' MergeSort. A stable sort (preserves original order of records with equal ' keys). Like HeapSort, easily adapted to any data type and guaranteed to run ' in O(N log N) time, but almost twice as fast. On the down side,' needs an extra array of N items, but these can be pointers if the keys ' themselves are larger than pointers. Works by repeatedly merging short ' sorted sequences (created by InsertionSort) into longer ones. Two versions ' are given. pMergeSortS is an indirect (pointerized) version for strings,' which can be adapted to doubles by changing the declaration of A(). ' MergeSortL is a direct version for longs, which can be adapted to integers.'' Speed: pMergeSortS sorts 500,000 random strings in 55.3 sec; sorts 100186 ' library call numbers in 9.8 sec; sorts 25479 dictionary words in 3.3 sec ' (random order), 2.9 sec (presorted) or 3.6 sec (reverse sorted). MergeSortL ' sorts 500,000 random longs in 42 seconds. Timed in Excel 2001 on an 800 mhz ' PowerBook.'' Bottom line: fast stable sort that easily handles all data types,' but a heavy memory user.' Usage: Dim S1(L To R) As StringDim P1(L To R) As LongDim P2(L To R) As LongDim L1(L To R) As LongDim L2(L To R) As Long For I = L To R S1(I) = GetRandomString() P1(I) = I L1(I) = GetRandomLong()Next IpMergeSortS L, R, S1, P1, P2MergeSortL L, R, L1, L2' CODE:Sub pMergeSortS(L As Long, R As Long, A() As String, P() As Long, Q() As Long) Dim LP As Long 'left pointer Dim RP As Long 'right pointer Dim OP As Long 'output pointer Dim MID As Long 'This version is for strings; for other data types, ' change declaration of A(). 'MergeSort recursively calls itself until we have lists short enough for ' InsertionSort. If R - L < 10 Then 'call an indirect (pointerized) version of InsertionSort pInsertS L, R, A, P Else 'if too long for InsertionSort, split list and recurse MID = (L + R) 2 pMergeSortS L, MID, A, P, Q pMergeSortS MID + 1, R, A, P, Q 'Each half of the array is sorted; now we'll merge them into the extra ' array. 'We'll work via pointers, to keep the extra array smaller. LP = L RP = MID + 1 OP = L Do 'Copy the pointer to the smaller string. If A(P(LP)) <= A(P(RP)) Then Q(OP) = P(LP) OP = OP + 1 LP = LP + 1 If LP > MID Then 'We ran out of the left half, so transfer the rest of the right ' half. Do Q(OP) = P(RP) OP = OP + 1 RP = RP + 1 Loop Until RP > R 'This merge is done. Exit Do End If Else 'This part is a mirror image of the last part. Q(OP) = P(RP) OP = OP + 1 RP = RP + 1 If RP > R Then Do Q(OP) = P(LP) OP = OP + 1 LP = LP + 1 Loop Until LP > MID Exit Do End If End If Loop 'Finally, we copy the pointers back from the extra array to the main array. For OP = L To R P(OP) = Q(OP) Next OP End IfEnd SubSub pInsertS(L As Long, R As Long, A() As String, P() As Long) Dim LP As Long Dim RP As Long Dim TMP As Long Dim T As String For RP = L + 1 To R TMP = P(RP) T = A(TMP) For LP = RP To L + 1 Step -1 If T < A(P(LP - 1)) Then P(LP) = P(LP - 1) Else Exit For Next LP P(LP) = TMP Next RPEnd SubSub MergeSortL(L As Long, R As Long, A() As Long, B() As Long) Dim LP As Long Dim RP As Long Dim OP As Long Dim MID As Long If R - L < 12 Then InsertL L, R, A() Else MID = (L + R) 2 MergeSortL L, MID, A, B MergeSortL MID + 1, R, A, B LP = L RP = MID + 1 OP = L Do If A(LP) <= A(RP) Then B(OP) = A(LP) OP = OP + 1 LP = LP + 1 If LP > MID Then Do B(OP) = A(RP) OP = OP + 1 RP = RP + 1 Loop Until RP > R Exit Do End If Else B(OP) = A(RP) OP = OP + 1 RP = RP + 1 If RP > R Then Do B(OP) = A(LP) OP = OP + 1 LP = LP + 1 Loop Until LP > MID Exit Do End If End If Loop For OP = L To R A(OP) = B(OP) Next OP End IfEnd SubSub InsertL(L As Long, R As Long, A() As Long) Dim LP As Long Dim RP As Long Dim TMP As Long For RP = L + 1 To R TMP = A(RP) For LP = RP To L + 1 Step -1 If TMP < A(LP - 1) Then A(LP) = A(LP - 1) Else Exit For Next LP A(LP) = TMP Next RPEnd Sub



Top 5 B2B SaaS Marketing Agencies for 2023
In recent years, the software-as-a-service (SaaS) sector has experienced exponential growth as more and more companies choose cloud-based solutions. Any SaaS company hoping to stay ahead of the curve in this quickly changing industry needs to invest in effective marketing. So selecting the best marketing agency can mean the difference