What is the optimal time complexity of solving Quadrants in which a given coordinate lies?

The optimized solution achieves a time complexity of O(n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Quadrants in which a given coordinate lies?

The space complexity is O(1) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in Quadrants in which a given coordinate lies?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for Quadrants in which a given coordinate lies?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

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Quadrants in which a given coordinate lies

Learn how to solve the 'Quadrants in which a given coordinate lies' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

Write a function find_quadrant(x, y) that takes two integers x and y representing a point on the Cartesian plane and returns a string indicating which quadrant the point lies in.

Return:

- 'Quadrant 1' if x > 0 and y > 0

- 'Quadrant 2' if x < 0 and y > 0

- 'Quadrant 3' if x < 0 and y < 0

- 'Quadrant 4' if x > 0 and y < 0

- 'Origin' if x == 0 and y == 0

- 'X-Axis' if y == 0 and x != 0

- 'Y-Axis' if x == 0 and y != 0

Constraints

•-10^4 <= x, y <= 10^4

Examples

Example 1

Input

find_quadrant(3, 5)

Output

'Quadrant 1'

Explanation

Both x=3 and y=5 are positive, so the point is in Quadrant 1 (upper-right).

Example 2

Input

find_quadrant(-2, 4)

Output

'Quadrant 2'

Explanation

x=-2 is negative and y=4 is positive, so the point is in Quadrant 2 (upper-left).

Example 3

Input

find_quadrant(-1, -7)

Output

'Quadrant 3'

Explanation

Both x=-1 and y=-7 are negative, so the point is in Quadrant 3 (lower-left).

Need a Hint?

Use simple arithmetic operators (like modulo `%`, division `//`), conditional checks, or loops to inspect number properties.

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

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