README.md

2001. Number of Pairs of Interchangeable Rectangles

You are given n rectangles represented by a 0-indexed 2D integer array rectangles, where rectangles[i] = [widthi, heighti] denotes the width and height of the ith rectangle.

Two rectangles i and j (i < j) are considered interchangeable if they have the same width-to-height ratio. More formally, two rectangles are interchangeable if widthi/heighti == widthj/heightj (using decimal division, not integer division).

Return the number of pairs of interchangeable rectangles in rectangles.

Example 1:

Input: rectangles = [[4,8],[3,6],[10,20],[15,30]]
Output: 6
Explanation: The following are the interchangeable pairs of rectangles by index (0-indexed):
- Rectangle 0 with rectangle 1: 4/8 == 3/6.
- Rectangle 0 with rectangle 2: 4/8 == 10/20.
- Rectangle 0 with rectangle 3: 4/8 == 15/30.
- Rectangle 1 with rectangle 2: 3/6 == 10/20.
- Rectangle 1 with rectangle 3: 3/6 == 15/30.
- Rectangle 2 with rectangle 3: 10/20 == 15/30.

Example 2:

Input: rectangles = [[4,5],[7,8]]
Output: 0
Explanation: There are no interchangeable pairs of rectangles.

Constraints:

• n == rectangles.length
• 1 <= n <= 105
• rectangles[i].length == 2
• 1 <= widthi, heighti <= 105

Solutions (Python)

1. Solution

class Solution:
    def interchangeableRectangles(self, rectangles: List[List[int]]) -> int:
        count = {}

        for width, height in rectangles:
            x = gcd(width, height)
            width, height = width // x, height // x
            if (width, height) not in count:
                count[(width, height)] = 0
            count[(width, height)] += 1

        return sum(x * (x - 1) // 2 for x in count.values())