JugglerJAF
Active Member
- Joined
- Feb 17, 2002
- Messages
- 297
- Office Version
- 365
- Platform
- Windows
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:
<tbody>
[TD="class: xl64"]A2[/TD]
[TD="class: xl64, width: 33"]B2[/TD]
[TD="class: xl64, width: 33"]C2[/TD]
[TD="class: xl64, width: 33"]D2[/TD]
[TD="class: xl64, width: 33"]E2[/TD]
[TD="class: xl64, width: 33"]F2[/TD]
[TD="class: xl64, width: 33"]G2[/TD]
[TD="class: xl64, width: 33"]H2[/TD]
[TD="class: xl64, width: 33"]I2[/TD]
[TD="class: xl64, width: 33"]J2[/TD]
[TD="class: xl64, width: 33"]K2[/TD]
[TD="class: xl64, width: 33"]L2[/TD]
[TD="class: xl64, width: 33"]M2[/TD]
[TD="class: xl64, width: 33"]N2[/TD]
[TD="class: xl64, width: 33"]O2[/TD]
[TD="class: xl64, width: 33"]P2[/TD]
[TD="class: xl64, width: 33"]Q2[/TD]
[TD="class: xl64, width: 33"]R2[/TD]
[TD="class: xl64, width: 33"]S2[/TD]
[TD="class: xl64, width: 33"]T2[/TD]
[TD="class: xl64, width: 33"]U2[/TD]
[TD="class: xl63"]6[/TD]
[TD="class: xl63"]37[/TD]
[TD="class: xl63"]35[/TD]
[TD="class: xl63"]7[/TD]
[TD="class: xl63"]8[/TD]
[TD="class: xl63"]9[/TD]
[TD="class: xl63"]12[/TD]
[TD="class: xl63"]10[/TD]
[TD="class: xl63"]11[/TD]
[TD="class: xl63"]54[/TD]
[TD="class: xl63"]14[/TD]
[TD="class: xl63"]16[/TD]
[TD="class: xl63"]18[/TD]
[TD="class: xl63"]19[/TD]
[TD="class: xl63"]17[/TD]
[TD="class: xl63"]34[/TD]
[TD="class: xl63"]53[/TD]
[TD="class: xl63"]27[/TD]
[TD="class: xl63"]28[/TD]
[TD="class: xl63"]13[/TD]
[TD="class: xl63"]4[/TD]
</tbody>
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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 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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:
[TABLE="width: 693"]
<tbody>[TR]
[TD]A2[/TD]
[TD]B2[/TD]
[TD]C2[/TD]
[TD]D2[/TD]
[TD]E2[/TD]
[TD]F2[/TD]
[TD]G2[/TD]
[TD]H2[/TD]
[TD]I2[/TD]
[TD]J2[/TD]
[TD]K2[/TD]
[TD]L2[/TD]
[TD]M2[/TD]
[TD]N2[/TD]
[TD]O2[/TD]
[TD]P2[/TD]
[TD]Q2[/TD]
[TD]R2[/TD]
[TD]S2[/TD]
[TD]T2[/TD]
[TD]U2[/TD]
[/TR]
[TR]
[TD]4[/TD]
[TD]6[/TD]
[TD]7[/TD]
[TD]8[/TD]
[TD]9[/TD]
[TD]37[/TD]
[TD]35[/TD]
[TD]12[/TD]
[TD]10[/TD]
[TD]11[/TD]
[TD]54[/TD]
[TD]14[/TD]
[TD]16[/TD]
[TD]18[/TD]
[TD]19[/TD]
[TD]17[/TD]
[TD]34[/TD]
[TD]53[/TD]
[TD]27[/TD]
[TD]28[/TD]
[TD]13[/TD]
[/TR]
</tbody>[/TABLE]
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.
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:
<tbody>
[TD="class: xl64"]A2[/TD]
[TD="class: xl64, width: 33"]B2[/TD]
[TD="class: xl64, width: 33"]C2[/TD]
[TD="class: xl64, width: 33"]D2[/TD]
[TD="class: xl64, width: 33"]E2[/TD]
[TD="class: xl64, width: 33"]F2[/TD]
[TD="class: xl64, width: 33"]G2[/TD]
[TD="class: xl64, width: 33"]H2[/TD]
[TD="class: xl64, width: 33"]I2[/TD]
[TD="class: xl64, width: 33"]J2[/TD]
[TD="class: xl64, width: 33"]K2[/TD]
[TD="class: xl64, width: 33"]L2[/TD]
[TD="class: xl64, width: 33"]M2[/TD]
[TD="class: xl64, width: 33"]N2[/TD]
[TD="class: xl64, width: 33"]O2[/TD]
[TD="class: xl64, width: 33"]P2[/TD]
[TD="class: xl64, width: 33"]Q2[/TD]
[TD="class: xl64, width: 33"]R2[/TD]
[TD="class: xl64, width: 33"]S2[/TD]
[TD="class: xl64, width: 33"]T2[/TD]
[TD="class: xl64, width: 33"]U2[/TD]
[TD="class: xl63"]6[/TD]
[TD="class: xl63"]37[/TD]
[TD="class: xl63"]35[/TD]
[TD="class: xl63"]7[/TD]
[TD="class: xl63"]8[/TD]
[TD="class: xl63"]9[/TD]
[TD="class: xl63"]12[/TD]
[TD="class: xl63"]10[/TD]
[TD="class: xl63"]11[/TD]
[TD="class: xl63"]54[/TD]
[TD="class: xl63"]14[/TD]
[TD="class: xl63"]16[/TD]
[TD="class: xl63"]18[/TD]
[TD="class: xl63"]19[/TD]
[TD="class: xl63"]17[/TD]
[TD="class: xl63"]34[/TD]
[TD="class: xl63"]53[/TD]
[TD="class: xl63"]27[/TD]
[TD="class: xl63"]28[/TD]
[TD="class: xl63"]13[/TD]
[TD="class: xl63"]4[/TD]
</tbody>
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SemiHidden="true" UnhideWhenUsed="true" Name="Note Heading"/> <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Body Text 2"/> <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Body Text 3"/> <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Body Text Indent 2"/> <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Body Text Indent 3"/> <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Block Text"/> <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Hyperlink"/> <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="FollowedHyperlink"/> <w:LsdException Locked="false" Priority="22" QFormat="true" Name="Strong"/> <w:LsdException Locked="false" Priority="20" QFormat="true" Name="Emphasis"/> <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Document Map"/> <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Plain Text"/> <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="E-mail Signature"/> <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="HTML Top of Form"/> <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="HTML Bottom of Form"/> <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Normal (Web)"/> <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="HTML Acronym"/> <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="HTML Address"/> <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="HTML Cite"/> <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="HTML Code"/> <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="HTML Definition"/> <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="HTML 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SemiHidden="true" UnhideWhenUsed="true" Name="Table Simple 1"/> <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table Simple 2"/> <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table Simple 3"/> <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table Classic 1"/> <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table Classic 2"/> <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table Classic 3"/> <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table Classic 4"/> <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table Colorful 1"/> <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table Colorful 2"/> <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table Colorful 3"/> <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table Columns 1"/> <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table Columns 2"/> <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table Columns 3"/> <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table Columns 4"/> <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table Columns 5"/> <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table Grid 1"/> <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table Grid 2"/> <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table Grid 3"/> <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table Grid 4"/> <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table Grid 5"/> <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table Grid 6"/> <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table Grid 7"/> <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table Grid 8"/> <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table List 1"/> <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table List 2"/> <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table List 3"/> <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table List 4"/> <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table List 5"/> <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table List 6"/> <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table List 7"/> <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table List 8"/> <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table 3D effects 1"/> <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table 3D effects 2"/> <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table 3D effects 3"/> <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table Contemporary"/> <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table Elegant"/> <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table Professional"/> <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table Subtle 1"/> <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table Subtle 2"/> <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table Web 1"/> <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table Web 2"/> <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table Web 3"/> <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Balloon Text"/> <w:LsdException Locked="false" Priority="39" Name="Table Grid"/> <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table Theme"/> <w:LsdException Locked="false" SemiHidden="true" Name="Placeholder Text"/> <w:LsdException Locked="false" Priority="1" QFormat="true" Name="No Spacing"/> <w:LsdException Locked="false" Priority="60" Name="Light Shading"/> <w:LsdException Locked="false" Priority="61" Name="Light List"/> <w:LsdException Locked="false" Priority="62" Name="Light Grid"/> <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1"/> <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2"/> <w:LsdException Locked="false" Priority="65" Name="Medium List 1"/> <w:LsdException Locked="false" Priority="66" Name="Medium List 2"/> <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1"/> <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2"/> <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3"/> <w:LsdException Locked="false" Priority="70" Name="Dark List"/> <w:LsdException Locked="false" Priority="71" Name="Colorful Shading"/> <w:LsdException Locked="false" Priority="72" Name="Colorful List"/> <w:LsdException Locked="false" Priority="73" Name="Colorful Grid"/> <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 1"/> <w:LsdException Locked="false" Priority="61" Name="Light List Accent 1"/> <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 1"/> <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 1"/> <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 1"/> <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 1"/> <w:LsdException Locked="false" SemiHidden="true" Name="Revision"/> <w:LsdException Locked="false" Priority="34" QFormat="true" Name="List Paragraph"/> <w:LsdException Locked="false" Priority="29" QFormat="true" Name="Quote"/> <w:LsdException Locked="false" Priority="30" QFormat="true" Name="Intense Quote"/> <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 1"/> <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 1"/> <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 1"/> <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 1"/> <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 1"/> <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 1"/> <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 1"/> <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 1"/> <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 2"/> <w:LsdException Locked="false" Priority="61" Name="Light List Accent 2"/> <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 2"/> <w:LsdException Locked="false" Priority="63" Name="Medium 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Name="Light Grid Accent 3"/> <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 3"/> <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 3"/> <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 3"/> <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 3"/> <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 3"/> <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 3"/> <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 3"/> <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 3"/> <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 3"/> <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 3"/> <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 3"/> <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 4"/> <w:LsdException Locked="false" Priority="61" Name="Light List Accent 4"/> <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 4"/> <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 4"/> <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 4"/> <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 4"/> <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 4"/> <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 4"/> <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 4"/> <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 4"/> <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 4"/> <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 4"/> <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 4"/> <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 4"/> <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 5"/> <w:LsdException Locked="false" Priority="61" Name="Light List Accent 5"/> <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 5"/> <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 5"/> <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 5"/> <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 5"/> <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 5"/> <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 5"/> <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 5"/> <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 5"/> <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 5"/> <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 5"/> <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 5"/> <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 5"/> <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 6"/> <w:LsdException Locked="false" Priority="61" Name="Light List Accent 6"/> <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 6"/> <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 6"/> <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 6"/> <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 6"/> <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 6"/> <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 6"/> <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 6"/> <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 6"/> <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 6"/> <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 6"/> <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 6"/> <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 6"/> <w:LsdException Locked="false" Priority="19" QFormat="true" Name="Subtle Emphasis"/> <w:LsdException Locked="false" Priority="21" QFormat="true" Name="Intense Emphasis"/> <w:LsdException Locked="false" Priority="31" QFormat="true" Name="Subtle Reference"/> <w:LsdException Locked="false" Priority="32" QFormat="true" Name="Intense Reference"/> <w:LsdException Locked="false" Priority="33" QFormat="true" Name="Book Title"/> <w:LsdException Locked="false" Priority="37" SemiHidden="true" UnhideWhenUsed="true" Name="Bibliography"/> <w:LsdException Locked="false" Priority="39" SemiHidden="true" UnhideWhenUsed="true" QFormat="true" Name="TOC Heading"/> <w:LsdException Locked="false" Priority="41" Name="Plain Table 1"/> <w:LsdException Locked="false" Priority="42" Name="Plain Table 2"/> <w:LsdException Locked="false" Priority="43" Name="Plain Table 3"/> <w:LsdException Locked="false" Priority="44" Name="Plain Table 4"/> <w:LsdException Locked="false" Priority="45" Name="Plain Table 5"/> <w:LsdException Locked="false" Priority="40" Name="Grid Table Light"/> <w:LsdException Locked="false" Priority="46" Name="Grid Table 1 Light"/> <w:LsdException Locked="false" Priority="47" Name="Grid Table 2"/> <w:LsdException Locked="false" Priority="48" Name="Grid Table 3"/> <w:LsdException Locked="false" Priority="49" Name="Grid Table 4"/> <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark"/> <w:LsdException Locked="false" Priority="51" Name="Grid Table 6 Colorful"/> <w:LsdException Locked="false" Priority="52" Name="Grid Table 7 Colorful"/> <w:LsdException Locked="false" Priority="46" Name="Grid Table 1 Light Accent 1"/> <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 1"/> <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 1"/> <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 1"/> <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 1"/> <w:LsdException Locked="false" Priority="51" Name="Grid Table 6 Colorful Accent 1"/> <w:LsdException Locked="false" Priority="52" Name="Grid Table 7 Colorful Accent 1"/> <w:LsdException Locked="false" Priority="46" Name="Grid Table 1 Light Accent 2"/> <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 2"/> <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 2"/> <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 2"/> <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 2"/> <w:LsdException Locked="false" Priority="51" Name="Grid Table 6 Colorful Accent 2"/> <w:LsdException Locked="false" Priority="52" Name="Grid Table 7 Colorful Accent 2"/> <w:LsdException Locked="false" Priority="46" Name="Grid Table 1 Light Accent 3"/> <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 3"/> <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 3"/> <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 3"/> <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 3"/> <w:LsdException Locked="false" Priority="51" Name="Grid Table 6 Colorful Accent 3"/> <w:LsdException Locked="false" Priority="52" Name="Grid Table 7 Colorful Accent 3"/> <w:LsdException Locked="false" Priority="46" Name="Grid Table 1 Light Accent 4"/> <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 4"/> <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 4"/> <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 4"/> <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 4"/> <w:LsdException Locked="false" Priority="51" Name="Grid Table 6 Colorful Accent 4"/> <w:LsdException Locked="false" Priority="52" Name="Grid Table 7 Colorful Accent 4"/> <w:LsdException Locked="false" Priority="46" Name="Grid Table 1 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Locked="false" Priority="52" Name="Grid Table 7 Colorful Accent 6"/> <w:LsdException Locked="false" Priority="46" Name="List Table 1 Light"/> <w:LsdException Locked="false" Priority="47" Name="List Table 2"/> <w:LsdException Locked="false" Priority="48" Name="List Table 3"/> <w:LsdException Locked="false" Priority="49" Name="List Table 4"/> <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark"/> <w:LsdException Locked="false" Priority="51" Name="List Table 6 Colorful"/> <w:LsdException Locked="false" Priority="52" Name="List Table 7 Colorful"/> <w:LsdException Locked="false" Priority="46" Name="List Table 1 Light Accent 1"/> <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 1"/> <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 1"/> <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 1"/> <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 1"/> <w:LsdException Locked="false" 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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:
[TABLE="width: 693"]
<tbody>[TR]
[TD]A2[/TD]
[TD]B2[/TD]
[TD]C2[/TD]
[TD]D2[/TD]
[TD]E2[/TD]
[TD]F2[/TD]
[TD]G2[/TD]
[TD]H2[/TD]
[TD]I2[/TD]
[TD]J2[/TD]
[TD]K2[/TD]
[TD]L2[/TD]
[TD]M2[/TD]
[TD]N2[/TD]
[TD]O2[/TD]
[TD]P2[/TD]
[TD]Q2[/TD]
[TD]R2[/TD]
[TD]S2[/TD]
[TD]T2[/TD]
[TD]U2[/TD]
[/TR]
[TR]
[TD]4[/TD]
[TD]6[/TD]
[TD]7[/TD]
[TD]8[/TD]
[TD]9[/TD]
[TD]37[/TD]
[TD]35[/TD]
[TD]12[/TD]
[TD]10[/TD]
[TD]11[/TD]
[TD]54[/TD]
[TD]14[/TD]
[TD]16[/TD]
[TD]18[/TD]
[TD]19[/TD]
[TD]17[/TD]
[TD]34[/TD]
[TD]53[/TD]
[TD]27[/TD]
[TD]28[/TD]
[TD]13[/TD]
[/TR]
</tbody>[/TABLE]
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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