Power of Two

Background Knowledge

The problem "Power of Two" involves determining whether a given integer n is a power of two. To understand this, it's essential to know what it means for a number to be a power of two. A power of two is any number that can be expressed as $2^x$, where $x$ is an integer. For example, 1, 2, 4, 8, and 16 are all powers of two because they can be expressed as $2^0$, $2^1$, $2^2$, $2^3$, and $2^4$, respectively.

In the context of bit manipulation, which is a crucial aspect of this problem, it's important to understand how numbers are represented in binary. In binary, each digit (or bit) represents a power of two. For instance, the number 8 in binary is 1000, where the leftmost bit represents $2^3$, and the other bits represent lower powers of two. This binary representation is key to solving the "Power of Two" problem efficiently.

Understanding the properties of powers of two and how they are represented in binary will help in devising an efficient algorithm. Specifically, recognizing that powers of two have exactly one bit set to 1 in their binary representation (e.g., 8 is 1000, 16 is 10000) can guide the development of a solution that leverages bitwise operations.