1725. Number Of Rectangles That Can Form The Largest Square
Description
You are given an array rectangles
where rectangles[i] = [li, wi]
represents the ith
rectangle of length li
and width wi
.
You can cut the ith
rectangle to form a square with a side length of k
if both k <= li
and k <= wi
. For example, if you have a rectangle [4,6]
, you can cut it to get a square with a side length of at most 4
.
Let maxLen
be the side length of the largest square you can obtain from any of the given rectangles.
Return the number of rectangles that can make a square with a side length of maxLen
.
Example 1:
Input: rectangles = [[5,8],[3,9],[5,12],[16,5]] Output: 3 Explanation: The largest squares you can get from each rectangle are of lengths [5,3,5,5]. The largest possible square is of length 5, and you can get it out of 3 rectangles.
Example 2:
Input: rectangles = [[2,3],[3,7],[4,3],[3,7]] Output: 3
Constraints:
1 <= rectangles.length <= 1000
rectangles[i].length == 2
1 <= li, wi <= 109
li != wi
Solutions
Solution 1: Single Pass
We define a variable $ans$ to record the count of squares with the current maximum side length, and another variable $mx$ to record the current maximum side length.
We traverse the array $rectangles$. For each rectangle $[l, w]$, we take $x = \min(l, w)$. If $mx < x$, it means we have found a larger side length, so we update $mx$ to $x$ and update $ans$ to $1$. If $mx = x$, it means we have found a side length equal to the current maximum side length, so we increase $ans$ by $1$.
Finally, we return $ans$.
The time complexity is $O(n)$, where $n$ is the length of the array $rectangles$. The space complexity is $O(1)$.
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