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+# Sqrt(x) Problem
+
+## Problem Description:
+
+Given a non-negative integer x, return the square root of x rounded down to the nearest integer. The returned integer should be non-negative as well.
+
+You must not use any built-in exponent function or operator.
+
+For example, do not use pow(x, 0.5) in c++ or x ** 0.5 in python.
+
+### Example 1:
+- **Input:** x = 4
+- **Output:** 2
+- **Explanation:** The square root of 4 is 2, so we return 2.
+
+### Example 2:
+- **Input:** x = 8
+- **Output:** 2
+- **Explanation:** The square root of 8 is 2.82842..., and since we round it down to the nearest integer, 2 is returned.
+ 
+### Constraints:
+- 0 <= x <= 231 - 1
+
+## Problem Understanding:
+
+My approach to problems starts with thinking like a human rather than immediately applying coding logic. 
+I ask myself how I would solve the problem without any programming knowledge. This helps me develop a simpler technique. 
+Sometimes, thinking in a programming language can make things more complicated.
+Initially, I may come up with a complex solution, but at least I can optimize it later. However, if I dive straight into coding and things get too complicated, I might not even reach a solution.
+For this problem, I approached it by identifying the range in which the square root of a number (e.g., 48) falls. This method helped me narrow down the possible answers before implementing the solution in code.
+
+## Time and Space Complexity
+
+The time complexity of the initial solution, where you're incrementing i one by one until i * i exceeds x, is indeed O(√x). This is because you're essentially searching for the square root by trying each integer value up to the square root of x.
+The space complexity is O(1) since you're only using a constant amount of extra space (the variable i).
+However, the time complexity can be improved by using a more efficient method ... (coming soon)
+
+🌟Thinking in this way is also useful for live coding practice. Because you're often asked how else it could be written. 
+The first solution is not always the most optimized, and we cannot always know that upfront. That's why we train ourselves to think in this way.
+