Rectangle Overlap

LeetCode 866 | Difficulty: Easy

Easy

Problem Description

An axis-aligned rectangle is represented as a list [x1, y1, x2, y2], where (x1, y1) is the coordinate of its bottom-left corner, and (x2, y2) is the coordinate of its top-right corner. Its top and bottom edges are parallel to the X-axis, and its left and right edges are parallel to the Y-axis.

Two rectangles overlap if the area of their intersection is positive. To be clear, two rectangles that only touch at the corner or edges do not overlap.

Given two axis-aligned rectangles rec1 and rec2, return true if they overlap, otherwise return false.

Example 1:

Input: rec1 = [0,0,2,2], rec2 = [1,1,3,3]
Output: true

Example 2:

Input: rec1 = [0,0,1,1], rec2 = [1,0,2,1]
Output: false

Example 3:

Input: rec1 = [0,0,1,1], rec2 = [2,2,3,3]
Output: false

Constraints:

- `rec1.length == 4`

- `rec2.length == 4`

- `-10^9 <= rec1[i], rec2[i] <= 10^9`

- `rec1` and `rec2` represent a valid rectangle with a non-zero area.

Topics: Math, Geometry

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Approach

Mathematical

Look for mathematical patterns or formulas. Consider: modular arithmetic, GCD/LCM, prime factorization, combinatorics, or geometric properties.

When to use

Problems with clear mathematical structure, counting, number properties.

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Solutions

Solution 1: C# (Best: 164 ms)

Metric	Value
Runtime	164 ms
Memory	38.2 MB
Date	2022-01-27

Solution

public class Solution {
    public bool IsRectangleOverlap(int[] rec1, int[] rec2) {
     int left = Math.Max(rec1[0], rec2[0]);
    int right = Math.Min(rec1[2], rec2[2]);
    int bottom = Math.Max(rec1[1], rec2[1]);
    int top = Math.Min(rec1[3], rec2[3]);
    int overlap = 0;
    if (right > left && top > bottom)
    {
        return true;
    }
    return false;
    }
}

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Complexity Analysis

Approach	Time	Space
Solution	$O(n)$	$O(1) to O(n)$

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Interview Tips

Key Points

• Start by clarifying edge cases: empty input, single element, all duplicates.