Calculate smallest number of adjustments to get columns in correct order

JugglerJAF

Active Member
Joined
Feb 17, 2002
Messages
264
This is possibly more of a maths question than an Excel question, but I thought it was the sort of thing that someone on here may be able to answer...

Say that I have a data extract from one system, and I need to change the order of the columns so that they eventually end up in the same order as an extract from another system.

Consider the following table:
A2B2C2D2E2F2G2H2I2J2K2L2M2N2O2P2Q2R2S2T2U2
6373578912101154141618191734532728134

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Accent 3"/> <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 3"/> <w:LsdException Locked="false" Priority="51" Name="List Table 6 Colorful Accent 3"/> <w:LsdException Locked="false" Priority="52" Name="List Table 7 Colorful Accent 3"/> <w:LsdException Locked="false" Priority="46" Name="List Table 1 Light Accent 4"/> <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 4"/> <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 4"/> <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 4"/> <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 4"/> <w:LsdException Locked="false" Priority="51" Name="List Table 6 Colorful Accent 4"/> <w:LsdException Locked="false" Priority="52" Name="List Table 7 Colorful Accent 4"/> <w:LsdException Locked="false" Priority="46" Name="List Table 1 Light Accent 5"/> <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 5"/> <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 5"/> <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 5"/> <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 5"/> <w:LsdException Locked="false" Priority="51" Name="List Table 6 Colorful Accent 5"/> <w:LsdException Locked="false" Priority="52" Name="List Table 7 Colorful Accent 5"/> <w:LsdException Locked="false" Priority="46" Name="List Table 1 Light Accent 6"/> <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 6"/> <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 6"/> <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 6"/> <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 6"/> <w:LsdException Locked="false" Priority="51" Name="List Table 6 Colorful Accent 6"/> <w:LsdException Locked="false" Priority="52" Name="List Table 7 Colorful Accent 6"/> </w:LatentStyles> </xml><![endif]--><!--[if gte mso 10]> <style> /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-priority:99; mso-style-parent:""; mso-padding-alt:0cm 5.4pt 0cm 5.4pt; mso-para-margin:0cm; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:10.0pt; font-family:"Times New Roman",serif;} </style> <![endif]-->I need to manually move the columns so that the numeric values are in order (but not yet in the actual correct final column). For example, if I were to cut Column U and insert at Column A, and then cut Columns E:G and insert at Column C, that would change the layout so that the first 5 columns are not in the correct order, but still with some more cuts and inserts to do to finish the process:
A2B2C2D2E2F2G2H2I2J2K2L2M2N2O2P2Q2R2S2T2U2
4678937351210115414161819173453272813

<tbody>
</tbody>

I need to figure out the minimum number of cuts and inserts required to move the columns to ascending order.

I know that in actual Excel terms, I could do this easily by sorting and choosing "left to right" instead of the default "top to bottom", but the actual data I'm working with doesn't contain the numeric column values, so it's more of a maths theory question "What is the minimum number of "moves" required to put these items in order"?

Think of it in terms of books on a bookshelf that that have been mixed up, what's the minimum number of moves required to put them back in alphabetical order? The best I've done for this original order is 8 moves, which I've accomplished a number of different ways.

Is there some rule or formula that can calculate the minimum number of moves for this, or any given "order" of books?

[edit] I forgot to clarify that you don't have to move one "book" at a time. You can move any number of adjacent books and it counts as 1 move as in the example above where I cut columns E:G.
 
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