By Robert Sedgewick
This publication is meant to survey crucial algorithms in use on desktops at the present time and educate the elemental recommendations to the becoming inhabitants drawn to turning into critical laptop clients.
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Extra info for Algorithms (Addison-Wesley series in computer science)
Matrices We can proceed in a similar manner to implement basic operations on twodimensional matrices, though the programs become more complicated. maxN] of real; N, i, j: integer; begin readln (N) ; for i:=O to N-l do for j:=O to N-l do read(p[i, j]); for i:=O to N-l do for j:=O to N-l do read(q[i, j]); for i:=O to N-l do for j:=O to N-l do r[i, j]:=p[i, j]+q[i, j]; for i:=O to N-l do for j:=O to N do if j=N then writeln else write(r[i, j]); end. Matrix multiplication is a more complicated operation.
Though the situation is beginning to change, the raison d’e^tre of many computer systems is their capability for doing fast, accurate numerical calculations. Computers have built-in capabilities to perform arithmetic on integers and floating-point representations of real numbers; for example, Pascal allows numbers to be of type integer or re;d, with all of the normal arithmetic operations defined on both types. Algorithms come into play when the operations must be performed on more complicated mathematical objects, such as polynomials or matrices.
For our example, Element r[i, j] is the dot product of the ith row of p with the jth column of q. The dot product is simply the sum of the N term-by-term multiplications p[i, l]*q[l, j]+p[i, 2]*q[2, j]+... o; for k:=iO to N-l do t:=t+p[i, k]*q[k, j]; r[i, j]:=t end ; Each of the N2 elements in the result matrix is computed with N multiplications, so about N3 operations are required to multiply two N by N matrices together. ) As with polynomials, sparse matrices (those with many zero elements) can be processed in a much more efficient manner using a linked list representation.