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Problem statement

Calvin is driving his favorite vehicle on the 101 freeway. He notices that the check engine light of his vehicle is on, and he wants to service it immediately to avoid any risks. Luckily, a service lane runs parallel to the highway. The length of the highway and the service lane is \$N\$ units. The service lane consists of \$N\$ segments of equal length and different width.

Calvin can enter to and exit from any segment. Let's call the entry segment as index \$i\$ and the exit segment as index j. Assume that the exit segment lies after the entry segment (\$i\$≤\$j\$) and 0≤\$i\$. Calvin has to pass through all segments from index \$i\$ to index \$j\$ (both inclusive).

Calvin has three types of vehicles - bike, car, and truck - represented by \$1\$, \$2\$ and \$3\$, respectively. These numbers also denote the width of the vehicle.

You are given an array width of length \$N\$, where \$width[k]\$ represents the width of the kth segment of the service lane. It is guaranteed that while servicing he can pass through at most \$1000\$ segments, including the entry and exit segments.

  • If \$width[k]=1\$, only the bike can pass through the \$k\$th segment.
  • If \$width[k]=2\$, the bike and the car can pass through the \$k\$th segment.
  • If \$width[k]=2\$, the bike and the car can pass through the \$k\$th segment.

Given the entry and exit point of Calvin's vehicle in the service lane, output the type of the largest vehicle which can pass through the service lane (including the entry and exit segments).

Input Format

The first line of input contains two integers, \$N\$ and \$T\$, where \$N\$ denotes the length of the freeway and \$T\$ the number of test cases. The next line has \$N\$ space-separated integers which represent the width array.

\$T\$ test cases follow. Each test case contains two integers, \$i\$ and \$j\$, where \$i\$ is the index of the segment through which Calvin enters the service lane and \$j\$ is the index of the lane segment through which he exits.

Constraints

  • \$2≤N≤100000\$
  • \$1≤T≤1000\$
  • \$0≤i<j<N\$
  • \$2≤j−i+1≤min(N,1000)\$
  • \$1≤width[k]≤3,where 0≤k<N\$

Output Format

For each test case, print the number that represents the largest vehicle type that can pass through the service lane.

\$Note\$: Calvin has to pass through all segments from index i to index j (both inclusive).

Sample Input

8 5 
2 3 1 2 3 2 3 3 
0 3
4 6 
6 7 
3 5 
0 7 

Sample Output

1
2
3
2
1

Explanation

Below is the representation of the lane:

|HIGHWAY|Lane|    ->    Width
0: |       |--|            2
1: |       |---|           3
2: |       |-|             1
3: |       |--|            2
4: |       |---|           3
5: |       |--|            2
6: |       |---|           3
7: |       |---|           3
  1. (0, 3): Because \$width[2] = 1\$, only the bike can pass through it.
  2. (4, 6): Here the largest allowed vehicle which can pass through the 5th segment is the car and for the 4th and 6th segment it's the truck. Hence the largest vehicle allowed in these segments is a car.
  3. (6, 7): In this example, the vehicle enters at the 6th segment and exits at the 7th segment. Both segments allow even trucks to pass through them. Hence the answer is 3.
  4. (3, 5): \$width[3] = width[5] = 2\$. While the 4th segment allows the truck, the 3rd and 5th allow up to a car. So \$2\$ will be the answer here.
  5. (0, 7): The bike is the only vehicle which can pass through the 2nd segment, which limits the strength of the whole lane to 1.

Ok, so here's my accepted answer for this problem:

import Control.Monad (replicateM)

main = do
    line1 <- getLine
    let (lengthFreeway, numberOfTests) = readTwoInts line1
    line2 <- getLine
    let serviceLane = readInts line2
    line3 <- replicateM numberOfTests getLine
    let testCases = map readTwoInts line3
    let answers = map (maxVehicleWidth serviceLane) testCases
    mapM print answers

readInts :: String -> [Int]
readInts line = map read $ words line

readTwoInts :: String -> (Int, Int)
readTwoInts line = (i1, i2)
    where i1:[i2] = readInts line

takePart :: Int -> Int -> [a] -> [a]
takePart _ _ [] = []
takePart start end _ | start > end = 
    error $ "takePart: start should be smaller than end. Start:" ++ show start 
        ++ ". End:" ++ show end
takePart start end xs = 
    reverse $ drop (length xs - end) $ reverse (drop start xs)

maxVehicleWidth :: [Int] -> (Int, Int) -> Int
maxVehicleWidth lane (entryPoint, exitPoint) = 
    -- (exitPoint + 1) is because the exitPoint is inclusive.
    minimum $ takePart entryPoint (exitPoint + 1) lane

So, how can I make this answer better, faster, more readable and elegant, in good Haskell style?

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What an utterly bizarre problem statement. For one thing bikes don't have check engine lights... I guess this boils down to “find the minimum value within a list subsequence” which you've got nailed.

You have the right idea with takePart but there's no need to flip the list turnways. The clue is in the name you picked, take.

betweenInclusive :: Int -> Int -> [a] -> [a]
betweenInclusive start end = take (end - start + 1) . drop start

Note that I moved the logic for including the end bound into this function. This makes more sense to me with a new name like betweenInclusive, as it's sort of a utility function on lists. I wouldn't bother with all of the error checking you were doing either, the Constraints section is sufficient to guarantee you'll only receive valid bounds.

You can clean up readTwoInts a bit too, it's odd to mix both (:) and literal lists ([x]) in a single pattern match.

readTwoInts :: String -> (Int, Int)
readTwoInts line = (i, j)
    where [i, j] = readInts line

I'd use fmap (<$>) to reduce the number of intermediate values present in main as well.

main :: IO ()
main = do (_, tests) <- readTwoInts <$> getLine
          width      <- readInts    <$> getLine
          bounds     <- replicateM tests (readTwoInts <$> getLine)
          mapM (print . maxVehicleWidth width) bounds
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  • \$\begingroup\$ What is \$ijs\$? A Haskell convention? Agreed about the bikes too... \$\endgroup\$ – Marcus Vinícius Monteiro Apr 15 '15 at 19:25
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    \$\begingroup\$ A pun on the variable names given in the problem statement. Probably would be better to name that bounds, I was going for a reflection of the problem statement (like using width) but then I chickened out on naming tests t, so I guess it ended up a little inconsistent. \$\endgroup\$ – bisserlis Apr 15 '15 at 19:54
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    \$\begingroup\$ Bike probably means motorbike here. \$\endgroup\$ – Franky Apr 16 '15 at 7:06

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