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Commit a4c93cd

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ACL Practice Contest C - clean up
1 parent 66ba519 commit a4c93cd

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‎practice2-c/Main.hs‎

Lines changed: 13 additions & 50 deletions
Original file line numberDiff line numberDiff line change
@@ -16,14 +16,6 @@ import Control.Exception (assert)
1616
comb2 :: (Integral a, Bits a) => a -> a
1717
comb2 n = (n `shiftR` 1) * ((n - 1) .|. 1)
1818

19-
prop_comb2 :: Integer -> QC.Property
20-
prop_comb2 n = comb2 n QC.=== n * (n - 1) `quot` 2
21-
22-
prop_floorSum_negate_a :: QC.NonNegative (QC.Small Int64) -> QC.Positive Int64 -> Int64 -> Int64 -> QC.Property
23-
prop_floorSum_negate_a (QC.NonNegative (QC.Small n)) (QC.Positive m) a b =
24-
let does_not_overflow = (\t -> toInteger (minBound :: Int64) <= t && t <= toInteger (maxBound :: Int64)) (toInteger b + toInteger a * (toInteger n - 1))
25-
in does_not_overflow QC.==> floorSum n m (- a) (b + a * (n - 1)) QC.=== floorSum n m a b
26-
2719
-- floorSum n m a b
2820
-- n: non-negative, m: positive
2921
floorSum :: Int64 -> Int64 -> Int64 -> Int64 -> Int64
@@ -33,53 +25,34 @@ floorSum 0 m a b = 0
3325
floorSum n 1 a b = a * comb2 n + n * b
3426
floorSum n m a b
3527
| a < 0 = floorSum n m (- a) (b + a * (n - 1))
36-
{-
28+
{-
3729
| a >= m || a < 0 = case a `divMod` m of
3830
(q, a') -> q * comb2 n + floorSum n m a' b
3931
-}
4032
| let m2 = m `quot` 2
4133
, abs a > m2 = case (a + m2) `divMod` m of
42-
(q, a') ->
43-
q * comb2 n + floorSum n m (a' - m2) b
34+
(q, a') -> q * comb2 n + floorSum n m (a' - m2) b
4435
| b >= m || b < 0 = case b `divMod` m of
4536
(q, b') -> q * n + floorSum n m a b'
4637
| n > m = case n `quotRem` m of
4738
(q, n') -> (q * n - comb2 (q + 1) * m) * a + q * floorSum m m a b + floorSum n' m a b
48-
-- | n < 100 = fromInteger $ floorSum_naive n m a b
49-
-- in -- fromInteger $ floorSum_naive n m a b
50-
-- - n * t - floorSum t (- a) (- m) (- b - m) + floorSum t (- a) (- m) (b - m)
51-
| otherwise = -- 0 < a < m, 0 <= b < m, 0 < n <= m
52-
-- 0 < a < m
53-
-- sum [ fromIntegral $ length [ i | i <- [0..n-1], floor ((toInteger a * toInteger i + toInteger b) % toInteger m) >= k ] | k <- [1..(floor $ (toInteger a * (toInteger n - 1) + toInteger b) % toInteger m)] ]
54-
-- sum [ fromIntegral $ length [ i | i <- [0..n-1], i >= - floor ((- toInteger m * toInteger k + toInteger b) % toInteger a) ] | k <- [1..(floor $ (toInteger a * (toInteger n - 1) + toInteger b) % toInteger m)] ]
55-
-- sum [ n - max 0 (- floor ((- toInteger m * toInteger k + toInteger b - toInteger m) % toInteger a)) | k <- [0..(floor $ (toInteger a * (toInteger n - 1) + toInteger b) % toInteger m) - 1] ]
39+
| otherwise =
40+
-- 0 < a < m, 0 <= b < m, 0 < n <= m
5641
let t = floor ((toInteger a * (toInteger n - 1) + toInteger b) % toInteger m)
5742
in n * t + floorSum t a (- m) (b - m)
58-
-- ceilSum (ceiling $ (a * (n - 1) + b) % m) a m (m - b)
5943

60-
{-
61-
ceilSum :: Int64 -> Int64 -> Int64 -> Int64 -> Int64
62-
ceilSum n m 0 b = n * ceiling (b % m)
63-
ceilSum 0 m a b = 0
64-
ceilSum n 1 a b = a * (n * (n - 1) `quot` 2) + n * b
65-
ceilSum n m a b
66-
| a >= m = case a `quotRem` m of
67-
(q, a') -> q * (n * (n - 1) `quot` 2) + ceilSum n m a' b
68-
| b >= m || b < 0 = case b `divMod` m of
69-
(q, b') -> q * n + ceilSum n m a b'
70-
| n > m = case n `quotRem` m of
71-
(q, n') -> (q * n - q * (q + 1) `quot` 2 * m) * a + q * ceilSum m m a b + ceilSum n' m a b
72-
| n < 100 = fromInteger $ ceilSum_naive n m a b
73-
| otherwise = n * (n - 1) `quot` 2 - floorSum n m (m - a) (- b) -- 0 < a < m, 0 <= b < m, 0 < n <= m
74-
75-
-}
7644
floorSum_naive :: Int64 -> Int64 -> Int64 -> Int64 -> Integer
7745
floorSum_naive n m a b = sum [ floor ((fromIntegral a * fromIntegral i + fromIntegral b) % fromIntegral m) | i <- [0..n-1] ]
7846

79-
{-
80-
ceilSum_naive :: Int64 -> Int64 -> Int64 -> Int64 -> Integer
81-
ceilSum_naive n m a b = sum [ ceiling ((fromIntegral a * fromIntegral i + fromIntegral b) % fromIntegral m) | i <- [0..n-1] ]
82-
-}
47+
main = do
48+
t <- readLn @Int
49+
replicateM_ t $ do
50+
[n,m,a,b] <- map fromIntegral . unfoldr (BS.readInt . BS.dropWhile isSpace) <$> BS.getLine
51+
print $ floorSum n m a b
52+
53+
prop_comb2 :: Integer -> QC.Property
54+
prop_comb2 n = comb2 n QC.=== n * (n - 1) `quot` 2
55+
8356
prop_floorSum :: QC.NonNegative (QC.Small Int64) -> QC.Positive Int64 -> Int64 -> Int64 -> QC.Property
8457
prop_floorSum (QC.NonNegative (QC.Small n)) (QC.Positive m) a b = QC.within (100 * 1000) $ toInteger (floorSum n m a b) QC.=== floorSum_naive n m a b
8558

@@ -90,13 +63,3 @@ prop_floorSum_r = QC.forAllShrink (QC.choose (1, 10^4)) QC.shrink $ \n -> n >= 1
9063
QC.forAllShrink (QC.choose (0, m - 1)) QC.shrink $ \b ->
9164
QC.within (100 * 1000) $ toInteger (floorSum n m a b) QC.=== floorSum_naive n m a b
9265

93-
{-
94-
prop_ceilSum :: QC.NonNegative (QC.Small Int64) -> QC.Positive Int64 -> Int64 -> Int64 -> QC.Property
95-
prop_ceilSum (QC.NonNegative (QC.Small n)) (QC.Positive m) a b = QC.within (100 * 1000) $ toInteger (ceilSum n m a b) QC.=== ceilSum_naive n m a b
96-
-}
97-
98-
main = do
99-
t <- readLn @Int
100-
replicateM_ t $ do
101-
[n,m,a,b] <- map fromIntegral . unfoldr (BS.readInt . BS.dropWhile isSpace) <$> BS.getLine
102-
print $ floorSum n m a b

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