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
方法：使用两个指针，从头开始，一个一次前进一个节点，一个前进2个节点，则最多2N，后两个指针可以重合；如果无环，则正常停止。
同样的，可以找到链表的中间节点。同上。
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.