Quadrants in which a given coordinate lies
Detailed guide and Python implementation for the 'Quadrants in which a given coordinate lies' problem.
1. Concept Overview
The 'Quadrants in which a given coordinate lies' problem is a key challenge in the Numbers section.
This implementation focuses on easy-level logic in Python.
We prioritize technical accuracy and code readability in our provided solutions.
2. Real-World Applications
3. Visual Intuition
Visualizing the logic flow for Quadrants in which a given coordinate lies.
4. Prerequisites
5. Step-by-Step Thinking
1. Understand the problem
Read the problem statement for Quadrants in which a given coordinate lies carefully.
2. Formulate brute force
Draft a simple iterative solution.
3. Identify inefficiency
Look for redundant calculations.
4. Optimize search path
Use hashing or sorting to speed up the process.
5. Final Implementation
Clean up the code for production standards.
Problem Statement
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
- •-10^4 <= x, y <= 10^4
Examples
find_quadrant(3, 5)
'Quadrant 1'
Both x=3 and y=5 are positive, so the point is in Quadrant 1 (upper-right).
find_quadrant(-2, 4)
'Quadrant 2'
x=-2 is negative and y=4 is positive, so the point is in Quadrant 2 (upper-left).
find_quadrant(-1, -7)
'Quadrant 3'
Both x=-1 and y=-7 are negative, so the point is in Quadrant 3 (lower-left).
Need a Hint?
Edge Cases to Watch
- Empty input structures
- Single element inputs
- Large numerical bounds
Ready to Solve?
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Interview Insights & Variations
Complexity Analysis Breakdown
Why Time: Directly evaluates all possibilities.
Why Space: Uses standard local memory.
Why Time: Optimized paths reduce total operations.
Why Space: May trade memory for speed.
Optimized Solution Python Code
Optimized Solution Python Code
def find_quadrant_opt(x, y):
if x == 0 or y == 0:
return "Origin" if x == 0 and y == 0 else ("Y-axis" if x == 0 else "X-axis")
mapping = {(True, True): 1, (False, True): 2, (False, False): 3, (True, False): 4}
quad = mapping[(x > 0, y > 0)]
suffixes = {1: "st", 2: "nd", 3: "rd", 4: "th"}
return f"{quad}{suffixes[quad]} Quadrant"Brute Force Code (Spoiler Guarded)
Brute Force Code (Spoiler Guarded)
def find_quadrant(x, y):
if x > 0 and y > 0: return "First Quadrant"
elif x < 0 and y > 0: return "Second Quadrant"
elif x < 0 and y < 0: return "Third Quadrant"
elif x > 0 and y < 0: return "Fourth Quadrant"
elif x == 0 and y == 0: return "Origin"
elif x == 0: return "Y-axis"
else: return "X-axis"Algorithm Pattern Checklist
When dealing with Numbers data patterns.
Core Prerequisites
Revision Key Notes
Common Mistakes & Pitfalls
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