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来自「浙江大学计算机学院数据结构课程的教学课件」· HTM 代码 · 共 60 行
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<pre align="left"><font face="Arial Black"><b><font face="Arial" size="4">
<font size="5" color="#ff0033">2.4 The Sparse Matrix Abstract Data Type</font>
<font color="#0000FF"> <i>Sparse Matrix</i></font> ------a matrix which contains many zero entries
<font color="#0033CC">DEFINITION</font>
_____________________________________________________
structure <font color="#CC0033"><font face="Arial, Helvetica, sans-serif" color="#FF0000">Sparse_Matrix</font></font> is
<font color="#0033CC"> object: </font>a set of triples,<font color="#0033CC"> <i><row,column, value></i>,</font> where<i><font color="#FF0033"> row</font></i> and
<i><font color="#FF0033">column</font></i> are integers and form a unique combination,
and <i><font color="#FF0033">value</font></i> comes from the set item.
<font color="#0033CC"> function:</font>
for all<i> a, b</i> <img src="image/Image4.gif" width="13" height="13"><font size="3"> Sparse_Matrix</font>, <i>x </i></font><font face="Arial Black"><b><font face="Arial" size="4"><img src="image/Image4.gif" width="13" height="13"></font></b></font><font face="Arial" size="4"> item,
<i> i, j, max_col, max_row</i><img src="image/Image4.gif" width="13" height="13"> index
<font color="#FF0099"> Sparse_Matrix Create(<i>max_row, max_col</i>) </font> ::=
return a <font color="#000000" size="3">Sparse_Matrix</font> that can hold up to
<font color="#0033CC" face="Arial, Helvetica, sans-serif"><i>max_item = max_row*max_col</i></font> and whose
maximum row size is max_row and whose
maximum column size is max_col.
<font color="#FF0099"> Sparse_Matrix Transpose( a) </font> ::=
return the matrix produced by interchanging
the <i><font color="#0033CC">row</font> </i>and <i><font color="#0033CC">column</font></i> value of every triple.
<font color="#FF0099"> Sparse_Matrix Add(a, b)</font> ::=
if the dimensions of a and b are the same
return the matrix produced by adding
corresponding items, namely those with
identical row and column value.
else return error
<font color="#FF0099">Sparse_Matrix Multiply (a, b</font></font><font face="Arial Black" color="#FF0099"><b><font face="Arial" size="4">)</font></b></font><font face="Arial" size="4" color="#FF0099"> </font><font face="Arial" size="4"> ::=
if number of <i><font color="#0033CC">column</font></i><font color="#0033CC"> </font>in <font face="Arial, Helvetica, sans-serif" color="#FF0000">a</font> equals number of <i><font color="#0033CC">row</font></i><font color="#0033CC"> </font>in <font face="Arial, Helvetica, sans-serif" color="#FF0000">b</font>
return the matrix<font color="#FF0033"><i> d</i></font> produced by multiplying <font face="Arial, Helvetica, sans-serif" color="#FF0000">a</font> by <font face="Arial, Helvetica, sans-serif" color="#FF0000">b</font><i> </i>
according to the formula:
<font color="#0033CC"> d [i][j] = </font><font face="Arial Black"><b><font face="Arial" size="4"><font color="#0033CC"><img src="image/sum0.gif" width="20" height="24"></font></font></b></font><font color="#0033CC"> (a[i][k]·b[k][j]) </font>where d <i>(i, j) </i>
is the <i>(i, j)</i>th element
else return error.
end <font color="#FF0033">Sparse_Matrix</font>
__________________________________________________________</font></b>
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