int main(){
int i;
/*Declare an integer n and assign it a value of 20.*/
int n = 20;
/*Allocate memory for an array of n integers using malloc.*/
int *numbers = malloc(n * sizeof(int));
/*Fill this array with random numbers, using rand().*/
initializeSeed();
for(i =0; i < n; i ++){
numbers[i] = randomNumber(100);/*Will return a number from 0 to 99*/
}
/*Print the contents of the array.*/
for(i = 0; i < n; i ++){
printf("Contents of array[%d]: %d\n", i, numbers[i]);
}
/*Pass this array along with n to the sort() function of part a.*/
sort(numbers,n);
/*Print the contents of the array.*/
for(i = 0; i < n; i ++){
printf("Contents of sorted array[%d]: %d\n", i, numbers[i]);
}
return 0;
}
BOOLEAN randomSchreier(
PermGroup *const G,
RandomSchreierOptions rOptions)
{
Unsigned noOfOriginalGens, successCount, level, finalLevel,
nonInvolRejectCount, levelLowestOrder;
unsigned long curOrder, lowestOrder;
Permutation **originalGen;
FactoredInt trueGroupOrder, factoredOrbLen;
Permutation *gen;
Permutation *randGen = newIdentityPerm( G->degree),
*h = newUndefinedPerm( G->degree),
*lowestOrderH = newUndefinedPerm( G->degree),
*tempPerm;
/* Set defaults for options. */
if ( rOptions.initialSeed == 0 )
rOptions.initialSeed = 47;
if ( rOptions.minWordLengthIncrement == UNKNOWN )
rOptions.minWordLengthIncrement = 7;
if ( rOptions.maxWordLengthIncrement == UNKNOWN )
rOptions.maxWordLengthIncrement = 23;
if ( rOptions.stopAfter == UNKNOWN )
if ( G->order )
rOptions.stopAfter = 10000;
else
rOptions.stopAfter = 40;
if ( rOptions.reduceGenOrder == UNKNOWN )
rOptions.reduceGenOrder = TRUE;
if ( rOptions.rejectNonInvols == UNKNOWN )
rOptions.rejectNonInvols = 0;
if ( rOptions.rejectHighOrder == UNKNOWN )
rOptions.rejectHighOrder = 0;
if ( rOptions.onlyEssentialInitGens == UNKNOWN )
rOptions.onlyEssentialInitGens = FALSE;
if ( rOptions.onlyEssentialAddedGens == UNKNOWN )
rOptions.onlyEssentialAddedGens = TRUE;
/* Initialize seed. */
initializeSeed( rOptions.initialSeed);
/* Check that fields of G that must be null initially actually are. Then
allocate these fields. */
if ( G->base || G->basicOrbLen || G->basicOrbit || G->schreierVec )
ERROR( "randschr", "A group field that must be null initially was "
"nonnull.")
G->base = allocIntArrayBaseSize();
G->basicOrbLen = allocIntArrayBaseSize();
G->basicOrbit = (UnsignedS **) allocPtrArrayBaseSize();
G->schreierVec = (Permutation ***) allocPtrArrayBaseSize();
/* If the true group order is known, set trueGroupOrder to it. Otherwise
allocate G->order and mark trueGroupOrder as undefined (i.e.,
noOfFactors == UNKNOWN). Then set G->order to 1. */
if ( G->order )
trueGroupOrder = *G->order;
else {
G->order = allocFactoredInt();
trueGroupOrder.noOfFactors = UNKNOWN;
}
G->order->noOfFactors = 0;
/* Delete identity generators from G if present. Return immediately if
G is the identity group. */
removeIdentityGens( G);
if ( !G->generator) { /* Should we allocate G->base, etc??? */
G->baseSize = 0;
return TRUE;
}
/* Adjoin an inverse image array to each permutation if absent. */
adjoinGenInverses( G);
/* Choose an initial segment of the base so that each generator moves
some base point. */
initializeBase( G);
/* Here we allocate and construct an array of pointers to the original
generators. */
noOfOriginalGens = 0;
originalGen = allocPtrArrayDegree();
for ( gen = G->generator ; gen ; gen = gen->next )
originalGen[++noOfOriginalGens] = gen;
/* Fill in the level of each generator, and make each generator essential
at its level and above. (????) */
for ( gen = G->generator ; gen ; gen = gen->next ) {
gen->level = levelIn( G, gen);
MAKE_NOT_ESSENTIAL_ALL( gen);
for ( level = 1 ; level <= gen->level ; ++level )
MAKE_ESSENTIAL_AT_LEVEL( gen, level);
}
/* Construct the orbit length, basic orbit, and Schreier vector arrays. Set
G->order (previously allocated) to the product of the basic orbit
lengths. */
G->order->noOfFactors = 0;
for ( level = 1 ; level <= G->baseSize ; ++level ) {
G->basicOrbLen[level] = 1;
G->basicOrbit[level] = allocIntArrayDegree();
G->schreierVec[level] = allocPtrArrayDegree();
if ( rOptions.onlyEssentialInitGens )
constructBasicOrbit( G, level, "FindEssential");
else
constructBasicOrbit( G, level, "AllGensAtLevel" );
}
/* The variable successCount will count the number of consecutive times
the quasi-random group element can be factored successfully. */
successCount = 0;
nonInvolRejectCount = 0;
while ( successCount < rOptions.stopAfter &&
(trueGroupOrder.noOfFactors == UNKNOWN ||
!factEqual( G->order, &trueGroupOrder)) ) {
randomizeGen( noOfOriginalGens, originalGen,
rOptions.minWordLengthIncrement,
rOptions.maxWordLengthIncrement, randGen);
if ( factorGroupElt( G, randGen, h, &finalLevel) )
++successCount;
else {
successCount = 0;
if ( rOptions.reduceGenOrder )
replaceByPower( G, finalLevel, h);
if ( nonInvolRejectCount >= rOptions.rejectNonInvols ||
isInvolution( h) ) {
if ( nonInvolRejectCount > 0 &&
(lowestOrder < (curOrder = permOrder(h)) ||
lowestOrder == curOrder && levelLowestOrder > finalLevel) ) {
tempPerm = h; h = lowestOrderH; lowestOrderH = tempPerm;
finalLevel = levelLowestOrder;
}
if ( finalLevel == G->baseSize+1 ) {
if ( G->baseSize >= options.maxBaseSize )
ERROR1i( "initializeBase",
"Base size exceeded maximum of ",
options.maxBaseSize, ". Rerun with -mb option.")
G->base[++G->baseSize] = pointMovedBy( h);
G->basicOrbLen[G->baseSize] = 1;
G->basicOrbit[G->baseSize] = allocIntArrayDegree();
G->schreierVec[G->baseSize] = allocPtrArrayDegree();
}
assignGenName( G, h);
addStrongGenerator( G, h, FALSE);
h = newUndefinedPerm( G->degree);
nonInvolRejectCount = 0;
}
else {
curOrder = permOrder( h);
if ( curOrder == 0 )
curOrder = ULONG_MAX;
if ( nonInvolRejectCount == 0 || curOrder < lowestOrder ||
(curOrder == lowestOrder && finalLevel > levelLowestOrder) ) {
copyPermutation( h, lowestOrderH);
lowestOrder = curOrder;
levelLowestOrder = finalLevel;
}
++nonInvolRejectCount;
}
}
}
freePtrArrayDegree( originalGen);
deletePermutation( randGen);
deletePermutation( h);
deletePermutation( lowestOrderH);
return trueGroupOrder.noOfFactors != UNKNOWN &&
factEqual( G->order, &trueGroupOrder);
}
