number-of-pairs-of-interchangeable-rectangles

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Algorithms

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

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

Return the number of pairs of interchangeable rectangles in <code>rectangles</code>.

&nbsp;
Example 1:

<pre>
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.
</pre>

Example 2:

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

&nbsp;
Constraints:

<ul>
	<li><code>n == rectangles.length</code></li>
	<li><code>1 &lt;= n &lt;= 105</code></li>
	<li><code>rectangles[i].length == 2</code></li>
	<li><code>1 &lt;= widthi, heighti &lt;= 105</code></li>
</ul>

interchangeableRectangles

Number of Pairs of Interchangeable Rectangles

Number of Good Pairs

number-of-good-pairs

好数对的数目

Count Nice Pairs in an Array

count-nice-pairs-in-an-array

统计一个数组中好对子的数目

Replace Non-Coprime Numbers in Array

replace-non-coprime-numbers-in-array

替换数组中的非互质数

Array

Hash Table

Math

Counting

Number Theory

用一个下标从 0 开始的二维整数数组&nbsp;<code>rectangles</code> 来表示 <code>n</code> 个矩形，其中 <code>rectangles[i] = [widthi, heighti]</code> 表示第 <code>i</code> 个矩形的宽度和高度。

如果两个矩形 <code>i</code> 和 <code>j</code>（<code>i &lt; j</code>）的宽高比相同，则认为这两个矩形 可互换 。更规范的说法是，两个矩形满足&nbsp;<code>widthi/heighti == widthj/heightj</code>（使用实数除法而非整数除法），则认为这两个矩形 可互换 。

计算并返回&nbsp;<code>rectangles</code> 中有多少对 可互换 矩形。

&nbsp;

示例 1：

<pre>
输入：rectangles = [[4,8],[3,6],[10,20],[15,30]]
输出：6
解释：下面按下标（从 0 开始）列出可互换矩形的配对情况：
- 矩形 0 和矩形 1 ：4/8 == 3/6
- 矩形 0 和矩形 2 ：4/8 == 10/20
- 矩形 0 和矩形 3 ：4/8 == 15/30
- 矩形 1 和矩形 2 ：3/6 == 10/20
- 矩形 1 和矩形 3 ：3/6 == 15/30
- 矩形 2 和矩形 3 ：10/20 == 15/30
</pre>

示例 2：

<pre>
输入：rectangles = [[4,5],[7,8]]
输出：0
解释：不存在成对的可互换矩形。
</pre>

&nbsp;

提示：

<ul>
	<li><code>n == rectangles.length</code></li>
	<li><code>1 &lt;= n &lt;= 105</code></li>
	<li><code>rectangles[i].length == 2</code></li>
	<li><code>1 &lt;= widthi, heighti &lt;= 105</code></li>
</ul>