Welcome to this quick but exciting lesson on Bit Manipulation Techniques. Bit manipulation is a powerful technique used in programming to efficiently solve problems that may seem complex or resource-intensive at first. By examining and manipulating the binary representations of data, we can develop solutions that satisfy the problem requirements while maintaining good time and space complexity.

In this lesson, we'll practice techniques such as setting and clearing bits, counting set bits, and bit masking. We will be using Go, a language that provides straightforward and effective tools for performing bitwise operations, to illustrate these techniques.

Take a look at the preview problem:

Go
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1package main
2
3import "fmt"
4
5func countSetBits(n int) int {
6    count := 0
7    for n != 0 {
8        n = n & (n - 1)
9        count++
10    }
11    return count
12}
13
14func main() {
15    n := 6
16    fmt.Println("Number of set bits:", countSetBits(n))
17}

This function counts the number of set bits (1s) in the binary representation of a number. The & operator is used for the bitwise AND operation. The n - 1 operation flips the least significant bit that is set (the rightmost 1 bit in the binary representation) of n to 0, and n = n & (n - 1) applies this change to n. The for loop continues until n becomes 0, and for each iteration, the count is increased, tracking the number of set bits.

For example, consider n = 6, which is 110 in binary:

• n - 1 is 5 (101 in binary);
• The bitwise AND operation 110 & 101 results in 100.
• The right-most 1 has been removed from n, and the count is increased by one.

Now, it's time to roll up your sleeves and put these techniques into practice. Our exercises will challenge you and help deepen your understanding of bit manipulation. Remember, the goal is not just to learn how to solve specific problems but to understand the fundamentals of bit manipulation and how to apply this knowledge to solve a wide variety of problems. Let's get started!