`' CombSort. A compact routine that sorts data in place (no extra memory needed)' and runs in approximately O(N log N) time. Not stable (does not preserve ' original order of records with equal keys). Like InsertionSort,' works by taking a key from the right side of the list and comparing it with ' keys to the left until the correct position is found to insert it. Differs ' from InsertionSort (and resembles ShellSort) by moving leftward by interval ' GAP instead of one key at a time. GAP is initially large (to move keys close ' to their final position rapidly) and is repeatedly reduced until it equals 1 ' and the list is sorted. Rare sequences of keys may not fit the series of GAP ' values, leading to slow sorting. Two versions are given. pCombSortS is an ' indirect (pointerized) version for strings, which can be adapted to doubles ' by changing the declaration of A(). CombSortL is a direct version for longs,' which can be adapted to integers.'' Reference: Stephen Lacy and Richard Box, "A Fast, Easy Sort", Byte,' April 1991, p.315 ff.'' Speed: pCombSortS sorts 500,000 random strings in 100 sec; sorts 100186 ' library call numbers in 16.5 sec; sorts 25479 dictionary words in 3.5 sec ' (random order), 2.7 sec (presorted) or 2.9 sec (reverse sorted). CombSortL ' sorts 500,000 random longs in 52 seconds. Timed in Excel 2001 on an 800 mhz ' PowerBook.'' Bottom line: about as fast as HeapSort, but lacks HeapSort's guarantee of O' (NlogN) worst case speed.' Usage: Dim S1(L To R) As StringDim P1(L To R) As LongDim L1(L To R) As Long For I = L To R S1(I) = GetRandomString() P1(I) = I L1(I) = GetRandomLong()Next IpCombSortS L, R, S1, P1CombSortL L, R, L1' CODE:Sub CombSortS(L As Long, R As Long, A() As String, P() As Long) Dim GAP As Long Dim SWAPPED As Boolean Dim I As Long Dim J As Long Dim TMP As Long 'Initialize GAP to length of list. GAP = CLng(1 + R - L) Do 'For each pass, divide GAP by 1.3. GAP = (10 * GAP) 13 'The most efficient series of final GAP values starts with 11. If GAP = 0 Then GAP = 1 ElseIf GAP = 9 Or GAP = 10 Then GAP = 11 End If 'Use SWAPPED to tell whether we made a pass without any exchanges. SWAPPED = False 'Compare and possibly swap values/pointers separated by GAP. For I = L To R - GAP J = I + GAP If A(P(I)) > A(P(J)) Then TMP = P(I) P(I) = P(J) P(J) = TMP SWAPPED = True End If Next I 'If GAP = 1 and we didn't move anything, we're done. Loop While SWAPPED Or GAP > 1End SubSub CombSortL(L As Long, R As Long, A() As Long) Dim GAP As Long Dim SWAPPED As Boolean Dim I As Long Dim J As Long Dim TMP As Long GAP = CLng(1 + R - L) Do GAP = (10 * GAP) 13 If GAP = 0 Then GAP = 1 ElseIf GAP = 9 Or GAP = 10 Then GAP = 11 End If SWAPPED = False For I = L To R - GAP J = I + GAP If A(I) > A(J) Then TMP = A(I) A(I) = A(J) A(J) = TMP SWAPPED = True End If Next I Loop While SWAPPED Or GAP > 1End Sub`

#### 7 Ways Technology Has Changed Traditional Payments

In today’s digital world, technology has changed how we make payments. From contactless cards to mobile wallets, it’s now easier