Problem 1913. GJam 2013 Veterans: Ocean View (Small)

Created by Richard Zapor

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This Challenge is derived from <a href = "http://code.google.com/codejam/contest/2334486/dashboard#s=p2">GJam 2013 Veterans Ocean View</a>. This is the Small data set witn N&lt;=50 and Q&lt;=4, guaranteed.The GJam story goes that as Supreme Ruler you are annoyed by complaints of non-ocean views on a hillside. To resolve the issue a minimum number of homes will be removed to provide a maximum number of ocean view homes. The Elevation of the homes should monotonically increase, no equal values, from element 1 thru the end.Succinct Challenge statement: Given a vector create the maximum length monotonically increasing vector by removing values. Report the number of values removed.Input: V , Vector length N&lt;=50 with values 1 thru 1000.Output: Q , minimum quantity of removed values to produce a valid vector [0:4]Examples: [V] [Q]<pre class="language-matlab">[1 4 3 3] [2] for [1 4] or [1 3]
[1 2 3 4 5] [0]
[4 3 2 1] [3]
</pre>Commentary:<pre class="language-matlab">1) The GJam Small test suite is not robust
2) nchoosek(50,4) is too slow for Cody and the 100 cases
3) The Large test suite is N&lt;=1000 with some delete cases >4
4) A Good Algorithm that solves the Large case is usually best to pursue
5) GJam Competition allows one Large submission within 10 minutes of download 
6) &lt;Large Suite Challenge>
</pre>

This Challenge is derived from <http://code.google.com/codejam/contest/2334486/dashboard#s=p2 GJam 2013 Veterans Ocean View>. This is the Small data set witn N<=50 and Q<=4, guaranteed.

The GJam story goes that as Supreme Ruler you are annoyed by complaints of non-ocean views on a hillside. To resolve the issue a minimum number of homes will be removed to provide a maximum number of ocean view homes. The Elevation of the homes should monotonically increase, no equal values, from element 1 thru the end.

*Succinct Challenge statement:* Given a vector create the maximum length monotonically increasing vector by removing values. Report the number of values removed.

*Input:* V , Vector length N<=50 with values 1 thru 1000.

*Output:* Q , minimum quantity of removed values to produce a valid vector [0:4]

*Examples:* [V] [Q]

[1 4 3 3] [2]  for [1 4] or [1 3]
  [1 2 3 4 5] [0]
  [4 3 2 1] [3]

*Commentary:*

1) The GJam Small test suite is not robust
 2) nchoosek(50,4) is too slow for Cody and the 100 cases
 3) The Large test suite is N<=1000 with some delete cases >4
 4) A Good Algorithm that solves the Large case is usually best to pursue
 5) GJam Competition allows one Large submission within 10 minutes of download 
 6) <Large Suite Challenge>

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Problem 1913. GJam 2013 Veterans: Ocean View (Small)

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Problem 1913. GJam 2013 Veterans: Ocean View (Small)

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