/*
*
* I took a brute force approach to this, using some rough math first to know that I should start around 18-20,
* After one day, I found a 19 card deal without a set, then continued on with 20
* this random guesser with infinite loops took 5 days on a powerful computer to randomly find the 20 nonset deal
* There was a 1 in 4,694,436,188,839,116,720 (I think) chance of this happening per iteration! (I got lucky on the random)
* I ran it on 21, but by the deadline the 20 is all I found. I think that this is the true largest anyway
* Here's the output of the 20 cards it found without a set:
A Purple Striped Oval with the number 1
A Green Striped Diamond with the number 2
A Green Solid Oval with the number 1
A Purple Open Squiggle with the number 3
A Purple Solid Squiggle with the number 2
A Purple Solid Oval with the number 1
A Purple Solid Squiggle with the number 1
A Green Striped Diamond with the number 1
A Purple Solid Oval with the number 2
A Green Open Diamond with the number 3
A Green Solid Oval with the number 2
A Green Striped Oval with the number 1
A Red Striped Diamond with the number 3
A Purple Striped Oval with the number 2
A Purple Striped Squiggle with the number 3
A Green Solid Diamond with the number 3
A Green Striped Oval with the number 2
A Green Solid Squiggle with the number 3
A Purple Striped Diamond with the number 3
A Red Solid Squiggle with the number 3
* Average number of available sets at -
* 12: 12!/(9!3!) * 1/79 = 2.78...
* 18: 18!/(15!3!) * 1/79 = 10.33
* 19: 19!/(16!3!) * 1/79 = 12.27
* 20: 20!/(17!3!) * 1/79 = 14.43
*
*/
void SetGame::findLargestNonSet()
{
vector<Card> NoSetCards;
vector<Card> testCards;
Deck testDeck;
int startNum = 19;
for (int num = 0; num < 3; num++)
{
// this will run for a long time and has a small chance of succeeding!!!
for (int i = 0; i < 10000; i++)
// while (true)
{
testDeck.Shuffle();
testDeck.Deal(startNum + num, testCards);
if (findAllSets(testCards, false).size() == 0)
{
cout << "Found no sets in a deal of " << startNum + num << " cards. Continuing with " << startNum + num + 1 << endl;
NoSetCards = testCards;
break;
}
else if (i % 100 == 0)
{
cout << "Testing " << startNum + num << " the " << i << "th time" << endl;
}
else if (i == 9999)
{
cout << "Found sets in 10000 random deals of " << startNum + num << " cards" << endl;
goto END;
}
testDeck.Replace(testCards);
}
}
END:
printCards(NoSetCards);
int x;
cin >> x;
}
