Multiset

This is a Set that is also ordered, the benefits is that you can store duplicates.

// empty multiset container
multiset<int, greater<int> > gquiz1;
// insert elements in random order
gquiz1.insert(40);
gquiz1.insert(50);
gquiz1.insert(50);  // 50 will be added again to the multiset unlike set
gquiz1.insert(10);

In the for loop, it will print x multiple times.

for (auto x: s) {
	cout << x << endl;
}

MATH239

Definition 1.8. Let $n\ge 0$ and $t\ge 1$ be integers. A multiset of size $n$ with elements of $t$ types is a sequence of nonnegative integers $(m_1,\dots ,m_t)$ such that $m_1+m_2+\cdots +m_t=n$

Theorem 1.9. For any $n\ge 0$ and $t\ge 1$, the number of $n$-element multisets with elements of $t$ types is $\left(\genfrac{}{}{0ex}{}{n+t-1}{t-1}\right)$