Given a positive number n and precision p, find the square root of number upto p decimal places using binary search.
Note : Prerequisite : Binary search
Input : number = 50, precision = 3 Output : 7.071 Input : number = 10, precision = 4 Output : 3.1622
We have discussed how to compute integral value of square root in Square Root using Binary Search
1) As the square root of number lies in range 0 <= squareRoot <= number, therefore, initialize start and end as : start = 0, end = number.
2) Compare the square of mid integer with the given number. If it is equal to the number, then we found our integral part, else look for the same in left or right side depending upon the scenario.
3) Once we are done with finding the integral part, start computing the fractional part.
4) Initialize the increment variable by 0.1 and iteratively compute the fractional part upto p places. For each iteration, increment changes to 1/10th of it’s previous value.
5) Finally return the answer computed.
Below is the implementation of above approach :
Time Complexity : The time required to compute the integral part is O(log(number)) and constant i.e, = precision for computing the fractional part. Therefore, overall time complexity is O(log(number) + precision) which is approximately equal to O(log(number)).
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