daily

Author: Zanger67

my-submissions/m1782.py

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+class Solution:
+    def maxAverageRatio(self, classes: List[List[int]], extraStudents: int) -> float:
+
+        # Min heap not including 100% ratios since
+        # their ratios wouldn't change
+        # (-1 * amount of ratio gain, total students, passing students)
+        hp = [
+            ((passing / tot - (passing + 1) / (tot + 1)), tot, passing) 
+            for passing, tot in classes 
+            if tot != passing
+        ]
+        heapify(hp)
+
+        while hp and extraStudents :
+            _, tot, passing = heappop(hp)
+
+            tot += 1
+            passing += 1
+            heappush(hp, ((passing / tot - (passing + 1) / (tot + 1)), tot, passing))
+            extraStudents -= 1
+
+        return (sum(passing / tot for _, tot, passing in hp) + (len(classes) - len(hp))) / len(classes)

my-submissions/m1792.md

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+Very interesting question. Simple in terms of it being a greedy heap question, but facinating in terms of how it highlights how ratios change as you augment them.
+
+I initially assumed that we'd simply be adding to the class that's denominator was the smallest since it'd have the largest ratio effect since smaller ratios are more sensitive.
+
+I then thought that for ratios with equal denominators, you should apply it to the case with a smaller numerator since the larger case is more "stable" and would "gain" less since its existing numerator amount would "decrease" a more since the increased denominator also affects it.
+
+Then I realized that this isn't always true so I adjusted the heap to be based on a precomputed heuristic that is the benefit of adding a excelling student to the given class directly. I'm curious as to the math and logical reasoning that causes this though! Will keep digging :D