Single for-loop traversal over 2D/3D arrays

[Paul A. Gagniuc]

This source code shows the traversal of a two-dimensional array by one for-loop structure. A 2D-array variable (A) is declared. A string variable t is initially set to empty. A variable v is set to zero and it represents the main counter of the for-loop. Another two variables (ie. i and j) are initialized with value zero and are the main coordinates for element identification. Each dimension of array A is stored in variables n and m, namely the number of rows in n and the number of columns in m. The upper limit of the for-loop is calculated based on the two known dimensions n and m. Thus, m times n establishes the upper limit of the for-loop. Here, the value of the counter v from the for-loop is used to calculate the i and j values that are used as an index to traverse the array variable A. The value of variable j is computed as the v % m and the result of this expression indicates the reminder (ex. 5 mod 3 is 2). The secret to this implementation is a condition that increments a variable i (rows) each time j (columns) equals zero. Thus, in this manner this approach provides the i and j values that a nested for-loop provides. At each iteration, the value from an element is added to the content of variable t. Once the end of the for-loop is reached, the value collected in variable t is printed in the output for inspection.

Please also see: Single "for-loop" traversal over three dimensional arrays.

Sub main()

    Dim A(0 To 1, 0 To 2) As String
    Dim i As Integer
    Dim t As String

    A(0, 0) = "a"
    A(0, 1) = "b"
    A(0, 2) = "c"
    A(1, 0) = "d"
    A(1, 1) = "e"
    A(1, 2) = "f"
    
    
    n = UBound(A, 1) - LBound(A, 1) + 1  ' rows
    m = UBound(A, 2) - LBound(A, 2) + 1  ' columns
    
    i = 0
    j = 0
    
    For v = 0 To (n * m) - 1
    
        j = v Mod m

        If (v <> 0 And j = 0) Then i = i + 1
        
        t = t & v & " A(" & i & "," & j & ")="
        t = t & A(i, j) & vbCrLf

    Next v
    
    Debug.Print (t)

End Sub

Some mirrored examples in different programming languages (including VB6), may also be of interest.