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Let me be real with you: when I saw today’s coding challenge for the first time, I was completely lost. Let's see if you can crack it.

Today we will cover:

• Bitwise AND of Numbers Range

• CAP Theorem in Practice

Read time: under 4 minutes

CODING CHALLENGE

Bitwise AND of Numbers Range

Given two integers left and right that represent the range [left, right], return the bitwise AND of all numbers in this range, inclusive.

Example 1:

Input: left = 5, right = 7
Output: 4

Example 2:

Input: left = 0, right = 0
Output: 0

Example 3:

Input: left = 1, right = 2147483647
Output: 0

Solve the problem here before reading the solution.

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SOLUTION

When you AND all numbers in a range together, only the bits that stay constant across every number survive. Everything else becomes zero.

Within the range [left , right], the least significant bits will change. But the most significant bits (the prefix) remain the same across the range. So you just need to find the longest common binary prefix of left and right.

Here is how to solve the problem:

1. Continuously right-shift both left and right numbers until they become equal. This will give you the longest common prefix.

2. Keep track of the number of shifts

3. Left-shift the prefix by the number of shifts to get the answer

For example:

• left = 5 (101 in binary)

• right = 7 (111 in binary)

Shifting right once gives:

• 5 becomes 2 (010 in binary)

• 7 becomes 3 (011 in binary)

Shift right one more time, both become 1.

1 is your prefix which we got by shifting right 2 times. Shift this prefix left 2 times, we get 4 (100 in binary) which is our answer.

SYSTEM DESIGN

CAP Theorem in Practice

When building distributed systems, you'll often hear about the CAP theorem. It states that when data is distributed across multiple servers, you can only have two out of these three properties: Consistency, Availability, and Partition Tolerance. Let's understand what this means in practice.

Consistency means all servers have the same data at any given time. If you write data to one server, all other servers should show this updated data. Availability means the system remains operational even if some servers fail. Partition Tolerance means the system continues to work even when network issues prevent servers from communicating with each other.

In real distributed systems, network partitions will happen. Servers will lose connection with each other due to network issues, hardware failures, or maintenance. This means Partition Tolerance isn't really optional, you must have it. So practically, you're choosing between Consistency and Availability.

If you choose Consistency over Availability (CP system), when a network partition occurs, some parts of your system become unavailable to maintain consistency. For example, if two database servers can't communicate, one might stop accepting writes to prevent inconsistent data.

If you choose Availability over Consistency (AP system), your system keeps working during network partitions, but different servers might show different data temporarily. Once the network issues resolve, the servers sync up their data.

Here's how popular databases handle this trade-off:

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