April 2024
Intermediate to advanced
832 pages
29h 31m
English
Content preview from Design and Analysis of Algorithms
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698 Design and Analysis of Algorithms
Many times we are only interested in knowing if a path exists or not. This can be shown by a path matrix
[ ], which can be derived from [B] by
p(i, j) = 1 if b(i, j) is non-zero = 0 otherwise;
Alternatively, [P] can be calculated by following the same algorithm as for [B] above, but by replacing
multiplication with logical AND operation and summation with OR operation. This may take less time on a
computer. Note that if any factor in a sequence being ORed is 1 then the result is 1. The following algorithm
by Warshall takes this into account to simplify the calculation of [P] further.
Algorithm Warshall: Given ...
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