Solve #2: gift shop.

02-gift-shop/input01.txt

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+11-22,95-115,998-1012,1188511880-1188511890,222220-222224,1698522-1698528,446443-446449,38593856-38593862,565653-565659,824824821-824824827,2121212118-2121212124

02-gift-shop/solve.py

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+#!/usr/bin/env python3
+
+import sys
+from typing import Optional
+
+def magnitude(x : int) -> int:
+    assert x >= 0
+    return len(str(x))
+
+def delta(order : int) -> int:
+    return 10**order + 1
+
+def sum_1_to_excl(x : int) -> int:
+    return x * (x - 1) // 2
+
+def sum_1_to_incl(x : int) -> int:
+    return x * (x + 1) // 2
+
+# incl. both bounds
+def sum_from_to_incl(lo : int, hi : int) -> int:
+    if lo > hi:
+        return 0
+
+    return sum_1_to_incl(hi) - sum_1_to_excl(lo)
+
+def div2(x : int) -> Optional[int]:
+    if x % 2:
+        return None
+    else:
+        return x // 2
+
+# inclusive both bounds
+def sum_invalid_ids(lo : int, hi : int) -> int:
+    total = 0
+
+    while True:
+        magnitude_lo = magnitude(lo)
+        order_lo = div2(magnitude_lo)
+        if order_lo is None:
+            # no invalid IDs in that order of magnitude
+            lo = 10**magnitude_lo
+            continue
+
+        magnitude_hi = magnitude(hi)
+        d = delta(order_lo)
+
+        if magnitude_lo > magnitude_hi:
+            # this can happen with odd magnitude_hi
+            break
+
+        elif magnitude_lo == magnitude_hi:
+            assert lo <= hi, f"{lo} <= {hi}"
+            total += d * sum_from_to_incl((lo-1)//d + 1, hi // d)
+            break
+
+        assert magnitude_lo < magnitude_hi
+        surrogate_hi = 10**magnitude_lo - 1
+        assert lo <= surrogate_hi, f"{lo} <= {surrogate_hi}"
+        total += d * sum_from_to_incl((lo-1)//d + 1, surrogate_hi // d)
+        lo = surrogate_hi + 1
+
+    return total
+
+if __name__ == '__main__':
+    ranges = [
+        (int(lo_s), int(hi_s))
+        for lo_s, hi_s in (
+            rng.split('-')
+            for rng in sys.stdin.read().strip().split(',')
+        )
+    ]
+
+    total = 0
+    for lo, hi in ranges:
+        total += sum_invalid_ids(lo, hi)
+
+    print(total)