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You are given a list of \$N\$ people who are attending ACM-ICPC World Finals. Each of them are either well versed in a topic or they are not. Find out the maximum number of topics a 2-person team can know. And also find out how many teams can know that maximum number of topics.

Note Suppose \$a\$, \$b\$, and \$c\$ are three different people, then \$(a,b)\$ and \$(b,c)\$ are counted as two different teams.

Input Format

The first line contains two integers, \$N\$ and \$M\$, separated by a single space, where \$N\$ represents the number of people, and \$M\$ represents the number of topics. \$N\$ lines follow. Each line contains a binary string of length \$M\$ If the \$i\$'th line's j'th character is 1, then the i'th person knows the \$j\$'th topic; otherwise, he doesn't know the topic.

Constraints

\$2 ≤ N ≤ 500\$
\$1 ≤ M ≤ 500\$

Output Format

On the first line, print the maximum number of topics a 2-person team can know. On the second line, print the number of 2-person teams that can know the maximum number of topics.

Imports System

Module Solution
    Public Sub Main()
        Dim input As String() = Console.Readline().Split(" ")
        Dim people As Integer = CInt(input(0))
        Dim topics As Integer = CInt(input(1))

        Dim peopleKnowledge(people-1)() As Char
        Dim maxScore As Integer = 0
        Dim teamsWithMaxScore As Integer = 0
        Dim score As Integer = 0

        For i As Integer = 0 To people-1
            peopleKnowledge(i) = Console.ReadLine().ToCharArray()
        Next i

        For i As Integer = 0 to people-2
            For j As Integer = i+1 To people-1
                score = GetTeamScore(peopleKnowledge(i),peopleKnowledge(j),topics)

                If score > maxScore Then
                    maxScore = score
                    teamsWithMaxScore = 1
                ElseIf score = maxScore Then
                    teamsWithMaxScore += 1
                End If
            Next j
        Next i

        Console.WriteLine(maxScore)
        Console.WriteLine(teamsWithMaxScore)
    End Sub

    Private Function GetTeamScore(m1 As Char(),m2 As Char(), topics As Integer) As Integer
        Dim score As Integer = 0

        For i as Integer = 0 to topics-1
            If m1(i).Equals("1"c) Or m2(i).Equals("1"c) Then
                score += 1
            End If
        Next i

        Return score
    End Function
End Module

Trying to become acquainted with VB.NET so I welcome any and all suggestions. This solution executes in 0.61s with \$N = M = 500\$; would love to know about any performance gains.

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Public Sub Main()
    Dim input = Console.ReadLine().Split(" ")
    'The variable name should describe what it is more specifically, "people" could mean 
    '   a List(Of Person), or be a Boolean For If there are people, etc.
    'You don't need to explicitly state the data type.  I don't, it's a matter of 
    '   personal (or company) style, i.e. no consensus either way.
    'Take note that you are setting the largest possible number of people or topics here 
    '   to be <= Int32.MaxValue (2,147,483,647) by casting use CInt().  This is fine 
    '   because your spec says it will be <= 500.  You could also use Int16 
    '   (max of 32,767).  My point is that you should be somewhat aware of the sizes of 
    '   data types you are using.
    Dim peopleCount = CInt(input(0))
    Dim topicsCount = CInt(input(1))

    'Arrays are great for low level or highly structured data, but this is neither.
    '   Lists provide many benefits over an array which we'll get to in a second.
    'The data is being input to you in a text representation of 0's and 1's, but the
    '   actual concept they represent is are they nowledgeable or not which is a Boolean.
    Dim peopleKnowledge As New List(Of List(Of Boolean))
    Dim maxScore As Integer = 0
    Dim teamsWithMaxScoreCount As Integer = 0


    For i = 0 To peopleCount - 1
        peopleKnowledge.Add(New List(Of Boolean))

        Dim CharArray = Console.ReadLine().ToCharArray()
        For Each ch In CharArray
            'Nowhere in your code was any validation that the only text input on the lines
            '   was 0, 1, Or CrLf (return) which is fine if you are the only person who 
            '   will ever use it, but other users won't always remember rules like that.
            Dim IsKnowledgeable = If(ch = "1", True, False)
            peopleKnowledge(i).Add(IsKnowledgeable)
        Next

        'No need for the "i" in "Next i"
    Next

    'Lists allow us to use For Each which helps the developer not have to worry about  
    '   getting the numbers in the loops right.
    'By starting i at 0 and j at 2, I assume you were trying (correctly) to prevent getting 
    '   team scores for a team of the same person twice.  The way you had it set up though
    '   only prevented the very first person being added to itself.  Every other person did  
    '   have a team score calculated for double their score.
    For Each PersonA In peopleKnowledge
        For Each PersonB In peopleKnowledge
            'This line prevents the getting a team score for a team of the same person twice.
            'PersonA and PersonB are both *references* to an object in peopleKnowledge.  
            '   This comparison compares if they are pointing at the same object, not if 
            '   the contents of their lists are the same.
            If PersonA Is PersonB Then Continue For

            Dim score = GetTeamScore(PersonA, PersonB)

            If score > maxScore Then
                maxScore = score
                teamsWithMaxScoreCount = 1
            ElseIf score = maxScore Then
                teamsWithMaxScoreCount += 1
            End If
        Next
    Next

    Console.WriteLine(maxScore)
    Console.WriteLine(teamsWithMaxScoreCount)
End Sub

Private Function GetTeamScore(PersonA As List(Of Boolean), PersonB As List(Of Boolean)) As Integer
    Dim score As Integer = 0

    'Nowhere in your code was any validation that every person's topic list of 1's and 0's  
    '   were equal in length which is fine if you are the only person who will ever use it, 
    '   but other users won't always remember rules like that.
    For i = 0 To PersonA.Count
        If PersonA(i) Or PersonB(i) Then
            score += 1
        End If
    Next

    Return score
End Function
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  • \$\begingroup\$ Hi @Zach, thanks for the review - I like the List solution, but my only question would be on performance for having to iterate over every 1 and 0 to create the Boolean List versus just using the array from .ToCharArray(). Also I think by going from i = 0 to people-2(i.e. first person to the second to last person) and from j = i+1 to people-1(i.e. person after the i'th person to the last person) shouldn't end up calculating a score for a team consisting of the same person. \$\endgroup\$ – Tony May 1 '16 at 21:18
  • \$\begingroup\$ @Tony Ah, you are right about the j = i + 1 thing. I misread it. My solution to that j = i + 1 thing would actually produce every team twice which is incorrect. \$\endgroup\$ – Zach Mierzejewski May 1 '16 at 21:44
  • \$\begingroup\$ @Tony The performance difference between our two ways of iterating over the 1's and 0's would be absolutely minuscule. I would call worrying about that performance a "premature optimization". In a situation like that, I would write whichever way is more readable to the next programmer. My way may actually be less readable than yours, or not (I'm slightly biased! :) \$\endgroup\$ – Zach Mierzejewski May 1 '16 at 21:54

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