Problem 1 : Fast one-hot checker
A bit vector is one-hot if and only if there is at most one 1 in the
vector. For example, 0000 and 00100 are one-hot and 00110 is not one-hot.
Please find the fastest way to check whether a bit vector is one-hot or not.

Problem 2 : 3-Inverter
Assume that a logical blackbox has three Boolean inputs x, y, z and
three Boolean outputs X, Y, Z where the outputs are defined as

X = ~x

Y = ~y

Z = ~z

Note that ~ stands for a NOT gate. Please realize this blackbox using
only two NOT gates, and as many as possible AND and OR gates.

Problem 3 : Is it a loop ?
Assume that we have a head pointer to a link-list. Also assume that
we know the list is single-linked. Can you come up an algorithm to check
whether this link list includes a loop by using O(n) time and O(1) space
where n is the length of the list? Furthermore, can you do so with O(n)
time and only one register?

Problem 4 : Detect same sequence
Assume that we have a m*n matrix A where both m >= 1K and n >= 100K. X_i is

a row vector of A where 1 <= i <= m. In other words, A = {X_1, X_2, ..., X_m}.

Please find a fastest algorithm to detect all pairs (X_i, X_j), where X_i == X
_j.