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Implement Integer Square Root
Problem: Implement Integer Square Root
Given a non-negative integer x, implement the sqrt(x) function and return the integer part of its square root. This means you should return floor(sqrt(x)).
Requirements:
- You must not use any built-in square root function (e.g.,
Math.sqrt,sqrt) or exponent operator (e.g.,**,pow). - Your solution must correctly handle large 32-bit signed integers without encountering overflow issues during intermediate calculations.
- You are required to explain the time and space complexity of your proposed solution.
Examples:
- If
x = 4, the function should return2. - If
x = 8,sqrt(8)is approximately2.828.... The function should return the integer part, which is2.
Expected Approach:
- Initially, solve the problem using a binary search algorithm.
- As a follow-up, discuss whether there exists a more efficient practical method, such as Newton's method. Compare its performance and characteristics with your binary search solution.
AI interview prep
Core dilemma
Implementing an integer square root function efficiently and correctly for large inputs without relying on built-in mathematical functions, while also demonstrating knowledge of advanced numerical methods.
Mid-level signals3
Senior signals3
Red flags4
2 tradeoffs and 2 stress tests locked
Interview prep
Unlock the interviewer X-Ray rubric, tradeoff matrix, stress tests, clarifying questions, and key concepts.
Implement Integer Square Root
Problem: Implement Integer Square Root
Given a non-negative integer x, implement the sqrt(x) function and return the integer part of its square root. This means you should return floor(sqrt(x)).
Requirements:
- You must not use any built-in square root function (e.g.,
Math.sqrt,sqrt) or exponent operator (e.g.,**,pow). - Your solution must correctly handle large 32-bit signed integers without encountering overflow issues during intermediate calculations.
- You are required to explain the time and space complexity of your proposed solution.
Examples:
- If
x = 4, the function should return2. - If
x = 8,sqrt(8)is approximately2.828.... The function should return the integer part, which is2.
Expected Approach:
- Initially, solve the problem using a binary search algorithm.
- As a follow-up, discuss whether there exists a more efficient practical method, such as Newton's method. Compare its performance and characteristics with your binary search solution.