day07: binary searching makes this go *much* faster

day07.py

@@ -5,17 +5,27 @@ from typing import Any, List
 
 
 def getMinFuelUse(crabs: List[int], increased: bool = False) -> int:
-    minFuel = inf
-    for pos in range(min(crabs), max(crabs) + 1):
+    min_num = min(crabs)
+    max_num = max(crabs)
+    avg = (min_num + max_num) // 2
+    while 1:
         if increased:
-            fuel = sum(triangular(abs(pos - c)) for c in crabs)
+            avg_fuel = sum(triangular(abs(avg - c)) for c in crabs)
+            avg_fuel_p = sum(triangular(abs(avg + 1 - c)) for c in crabs)
+            avg_fuel_m = sum(triangular(abs(avg - 1 - c)) for c in crabs)
         else:
-            fuel = sum(abs(pos - c) for c in crabs)
+            avg_fuel = sum(abs(avg - c) for c in crabs)
+            avg_fuel_p = sum(abs(avg + 1 - c) for c in crabs)
+            avg_fuel_m = sum(abs(avg - 1 - c) for c in crabs)
 
-        if fuel < minFuel:
-            minFuel = fuel
-
-    return minFuel
+        if avg_fuel_m < avg_fuel:
+            max_num = avg
+            avg = (min_num + avg) // 2
+        elif avg_fuel_p < avg_fuel:
+            min_num = avg
+            avg = (max_num + avg) // 2
+        else:
+            return avg_fuel
 
 
 class Day(AOCDay):