Guess the Root
Given a non-negative integer n, find a number r such that r * r = n and round down to the nearest integer.
Can you implement this without using the built-in square root?
Constraints
0 ≤ n < 2 ** 31
https://binarysearch.com/problems/Guess-the-Root
ExamplesPermalink
Example 1Permalink
Input
- n =
9
Output
- answer =
3
Explanation
3 is the square root of 9.
Example 2Permalink
Input
- n =
26
Output
- answer =
5
Explanation
~5.09901951359 is the square root of 26 and rounding down gives us 5.
SolutionPermalink
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| int solve(int n) | |
| { | |
| if (n <= 1) | |
| return n; | |
| float guess = n / 2; | |
| long prev = 0; | |
| while (true) | |
| { | |
| guess = 0.5 * (guess + n / guess); | |
| if (floor(guess) == prev) | |
| { | |
| break; | |
| } | |
| else | |
| { | |
| prev = floor(guess); | |
| } | |
| } | |
| long a = (prev - 1) * (prev - 1); | |
| long b = prev * prev; | |
| long c = (prev + 1) * (prev + 1); | |
| if (a <= n && b > n) | |
| return prev - 1; | |
| else if (b <= n && c > n) | |
| return prev; | |
| else | |
| return prev + 1; | |
| } |
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