2001. Number of Pairs of Interchangeable Rectangles

Description

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

Solution: Hash Table

• Time complexity: O(n)
• Space complexity: O(n)

 

JavaScript

/**
 * @param {number[][]} rectangles
 * @return {number}
 */
const interchangeableRectangles = function (rectangles) {
  const interchangeMap = rectangles.reduce((map, [width, height]) => {
    const division = width / height;
    const count = map.get(division) ?? 0;

    return map.set(division, count + 1);
  }, new Map());
  let result = 0;

  for (const [_, count] of interchangeMap) {
    result += (count * (count - 1)) / 2;
  }
  return result;
};