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Author: hogan-tech

3625-count-number-of-trapezoids-ii/3625-count-number-of-trapezoids-ii.py

@@ -0,0 +1,65 @@
+# time complexity: O(n^2)
+# space complexity: O(n^2)
+from collections import defaultdict
+from typing import List
+
+
+class Solution:
+    def countTrapezoids(self, points: List[List[int]]) -> int:
+        n = len(points)
+        inf = 10**9 + 7
+        slopeToIntercept = defaultdict(list)
+        midToSlope = defaultdict(list)
+        result = 0
+
+        for i in range(n):
+            x1, y1 = points[i]
+            for j in range(i + 1, n):
+                x2, y2 = points[j]
+                dx = x1 - x2
+                dy = y1 - y2
+
+                if x2 == x1:
+                    k = inf
+                    b = x1
+                else:
+                    k = (y2 - y1) / (x2 - x1)
+                    b = (y1 * dx - x1 * dy) / dx
+
+                mid = (x1 + x2) * 10000 + (y1 + y2)
+                slopeToIntercept[k].append(b)
+                midToSlope[mid].append(k)
+
+        for sti in slopeToIntercept.values():
+            if len(sti) == 1:
+                continue
+
+            counter = defaultdict(int)
+            for bVal in sti:
+                counter[bVal] += 1
+
+            totalSum = 0
+            for count in counter.values():
+                result += totalSum * count
+                totalSum += count
+
+        for mts in midToSlope.values():
+            if len(mts) == 1:
+                continue
+
+            counter = defaultdict(int)
+            for kVal in mts:
+                counter[kVal] += 1
+
+            totalSum = 0
+            for count in counter.values():
+                result -= totalSum * count
+                totalSum += count
+
+        return result
+
+
+points = [[-3, 2], [3, 0], [2, 3], [3, 2], [2, -3]]
+print(Solution().countTrapezoids(points))
+points = [[0, 0], [1, 0], [0, 1], [2, 1]]
+print(Solution().countTrapezoids(points))