2001. Number of Pairs of Interchangeable Rectangles - Explanation

class Solution:
    def interchangeableRectangles(self, rectangles: List[List[int]]) -> int:
        res = 0
        for i in range(1, len(rectangles)):
            for j in range(i):
                if rectangles[i][0] / rectangles[i][1] == rectangles[j][0] / rectangles[j][1]:
                    res += 1
        return res

class Solution:
    def interchangeableRectangles(self, rectangles: List[List[int]]) -> int:
        count = {}
        for w, h in rectangles:
            count[w / h] = 1 + count.get(w / h, 0)

        res = 0
        for c in count.values():
            if c > 1:
                res += (c * (c - 1)) // 2
        return res

class Solution:
    def interchangeableRectangles(self, rectangles: List[List[int]]) -> int:
        count = {}
        res = 0
        for w, h in rectangles:
            res += count.get(w / h, 0)
            count[w / h] = 1 + count.get(w / h, 0)
        return res

class Solution:
    def hash(self, a: int, b: int) -> int:
        mask = a
        mask |= (b << 31)
        return mask

    def interchangeableRectangles(self, rectangles: List[List[int]]) -> int:
        res = 0
        count = {}
        for rect in rectangles:
            gcd = math.gcd(rect[0], rect[1])
            key = self.hash(rect[0] // gcd, rect[1] // gcd)
            res += count.get(key, 0)
            count[key] = count.get(key, 0) + 1
        return res