6 Perfect Square
Problem Statement
Write a Recursive Solution to Check if a Given Number is a Perfect Square or Not.
The problem is to determine whether a given positive number is a perfect square or not. A square number or perfect square is an integer that is the square of an integer; in other words, it is the product of some integer with itself.
Examples
| Input | Output | Explanation |
|---|---|---|
| 16 | True | 16 is a perfect square because 4 * 4 = 16. |
| 14 | False | 14 is not a perfect square because there is no integer whose square is equal to 14. |
| 9 | True | 9 is a perfect square because 3 * 3 = 9. |
Constraints:
- 1 <= n <= 104
Try it yourself
Try solving this question here:
🎯 STRICT STANDOUT — Problem cue: Perfect Square
1. Why
Find i with i²=n. Linear O(n); binary search on i is O(log n). Recursion optional on BS form.
2. Big-O (K11)
Linear i scan O(n); binary mid*mid vs n: O(log n); recursive BS stack O(log n)3. Pattern + when-NOT
BINARY SEARCH ON ANSWER. When-NOT: recurse i=i+1 to n (O(n) stack).
4. Edge
0,1 true; 2 false; 16 true; 14 false; neg false; mid*mid overflow → long5. Panel
Q: Why BS works? A: i² monotone for i≥0.
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