II. Notes on Data Structuring * - Cornell University

end
NOTES ON DATA STRUCTURING 129
n.w: = n.w + next.w;
if n. b >i wordlength then begin n. w: -- n. w + 1 ;
end
n. b: = n. b - wordlength
Since this appears acceptably efficient we will code the other operations of
the outer loop, starting with the most dimcult"
next" = rain (sieve);
Here we do not wish to start our search for the minimum at the beginning
of the sieve set each time, since towards the end of the process this would
involve scanning many empty words. We therefore take advantage of the
fact that the new value of next must be larger than the old value.
The search consists of two parts, first finding a nonempty word, and then
its first bit. But if the search for a word reaches the end of the array, the
whole program is completed
while sieve [next. w] = { } do {next. w: = next. w + 1 ;
if next. w > W then exit primefinder };
next. b: = min (sieve [next. w]);
The remaining operations are trivial Since the outer loop is terminated
by an exit, there is no need to test a separate while condition; and the
statement
primes" v {next };
can be coded as
primes [next. w]: v {next. b }.
The whole program including initialisation is as follows"
primes, sieve:array 0.. W of powerset 0.. wordlength - 1 ;
begin primefinder;
n, next:(w, b:integer);
for t:O.. W do begin primes [t]: = ( };
end;
sieve [0]: - (0, 1 };
next. w: = O;
while true do
sieve [t]: = range (0.. wordlength - 1
begin while sieve [next. w] = ( ) do