小于或等于 NN 的预定义数字的最佳可能组合总和

Question

我有一个管道长度列表，我需要将这些长度安装在最大允许长度内以获得最佳产量

例如，最大允许长度为 90，我需要制作的部分是：

25、60、13、48、23、29、27、22

为了最适合 90 以内的数字，我有一组这些数字：

60、29（共 89 个）

27、25、13、23（共 88 个）

48、22（共 70 个）

我找到this 对类似问题的回答，但我不知道如何将其转换为在 excel 或 javascript 或 php 中使用

任何帮助将不胜感激。

谢谢。

Answer 1

这是一种可能的解决方案。但它是一种蛮力算法，所以它不是尽可能快。

function bestComb(nums, target) {
  var combinations = [];
  var sums = [];
  function loop(idx, comb, sum) {
    if(idx >= nums.length || sum + nums[idx] > target) {
      combinations.push(comb.slice());
      sums.push(sum);
      return;
    }
    for(var i = idx; i < nums.length; i++) {
      if(sum + nums[i] > target) break;
      if(sum + nums[i] === target) {
        combinations.push(comb.slice());
        combinations[combinations.length - 1].push(nums[i]);
        sums.push(sum + nums[i]);
        break;
      }
      comb.push(nums[i]);
      loop(i + 1, comb, sum + nums[i]);
      comb.pop();
    }
  }

  nums = nums.slice();
  nums.sort(function(a,b) {return a - b});
  loop(0, [], 0);

  if(sums.length === 0) return null;
  var maxSum = sums[0],
      maxComb = combinations[0];
  for(var i = 1; i < sums.length; i++) {
    if(sums[i] > maxSum || sums[i] === maxSum && combinations[i].length < maxComb.length) {
      maxSum = sums[i];
      maxComb = combinations[i];
    }
  }

  return maxComb;
}

var nums = [25, 60, 13, 48, 23, 29, 27, 22];

var solution = bestComb(nums, 90);

console.log(solution);

Answer 2

这是基于 John Coleman 的 VBA 代码。它将创建一个包含所有 255 (2 ⁸-1) 个候选者的列表，并将它们按从好到坏的顺序排列：

Sub MAIN()
    Dim i As Long, st As String
    Dim a(1 To 8) As Integer
    Dim ary

    a(1) = 25
    a(2) = 60
    a(3) = 13
    a(4) = 48
    a(5) = 23
    a(6) = 29
    a(7) = 27
    a(8) = 22

    st = ListSubsets(a)
    ary = Split(st, vbCrLf)

    For i = LBound(ary) + 1 To UBound(ary) - 1
        Cells(i, 2) = Replace(ary(i + 1), " ", "")
    Next i

    Call DistributeData
    Call SortData
End Sub

Function ListSubsets(Items As Variant) As String
    Dim CodeVector() As Integer
    Dim i As Integer
    Dim lower As Integer, upper As Integer
    Dim SubList As String
    Dim NewSub As String
    Dim done As Boolean
    Dim OddStep As Boolean

    OddStep = True
    lower = LBound(Items)
    upper = UBound(Items)

    ReDim CodeVector(lower To upper) 'it starts all 0
    Do Until done
        'Add a new subset according to current contents
        'of CodeVector

        NewSub = ""
        For i = lower To upper
            If CodeVector(i) = 1 Then
                If NewSub = "" Then
                    NewSub = Items(i)
                Else
                    NewSub = NewSub & ", " & Items(i)
                End If
            End If
        Next i
        If NewSub = "" Then NewSub = "{}" 'empty set
        SubList = SubList & vbCrLf & NewSub
        'now update code vector
        If OddStep Then
            'just flip first bit
            CodeVector(lower) = 1 - CodeVector(lower)
        Else
            'first locate first 1
            i = lower
            Do While CodeVector(i) <> 1
                i = i + 1
            Loop
            'done if i = upper:
            If i = upper Then
                done = True
            Else
                'if not done then flip the *next* bit:
                i = i + 1
                CodeVector(i) = 1 - CodeVector(i)
            End If
        End If
        OddStep = Not OddStep 'toggles between even and odd steps
    Loop
    ListSubsets = SubList
End Function

Sub DistributeData()
    Columns("B:B").Select
    Selection.TextToColumns Destination:=Range("B1"), DataType:=xlDelimited, _
        TextQualifier:=xlDoubleQuote, ConsecutiveDelimiter:=False, Tab:=False, _
        Semicolon:=False, Comma:=True, Space:=False, Other:=False, FieldInfo _
        :=Array(Array(1, 1), Array(2, 1), Array(3, 1)), TrailingMinusNumbers:=True

        Range("A1:A255").Formula = "=if(sum(B1:I1)>=90,9999,90-sum(B1:I1))"
End Sub

Sub SortData()
    Range("A1:I255").Select
    Application.CutCopyMode = False
    ActiveWorkbook.Worksheets("Sheet5").Sort.SortFields.Clear
    ActiveWorkbook.Worksheets("Sheet5").Sort.SortFields.Add Key:=Range("A1:A255") _
        , SortOn:=xlSortOnValues, Order:=xlAscending, DataOption:=xlSortNormal
    With ActiveWorkbook.Worksheets("Sheet5").Sort
        .SetRange Range("A1:I255")
        .Header = xlGuess
        .MatchCase = False
        .Orientation = xlTopToBottom
        .SortMethod = xlPinYin
        .Apply
    End With

End Sub

所以最好的组合是：

{60,29} 和 {25,13,​​29,22}

参考：

John Coleman's Code