;
	else               //不存在这样的元素时插入一个元素  
	{
		for (k1 = t.nums - 1; k1 >= k; k1--)
		{
			t.data[k1 + 1].r = t.data[k1].r;
			t.data[k1 + 1].c = t.data[k1].c;
			t.data[k1 + 1].d = t.data[k1].d;
		}
		t.data[k].r = i;
		t.data[k].c = j;
		t.data[k].d = x;
		t.nums++;
	}
	return true;
}
//将指定位置的元素值赋给变量 
bool Assign(TSMatrix t, ElemType &x, int i, int j)
{
	int k = 0;
	if (i >= t.rows || j >= t.cols)
		return false;
	while (k<t.nums && i>t.data[k].r)
		k++;    //查找行  
	while (k<t.nums && i == t.data[k].r && j>t.data[k].c)
		k++;  //查找列  
	if (t.data[k].r == i && t.data[k].c == j)
		x = t.data[k].d;
	else
		x = 0;         //在三元组中没有找到表示是零元素  
	return true;
}


//三元组下矩阵转置 
void TranTat_1(TSMatrix t, TSMatrix &tb)
{
	int k, k1 = 0, v;		//k1记录tb中的元素个数
	tb.rows = t.rows;
	tb.cols = t.cols;
	tb.nums = t.nums;
	if (t.nums != 0)	//当存在非零元素时执行转置
	{
		for (v = 0; v < t.cols; v++)
		{
			for (k = 0; k < t.nums; k++)		//k用于扫描t.data的所有元素
			{
				if (t.data[k].c == v)		//找到一个列号为v的元素
				{
					tb.data[k].r = t.data[k].c;		//将行列交换后添加到tb中
					tb.data[k].c = t.data[k].r;
					tb.data[k].d = t.data[k].d;
					k1++;
				}
			}
		}
	}

}
//十字链表下矩阵转置 
void TranTat_2(ElemType a[M][N], ElemType c[M][N])
{
	int i,j;
	for (i = 0; i < M; i++)
	{
		for (j = 0; j < N; j++)
			c[j][i] = a[i][j];
	}

}


//三元组下矩阵相加 
bool  AddMat_1(TSMatrix a, TSMatrix b, TSMatrix &c)
{
	int i, j;
	ElemType x, y, z;
	if (a.rows != b.rows || a.cols != b.cols)
		return false;            //行数或列数不等时不能相加
	c.rows = a.rows;
	c.cols = a.cols;       //c的行列数与a的相同  
	c.nums = 0;
	for (i = 0; i<M; i++)
		for (j = 0; j<N; j++)
		{
			Assign(a, x, i, j);
			Assign(b, y, i, j);
			z = x + y;
			if (z!=0)
				Value(c, z, i, j);
		}
	return true;
}
//十字链表下矩阵相加 
void AddMat_2(ElemType a[M][N], ElemType b[M][N], ElemType c[M][N])
{
	int i;
	int j;
	for (i = 0; i < M; i++)
	{
		for (j = 0; j < N; j++)
		{
			c[i][j] = a[i][j] + b[i][j];
		}
	}
}


//三元组下矩阵相乘 
bool  MulMat_1(TSMatrix a, TSMatrix b, TSMatrix &c)
{
	int i, j;
	ElemType x, y, z;
	if (a.rows != b.rows || a.cols != b.cols)
		return false;            //行数或列数不等时不能相乘
	c.rows = a.rows;
	c.cols = a.cols;       //c的行列数与a的相同  
	c.nums = 0;
	for (i = 0; i<M; i++)
		for (j = 0; j<N; j++)
		{
			Assign(a, x, i, j);
			Assign(b, y, i, j);
			z = x * y;
			if (z)
				Value(c, z, i, j);
		}
	return true;
}
//十字链表下矩阵相乘 
void  MulMat_2(ElemType a[M][N], ElemType b[M][N], ElemType c[M][N])
{
	int i;
	int j;
	int k;
	int temp;
	for (i = 0; i < M; i++)
	{
		for (j = 0; j < N; j++)
		{
			temp = 0;
			for (k = 0; k < 4; k++)
			{
				temp = temp + a[i][k] * b[k][j];
			}
			c[i][j] = temp;
		}

	}
}


//主函数实现
int main()
{
	TSMatrix ta, tb, tc;

	MatNode *td,*tf;

	int x,y,z;

	ElemType a[M][N] = { 1, 0, 3, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1 };
	ElemType b[M][N] = { 3, 0, 0, 0, 0, 4, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2 };
	ElemType c[M][N] = { 0 };

	while (1)
	{
		cout << "提示：输入1----是三元组下的矩阵运算" << endl;
		cout << "      输入2----是十字链表下的矩阵运算" << endl;
		cout << "      输入3----退出" << endl;
		cout << "请输入：";
		cin >> x;
		switch (x)
		{
		case 1:
			cout << "提示：输入1----三元组下矩阵的转置运算" << endl;
			cout << "      输入2----三元组下矩阵的相加运算" << endl;
			cout << "      输入3----三元组下矩阵的相乘运算" << endl;
			cout << "请输入：";
			cin >> y;
			switch (y)
			{
			case 1:
				Create_1(ta, a);
				cout << "输出三元组下矩阵a：" << endl;
				DispMat_1(ta);
				cout << "三元组下矩阵a转置：" << endl;
				TranTat_1(ta, tc);
				DispMat_1(tc);
				break;
			case 2:
				Create_1(ta, a);
				Create_1(tb, b);
				cout << "三元组下矩阵a,b相加：" << endl;
				AddMat_1(ta, tb, tc);
				DispMat_1(tc);
				break;
			case 3:
				Create_1(ta, a);
				Create_1(tb, b);
				cout << "三元组下矩阵a,b相乘：" << endl;
				MulMat_1(ta, tb, tc);
				DispMat_1(tc);
				break;
			}
			break;
		case 2:
			cout << "提示：输入1----十字链表下矩阵的转置运算" << endl;
			cout << "      输入2----十字链表下矩阵的相加运算" << endl;
			cout << "      输入3----十字链表下矩阵的相乘运算" << endl;
			cout << "请输入：";
			cin >> z;
			switch (z)
			{
			case 1:
				Create_2(td,a);
				cout << "输出十字链表下矩阵a：" << endl;
				DispMat_2(td);
				cout << "十字链表下矩阵a转置：" << endl;
				TranTat_2(a, c);
				Create_2(tf, c);
				DispMat_2(tf);
				break;
			case 2:
				cout << "十字链表下矩阵a,b相加：" << endl;
				AddMat_2(a, b, c);
				Create_2(tf, c);
				DispMat_2(tf);
				break;
			case 3:
				cout << "十字链表下矩阵a,b相乘：" << endl;
				MulMat_2(a, b, c);
				Create_2(tf, c);
				DispMat_2(tf);
				break;
			}
		case 3: break; 
		}
	}
	cout << endl;
	system("pause");
}