New PDF release: Combinatorial Algorithms. For Computers and Calculators

By Albert Nijenhuis

ISBN-10: 0125192606

ISBN-13: 9780125192606

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1. In the remaining η + k — 1 spaces, distribute the η balls with no more than one ball occupying any space. There are obviously m ways of doing this. In each of the other k — 1 spaces which remain, place a vertical bar. W e n o w have a pattern like the one shown in Fig. 2. 2 N o w w e think of the vertical bars as representing cell boundaries. Hence, in Fig. 2 there are 5 cells containing, respectively, 2, 0, 1, 3, 1 balls. It is n o w clear that there are precisely (2) J(n,k)-( n + ^ 1 ) compositions of η into k parts.

Number of elements in desired subset. A ( I ) is the Ith element of the output subset (1=1,K). T o be set = . FALSE . before first call for a new sequence; = . TRUE . if current output is not the last subset; = . FALSE . if current output is the last. 3: N E X T (5) (6) (7) None. SUBROUTINE NEXKSB( Ν , Κ, A,MTC) INTEGER A ( K ) , H LOGICAL MTC I F ( M T C ) GO TO 40 M2=0 H=K GO TO 50 I F ( M 2 . L T . N - H ) H=0 H=H+1 M2=A(K+1-H) DO 51 J = 1 , H A(K+J-H)=M2+J MTC=A(1) . N E . N - K + 1 RETURN END 40 50 51 SUBROUTINE SPECIFICATIONS (NXKSRD) Name of subroutine: NXKSRD .

Flj} and its successor (or predecessor) belong to different segments. W h e n that happens w e have two cases which are symbolized by (4) {1,2, . . , j - l , m - l } â { l , 2 , . . ,j-2,ro-l,ro} G A ( m , j) It is therefore imperative to find these values of m and j quickly. , with the small values of j and m. In fact, if w e reduce j in the sets in (4) by one unit (the reader is invited to see that the same thing happens if j is further reduced) w e w o u l d b e looking for F{1,2, . .

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Combinatorial Algorithms. For Computers and Calculators by Albert Nijenhuis


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