稀疏矩阵乘法

Posted 2021-01-17 kaleidoscope

#include <iostream>
#include <malloc.h>
#include <cstdio>
using namespace std;
#define M	4
#define N	4
#define MaxSize 100
typedef int ElemType;
typedef struct
{
	int		r;
	int		c;
	ElemType	d;      /* /元素值 */
} TupNode;                      /* /三元组定义 */
typedef struct
{
	int	rows;
	int	cols;
	int	nums;
	TupNode data[MaxSize];
} TSMatrix;                     /* /三元组顺序表定义 */
void CreatMat( TSMatrix &t, ElemType A[M][N] )
{
	t.rows	= M;
	t.cols	= N;
	t.nums	= 0;
	for ( int i = 0; i < M; i++ )
		for ( int j = 0; j < N; j++ )
			if ( A[i][j] != 0 )
			{
				t.data[t.nums].r	= i;
				t.data[t.nums].c	= j;
				t.data[t.nums].d	= A[i][j];
				t.nums++;
			}
}


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++;
	while ( k<t.nums &&i == t.data[k].r &&j>t.data[k].c )
		k++;
	if ( t.data[k].r == i && t.data[k].c == j )
		t.data[k].d = x;
	else{
		for ( k1 = t.nums - 1; k1 >= k; k1-- )
		{
			t.data[k1 + 1].r	= t.data[k].r;
			t.data[k1 + 1].c	= t.data[k].c;
			t.data[k1 + 1].d	= t.data[k].d;
		}
		t.data[k].r	= i;
		t.data[k].c	= j;
		t.data[k].d	= x;
		t.nums++;
	}
	return(true);
}


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++;
	while ( k<t.nums &&i == t.data[k].r &&j>t.data[k].c )
		k++;
	if ( t.data[k].r == i && t.data[k].c == j )
		x = t.data[k].d;
	else
		x = 0;
	return(true);
}


void DispMat( TSMatrix t )
{
	if ( t.nums <= 0 )
		return;
	printf( "	%d	%d	%d
", t.rows, t.cols, t.nums );
	printf( "	-----------------
" );
	for ( int i = 0; i < t.nums; i++ )
		printf( "	%d	%d	%d
", t.data[i].r, t.data[i].c, t.data[i].d );
}


void TranMat( TSMatrix t, TSMatrix &tb )
{
	int i, j, k = 0;
	tb.rows = t.cols;
	tb.cols = t.rows;
	tb.nums = t.nums;
	if ( t.nums != 0 )
	{
		for ( i = 0; i < t.cols; i++ )
			for ( j = 0; j < t.nums; j++ )
				if ( t.data[j].c == i )
				{
					tb.data[k].r	= t.data[j].c;
					tb.data[k].c	= t.data[j].r;
					tb.data[k].d	= t.data[j].d;
					k++;
				}
	}
}


bool MatAdd( TSMatrix a, TSMatrix b, TSMatrix &c )
{
	int		i = 0, j = 0, k = 0;
	ElemType	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 ) /* /先控制行相等 */
		{
			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  {
				v = a.data[i].d + b.data[j].d;
				if ( v != 0 )
				{
					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 )
		{
			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  {
			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++;
		}
		c.nums = k;
	}
	return(true);
}


int getvalue( TSMatrix c, int i, int j )
{
	int k = 0;
	while ( k < c.nums && (c.data[k].r != i || c.data[k].c != j) )
		k++;
	if ( k < c.nums )
		return(c.data[k].d);
	else
		return(0);
}


bool MatMul( TSMatrix a, TSMatrix b, TSMatrix &c )
{
	int		i, j, k, p = 0;
	ElemType	s;
	if ( a.cols != b.rows )
		return(false);
	for ( i = 0; i < a.rows; i++ )
		for ( j = 0; j < b.cols; j++ )
		{
			s = 0;
			for ( k = 0; k < a.cols; k++ )
				s += getvalue( a, i, k ) * getvalue( b, k, j );
			if ( s != 0 )
			{
				c.data[p].r	= i;
				c.data[p].c	= j;
				c.data[p].d	= s;
				p++;
			}
		}
	c.rows	= a.rows;
	c.cols	= b.cols;
	c.nums	= p;
	return(true);
}


int main()
{
	ElemType	a1[N][N]	= { { 1, 0, 3, 0 }, { 0, 1, 0, 0 }, { 0, 0, 1, 0 }, { 0, 0, 1, 1 } };
	ElemType	b1[M][M]	= { { 3, 0, 0, 0 }, { 0, 4, 0, 0 }, { 0, 0, 1, 0 }, { 0, 0, 0, 2 } };
	TSMatrix	a, b, c;
	CreatMat( a, a1 );
	CreatMat( b, b1 );
	printf( "a的三元组:
" );
	DispMat( a );
	printf( "b的三元组:
" );
	DispMat( b );
	printf( "a转置为c
" );
	TranMat( a, c );
	printf( "c的三元组
" );
	DispMat( c );
	printf( "c=a+b
" );
	MatAdd( a, b, c );
	printf( "c的三元组：
" );
	DispMat( c );
	printf( "c=a*b
" );
	MatMul( a, b, c );
	printf( "c的三元组:
" );
	DispMat( c );
	return(0);
}