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 = 4Output: 2Explanation: The square root of 4 is 2, so we return 2.Example 2:Input: x = 8Output: 2Explanation: The square root of 8 is 2.82842..., and since we round it down to the nearest integer, 2 is returned.
Question
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 = 4Output: 2Explanation: The square root of 4 is 2, so we return 2.Example 2:Input: x = 8Output: 2Explanation: The square root of 8 is 2.82842..., and since we round it down to the nearest integer, 2 is returned.
Solution
Sure, here is a Python solution using binary search:
def sqrt(x):
if x < 2:
return x
left, right = 2, x // 2
while left <= right:
pivot = left + (right - left) // 2
num = pivot * pivot
if num > x:
right = pivot -1
elif num < x:
left = pivot + 1
else:
return pivot
return right
This function works by performing a binary search for the square root of x. It starts with a range of possible values for the square root, from 2 to x // 2. It then repeatedly calculates the square of the midpoint of this range, and adjusts the range based on whether this square is too high or too low. When the range has been narrowed down to a single value, this value is the square root of x, rounded down to the nearest integer.
Similar Questions
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Krish, a curious explorer in a unique computational environment, explores numerical transformations. The system swiftly calculates and displays the cube for positive numbers, while it diligently calculates and returns the square value for negative numbers.Write a program to achieve this and use the return statement accordingly.Input format :The input consists of a single integer n.Output format :The output displays "Cube value: " followed by the cube value of n if the number is positive and terminates.The output displays "Squared value: " followed by the squared value of n if the number is negative or zero and terminates.Refer to the sample output for the formatting specifications.Code constraints :In the given scenario, the test cases fall under the following constraints:-100 ≤ n ≤ 100Sample test cases :Input 1 :100Output 1 :Cube value: 1000000Input 2 :-20Output 2 :Squared value: 400Input 3 :0Output 3 :Squared value: 0
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