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commons-math-2.1 added
| author | dwinter |
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| date | Tue, 04 Jan 2011 10:02:07 +0100 |
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<HTML> <BODY BGCOLOR="white"> <PRE> <FONT color="green">001</FONT> /*<a name="line.1"></a> <FONT color="green">002</FONT> * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a> <FONT color="green">003</FONT> * contributor license agreements. See the NOTICE file distributed with<a name="line.3"></a> <FONT color="green">004</FONT> * this work for additional information regarding copyright ownership.<a name="line.4"></a> <FONT color="green">005</FONT> * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a> <FONT color="green">006</FONT> * (the "License"); you may not use this file except in compliance with<a name="line.6"></a> <FONT color="green">007</FONT> * the License. You may obtain a copy of the License at<a name="line.7"></a> <FONT color="green">008</FONT> *<a name="line.8"></a> <FONT color="green">009</FONT> * http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a> <FONT color="green">010</FONT> *<a name="line.10"></a> <FONT color="green">011</FONT> * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a> <FONT color="green">012</FONT> * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a> <FONT color="green">013</FONT> * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a> <FONT color="green">014</FONT> * See the License for the specific language governing permissions and<a name="line.14"></a> <FONT color="green">015</FONT> * limitations under the License.<a name="line.15"></a> <FONT color="green">016</FONT> */<a name="line.16"></a> <FONT color="green">017</FONT> package org.apache.commons.math.genetics;<a name="line.17"></a> <FONT color="green">018</FONT> <a name="line.18"></a> <FONT color="green">019</FONT> import java.util.ArrayList;<a name="line.19"></a> <FONT color="green">020</FONT> import java.util.Arrays;<a name="line.20"></a> <FONT color="green">021</FONT> import java.util.Collections;<a name="line.21"></a> <FONT color="green">022</FONT> import java.util.Comparator;<a name="line.22"></a> <FONT color="green">023</FONT> import java.util.List;<a name="line.23"></a> <FONT color="green">024</FONT> <a name="line.24"></a> <FONT color="green">025</FONT> /**<a name="line.25"></a> <FONT color="green">026</FONT> * <p><a name="line.26"></a> <FONT color="green">027</FONT> * Random Key chromosome is used for permutation representation. It is a vector<a name="line.27"></a> <FONT color="green">028</FONT> * of a fixed length of real numbers in [0,1] interval. The index of the i-th<a name="line.28"></a> <FONT color="green">029</FONT> * smallest value in the vector represents an i-th member of the permutation.<a name="line.29"></a> <FONT color="green">030</FONT> * </p><a name="line.30"></a> <FONT color="green">031</FONT> *<a name="line.31"></a> <FONT color="green">032</FONT> * <p><a name="line.32"></a> <FONT color="green">033</FONT> * For example, the random key [0.2, 0.3, 0.8, 0.1] corresponds to the<a name="line.33"></a> <FONT color="green">034</FONT> * permutation of indices (3,0,1,2). If the original (unpermuted) sequence would<a name="line.34"></a> <FONT color="green">035</FONT> * be (a,b,c,d), this would mean the sequence (d,a,b,c).<a name="line.35"></a> <FONT color="green">036</FONT> * </p><a name="line.36"></a> <FONT color="green">037</FONT> *<a name="line.37"></a> <FONT color="green">038</FONT> * <p><a name="line.38"></a> <FONT color="green">039</FONT> * With this representation, common operators like n-point crossover can be<a name="line.39"></a> <FONT color="green">040</FONT> * used, because any such chromosome represents a valid permutation.<a name="line.40"></a> <FONT color="green">041</FONT> * </p><a name="line.41"></a> <FONT color="green">042</FONT> *<a name="line.42"></a> <FONT color="green">043</FONT> * <p><a name="line.43"></a> <FONT color="green">044</FONT> * Since the chromosome (and thus its arrayRepresentation) is immutable, the<a name="line.44"></a> <FONT color="green">045</FONT> * array representation is sorted only once in the constructor.<a name="line.45"></a> <FONT color="green">046</FONT> * </p><a name="line.46"></a> <FONT color="green">047</FONT> *<a name="line.47"></a> <FONT color="green">048</FONT> * <p><a name="line.48"></a> <FONT color="green">049</FONT> * For details, see:<a name="line.49"></a> <FONT color="green">050</FONT> * <ul><a name="line.50"></a> <FONT color="green">051</FONT> * <li>Bean, J.C.: Genetic algorithms and random keys for sequencing and<a name="line.51"></a> <FONT color="green">052</FONT> * optimization. ORSA Journal on Computing 6 (1994) 154–160</li><a name="line.52"></a> <FONT color="green">053</FONT> * <li>Rothlauf, F.: Representations for Genetic and Evolutionary Algorithms.<a name="line.53"></a> <FONT color="green">054</FONT> * Volume 104 of Studies in Fuzziness and Soft Computing. Physica-Verlag,<a name="line.54"></a> <FONT color="green">055</FONT> * Heidelberg (2002)</li><a name="line.55"></a> <FONT color="green">056</FONT> * </ul><a name="line.56"></a> <FONT color="green">057</FONT> * </p><a name="line.57"></a> <FONT color="green">058</FONT> *<a name="line.58"></a> <FONT color="green">059</FONT> * @param <T><a name="line.59"></a> <FONT color="green">060</FONT> * type of the permuted objects<a name="line.60"></a> <FONT color="green">061</FONT> * @since 2.0<a name="line.61"></a> <FONT color="green">062</FONT> * @version $Revision: 811685 $ $Date: 2009-09-05 13:36:48 -0400 (Sat, 05 Sep 2009) $<a name="line.62"></a> <FONT color="green">063</FONT> */<a name="line.63"></a> <FONT color="green">064</FONT> public abstract class RandomKey<T> extends AbstractListChromosome<Double> implements PermutationChromosome<T> {<a name="line.64"></a> <FONT color="green">065</FONT> <a name="line.65"></a> <FONT color="green">066</FONT> /**<a name="line.66"></a> <FONT color="green">067</FONT> * Cache of sorted representation (unmodifiable).<a name="line.67"></a> <FONT color="green">068</FONT> */<a name="line.68"></a> <FONT color="green">069</FONT> private final List<Double> sortedRepresentation;<a name="line.69"></a> <FONT color="green">070</FONT> <a name="line.70"></a> <FONT color="green">071</FONT> /**<a name="line.71"></a> <FONT color="green">072</FONT> * Base sequence [0,1,...,n-1], permuted accorting to the representation (unmodifiable).<a name="line.72"></a> <FONT color="green">073</FONT> */<a name="line.73"></a> <FONT color="green">074</FONT> private final List<Integer> baseSeqPermutation;<a name="line.74"></a> <FONT color="green">075</FONT> <a name="line.75"></a> <FONT color="green">076</FONT> /**<a name="line.76"></a> <FONT color="green">077</FONT> * Constructor.<a name="line.77"></a> <FONT color="green">078</FONT> *<a name="line.78"></a> <FONT color="green">079</FONT> * @param representation list of [0,1] values representing the permutation<a name="line.79"></a> <FONT color="green">080</FONT> */<a name="line.80"></a> <FONT color="green">081</FONT> public RandomKey(List<Double> representation) {<a name="line.81"></a> <FONT color="green">082</FONT> super(representation);<a name="line.82"></a> <FONT color="green">083</FONT> // store the sorted representation<a name="line.83"></a> <FONT color="green">084</FONT> List<Double> sortedRepr = new ArrayList<Double> (getRepresentation());<a name="line.84"></a> <FONT color="green">085</FONT> Collections.sort(sortedRepr);<a name="line.85"></a> <FONT color="green">086</FONT> sortedRepresentation = Collections.unmodifiableList(sortedRepr);<a name="line.86"></a> <FONT color="green">087</FONT> // store the permutation of [0,1,...,n-1] list for toString() and isSame() methods<a name="line.87"></a> <FONT color="green">088</FONT> baseSeqPermutation = Collections.unmodifiableList(<a name="line.88"></a> <FONT color="green">089</FONT> decodeGeneric(baseSequence(getLength()), getRepresentation(), sortedRepresentation)<a name="line.89"></a> <FONT color="green">090</FONT> );<a name="line.90"></a> <FONT color="green">091</FONT> }<a name="line.91"></a> <FONT color="green">092</FONT> <a name="line.92"></a> <FONT color="green">093</FONT> /**<a name="line.93"></a> <FONT color="green">094</FONT> * Constructor.<a name="line.94"></a> <FONT color="green">095</FONT> *<a name="line.95"></a> <FONT color="green">096</FONT> * @param representation array of [0,1] values representing the permutation<a name="line.96"></a> <FONT color="green">097</FONT> */<a name="line.97"></a> <FONT color="green">098</FONT> public RandomKey(Double[] representation) {<a name="line.98"></a> <FONT color="green">099</FONT> this(Arrays.asList(representation));<a name="line.99"></a> <FONT color="green">100</FONT> }<a name="line.100"></a> <FONT color="green">101</FONT> <a name="line.101"></a> <FONT color="green">102</FONT> /**<a name="line.102"></a> <FONT color="green">103</FONT> * {@inheritDoc}<a name="line.103"></a> <FONT color="green">104</FONT> */<a name="line.104"></a> <FONT color="green">105</FONT> public List<T> decode(List<T> sequence) {<a name="line.105"></a> <FONT color="green">106</FONT> return decodeGeneric(sequence, getRepresentation(), sortedRepresentation);<a name="line.106"></a> <FONT color="green">107</FONT> }<a name="line.107"></a> <FONT color="green">108</FONT> <a name="line.108"></a> <FONT color="green">109</FONT> /**<a name="line.109"></a> <FONT color="green">110</FONT> * Decodes a permutation represented by <code>representation</code> and<a name="line.110"></a> <FONT color="green">111</FONT> * returns a (generic) list with the permuted values.<a name="line.111"></a> <FONT color="green">112</FONT> *<a name="line.112"></a> <FONT color="green">113</FONT> * @param <S> generic type of the sequence values<a name="line.113"></a> <FONT color="green">114</FONT> * @param sequence the unpermuted sequence<a name="line.114"></a> <FONT color="green">115</FONT> * @param representation representation of the permutation ([0,1] vector)<a name="line.115"></a> <FONT color="green">116</FONT> * @param sortedRepr sorted <code>representation</code><a name="line.116"></a> <FONT color="green">117</FONT> * @return list with the sequence values permuted according to the representation<a name="line.117"></a> <FONT color="green">118</FONT> */<a name="line.118"></a> <FONT color="green">119</FONT> private static <S> List<S> decodeGeneric(List<S> sequence, List<Double> representation, List<Double> sortedRepr) {<a name="line.119"></a> <FONT color="green">120</FONT> int l = sequence.size();<a name="line.120"></a> <FONT color="green">121</FONT> <a name="line.121"></a> <FONT color="green">122</FONT> if (representation.size() != l) {<a name="line.122"></a> <FONT color="green">123</FONT> throw new IllegalArgumentException(String.format("Length of sequence for decoding (%s) has to be equal to the length of the RandomKey (%s)", l, representation.size()));<a name="line.123"></a> <FONT color="green">124</FONT> }<a name="line.124"></a> <FONT color="green">125</FONT> if (representation.size() != sortedRepr.size()) {<a name="line.125"></a> <FONT color="green">126</FONT> throw new IllegalArgumentException(String.format("Representation and sortedRepr must have same sizes, %d != %d", representation.size(), sortedRepr.size()));<a name="line.126"></a> <FONT color="green">127</FONT> }<a name="line.127"></a> <FONT color="green">128</FONT> <a name="line.128"></a> <FONT color="green">129</FONT> List<Double> reprCopy = new ArrayList<Double> (representation);// do not modify the orig. representation<a name="line.129"></a> <FONT color="green">130</FONT> <a name="line.130"></a> <FONT color="green">131</FONT> // now find the indices in the original repr and use them for permuting<a name="line.131"></a> <FONT color="green">132</FONT> List<S> res = new ArrayList<S> (l);<a name="line.132"></a> <FONT color="green">133</FONT> for (int i=0; i<l; i++) {<a name="line.133"></a> <FONT color="green">134</FONT> int index = reprCopy.indexOf(sortedRepr.get(i));<a name="line.134"></a> <FONT color="green">135</FONT> res.add(sequence.get(index));<a name="line.135"></a> <FONT color="green">136</FONT> reprCopy.set(index, null);<a name="line.136"></a> <FONT color="green">137</FONT> }<a name="line.137"></a> <FONT color="green">138</FONT> return res;<a name="line.138"></a> <FONT color="green">139</FONT> }<a name="line.139"></a> <FONT color="green">140</FONT> <a name="line.140"></a> <FONT color="green">141</FONT> /**<a name="line.141"></a> <FONT color="green">142</FONT> * Returns <code>true</code> iff <code>another</code> is a RandomKey and<a name="line.142"></a> <FONT color="green">143</FONT> * encodes the same permutation.<a name="line.143"></a> <FONT color="green">144</FONT> *<a name="line.144"></a> <FONT color="green">145</FONT> * @param another chromosome to compare<a name="line.145"></a> <FONT color="green">146</FONT> * @return true iff chromosomes encode the same permutation<a name="line.146"></a> <FONT color="green">147</FONT> */<a name="line.147"></a> <FONT color="green">148</FONT> @Override<a name="line.148"></a> <FONT color="green">149</FONT> protected boolean isSame(Chromosome another) {<a name="line.149"></a> <FONT color="green">150</FONT> // type check<a name="line.150"></a> <FONT color="green">151</FONT> if (! (another instanceof RandomKey<?>))<a name="line.151"></a> <FONT color="green">152</FONT> return false;<a name="line.152"></a> <FONT color="green">153</FONT> RandomKey<?> anotherRk = (RandomKey<?>) another;<a name="line.153"></a> <FONT color="green">154</FONT> // size check<a name="line.154"></a> <FONT color="green">155</FONT> if (getLength() != anotherRk.getLength())<a name="line.155"></a> <FONT color="green">156</FONT> return false;<a name="line.156"></a> <FONT color="green">157</FONT> <a name="line.157"></a> <FONT color="green">158</FONT> // two different representations can still encode the same permutation<a name="line.158"></a> <FONT color="green">159</FONT> // the ordering is what counts<a name="line.159"></a> <FONT color="green">160</FONT> List<Integer> thisPerm = this.baseSeqPermutation;<a name="line.160"></a> <FONT color="green">161</FONT> List<Integer> anotherPerm = anotherRk.baseSeqPermutation;<a name="line.161"></a> <FONT color="green">162</FONT> <a name="line.162"></a> <FONT color="green">163</FONT> for (int i=0; i<getLength(); i++) {<a name="line.163"></a> <FONT color="green">164</FONT> if (thisPerm.get(i) != anotherPerm.get(i))<a name="line.164"></a> <FONT color="green">165</FONT> return false;<a name="line.165"></a> <FONT color="green">166</FONT> }<a name="line.166"></a> <FONT color="green">167</FONT> // the permutations are the same<a name="line.167"></a> <FONT color="green">168</FONT> return true;<a name="line.168"></a> <FONT color="green">169</FONT> }<a name="line.169"></a> <FONT color="green">170</FONT> <a name="line.170"></a> <FONT color="green">171</FONT> /**<a name="line.171"></a> <FONT color="green">172</FONT> * {@inheritDoc}<a name="line.172"></a> <FONT color="green">173</FONT> */<a name="line.173"></a> <FONT color="green">174</FONT> @Override<a name="line.174"></a> <FONT color="green">175</FONT> protected void checkValidity(java.util.List<Double> chromosomeRepresentation) throws InvalidRepresentationException {<a name="line.175"></a> <FONT color="green">176</FONT> for (double val : chromosomeRepresentation) {<a name="line.176"></a> <FONT color="green">177</FONT> if (val < 0 || val > 1) {<a name="line.177"></a> <FONT color="green">178</FONT> throw new InvalidRepresentationException("Values of representation must be in [0,1] interval");<a name="line.178"></a> <FONT color="green">179</FONT> }<a name="line.179"></a> <FONT color="green">180</FONT> }<a name="line.180"></a> <FONT color="green">181</FONT> }<a name="line.181"></a> <FONT color="green">182</FONT> <a name="line.182"></a> <FONT color="green">183</FONT> <a name="line.183"></a> <FONT color="green">184</FONT> /**<a name="line.184"></a> <FONT color="green">185</FONT> * Generates a representation corresponding to a random permutation of<a name="line.185"></a> <FONT color="green">186</FONT> * length l which can be passed to the RandomKey constructor.<a name="line.186"></a> <FONT color="green">187</FONT> *<a name="line.187"></a> <FONT color="green">188</FONT> * @param l<a name="line.188"></a> <FONT color="green">189</FONT> * length of the permutation<a name="line.189"></a> <FONT color="green">190</FONT> * @return representation of a random permutation<a name="line.190"></a> <FONT color="green">191</FONT> */<a name="line.191"></a> <FONT color="green">192</FONT> public static final List<Double> randomPermutation(int l) {<a name="line.192"></a> <FONT color="green">193</FONT> List<Double> repr = new ArrayList<Double>(l);<a name="line.193"></a> <FONT color="green">194</FONT> for (int i=0; i<l; i++) {<a name="line.194"></a> <FONT color="green">195</FONT> repr.add(GeneticAlgorithm.getRandomGenerator().nextDouble());<a name="line.195"></a> <FONT color="green">196</FONT> }<a name="line.196"></a> <FONT color="green">197</FONT> return repr;<a name="line.197"></a> <FONT color="green">198</FONT> }<a name="line.198"></a> <FONT color="green">199</FONT> <a name="line.199"></a> <FONT color="green">200</FONT> /**<a name="line.200"></a> <FONT color="green">201</FONT> * Generates a representation corresponding to an identity permutation of<a name="line.201"></a> <FONT color="green">202</FONT> * length l which can be passed to the RandomKey constructor.<a name="line.202"></a> <FONT color="green">203</FONT> *<a name="line.203"></a> <FONT color="green">204</FONT> * @param l<a name="line.204"></a> <FONT color="green">205</FONT> * length of the permutation<a name="line.205"></a> <FONT color="green">206</FONT> * @return representation of an identity permutation<a name="line.206"></a> <FONT color="green">207</FONT> */<a name="line.207"></a> <FONT color="green">208</FONT> public static final List<Double> identityPermutation(int l) {<a name="line.208"></a> <FONT color="green">209</FONT> List<Double> repr = new ArrayList<Double>(l);<a name="line.209"></a> <FONT color="green">210</FONT> for (int i=0; i<l; i++) {<a name="line.210"></a> <FONT color="green">211</FONT> repr.add((double)i/l);<a name="line.211"></a> <FONT color="green">212</FONT> }<a name="line.212"></a> <FONT color="green">213</FONT> return repr;<a name="line.213"></a> <FONT color="green">214</FONT> }<a name="line.214"></a> <FONT color="green">215</FONT> <a name="line.215"></a> <FONT color="green">216</FONT> /**<a name="line.216"></a> <FONT color="green">217</FONT> * Generates a representation of a permutation corresponding to the<a name="line.217"></a> <FONT color="green">218</FONT> * <code>data</code> sorted by <code>comparator</code>. The<a name="line.218"></a> <FONT color="green">219</FONT> * <code>data</code> is not modified during the process.<a name="line.219"></a> <FONT color="green">220</FONT> *<a name="line.220"></a> <FONT color="green">221</FONT> * This is useful if you want to inject some permutations to the initial<a name="line.221"></a> <FONT color="green">222</FONT> * population.<a name="line.222"></a> <FONT color="green">223</FONT> *<a name="line.223"></a> <FONT color="green">224</FONT> * @param <S> type of the data<a name="line.224"></a> <FONT color="green">225</FONT> * @param data list of data determining the order<a name="line.225"></a> <FONT color="green">226</FONT> * @param comparator how the data will be compared<a name="line.226"></a> <FONT color="green">227</FONT> * @return list representation of the permutation corresponding to the parameters<a name="line.227"></a> <FONT color="green">228</FONT> */<a name="line.228"></a> <FONT color="green">229</FONT> public static <S> List<Double> comparatorPermutation(List<S> data, Comparator<S> comparator) {<a name="line.229"></a> <FONT color="green">230</FONT> List<S> sortedData = new ArrayList<S> (data);<a name="line.230"></a> <FONT color="green">231</FONT> Collections.sort(sortedData, comparator);<a name="line.231"></a> <FONT color="green">232</FONT> <a name="line.232"></a> <FONT color="green">233</FONT> return inducedPermutation(data, sortedData);<a name="line.233"></a> <FONT color="green">234</FONT> }<a name="line.234"></a> <FONT color="green">235</FONT> <a name="line.235"></a> <FONT color="green">236</FONT> /**<a name="line.236"></a> <FONT color="green">237</FONT> * Generates a representation of a permutation corresponding to a<a name="line.237"></a> <FONT color="green">238</FONT> * permutation which yields <code>permutedData</code> when applied to<a name="line.238"></a> <FONT color="green">239</FONT> * <code>originalData</code>.<a name="line.239"></a> <FONT color="green">240</FONT> *<a name="line.240"></a> <FONT color="green">241</FONT> * This method can be viewed as an inverse to {@link #decode(List)}.<a name="line.241"></a> <FONT color="green">242</FONT> *<a name="line.242"></a> <FONT color="green">243</FONT> * @param <S> type of the data<a name="line.243"></a> <FONT color="green">244</FONT> * @param originalData the original, unpermuted data<a name="line.244"></a> <FONT color="green">245</FONT> * @param permutedData the data, somehow permuted<a name="line.245"></a> <FONT color="green">246</FONT> * @return representation of a permutation corresponding to the permutation <code>originalData -> permutedData</code><a name="line.246"></a> <FONT color="green">247</FONT> * @throws IllegalArgumentException iff the <code>permutedData</code> and <code>originalData</code> contains different data<a name="line.247"></a> <FONT color="green">248</FONT> */<a name="line.248"></a> <FONT color="green">249</FONT> public static <S> List<Double> inducedPermutation(List<S> originalData, List<S> permutedData) throws IllegalArgumentException {<a name="line.249"></a> <FONT color="green">250</FONT> if (originalData.size() != permutedData.size()) {<a name="line.250"></a> <FONT color="green">251</FONT> throw new IllegalArgumentException("originalData and permutedData must have same length");<a name="line.251"></a> <FONT color="green">252</FONT> }<a name="line.252"></a> <FONT color="green">253</FONT> int l = originalData.size();<a name="line.253"></a> <FONT color="green">254</FONT> <a name="line.254"></a> <FONT color="green">255</FONT> List<S> origDataCopy = new ArrayList<S> (originalData);<a name="line.255"></a> <FONT color="green">256</FONT> <a name="line.256"></a> <FONT color="green">257</FONT> Double[] res = new Double[l];<a name="line.257"></a> <FONT color="green">258</FONT> for (int i=0; i<l; i++) {<a name="line.258"></a> <FONT color="green">259</FONT> int index = origDataCopy.indexOf(permutedData.get(i));<a name="line.259"></a> <FONT color="green">260</FONT> if (index == -1) {<a name="line.260"></a> <FONT color="green">261</FONT> throw new IllegalArgumentException("originalData and permutedData must contain the same objects.");<a name="line.261"></a> <FONT color="green">262</FONT> }<a name="line.262"></a> <FONT color="green">263</FONT> res[index] = (double) i / l;<a name="line.263"></a> <FONT color="green">264</FONT> origDataCopy.set(index, null);<a name="line.264"></a> <FONT color="green">265</FONT> }<a name="line.265"></a> <FONT color="green">266</FONT> return Arrays.asList(res);<a name="line.266"></a> <FONT color="green">267</FONT> }<a name="line.267"></a> <FONT color="green">268</FONT> <a name="line.268"></a> <FONT color="green">269</FONT> /**<a name="line.269"></a> <FONT color="green">270</FONT> * {@inheritDoc}<a name="line.270"></a> <FONT color="green">271</FONT> */<a name="line.271"></a> <FONT color="green">272</FONT> @Override<a name="line.272"></a> <FONT color="green">273</FONT> public String toString() {<a name="line.273"></a> <FONT color="green">274</FONT> return String.format("(f=%s pi=(%s))", getFitness(), baseSeqPermutation);<a name="line.274"></a> <FONT color="green">275</FONT> }<a name="line.275"></a> <FONT color="green">276</FONT> <a name="line.276"></a> <FONT color="green">277</FONT> /**<a name="line.277"></a> <FONT color="green">278</FONT> * Helper for constructor. Generates a list of natural numbers (0,1,...,l-1).<a name="line.278"></a> <FONT color="green">279</FONT> *<a name="line.279"></a> <FONT color="green">280</FONT> * @param l length of list to generate<a name="line.280"></a> <FONT color="green">281</FONT> * @return list of integers from 0 to l-1<a name="line.281"></a> <FONT color="green">282</FONT> */<a name="line.282"></a> <FONT color="green">283</FONT> private static List<Integer> baseSequence(int l) {<a name="line.283"></a> <FONT color="green">284</FONT> List<Integer> baseSequence = new ArrayList<Integer> (l);<a name="line.284"></a> <FONT color="green">285</FONT> for (int i=0; i<l; i++) {<a name="line.285"></a> <FONT color="green">286</FONT> baseSequence.add(i);<a name="line.286"></a> <FONT color="green">287</FONT> }<a name="line.287"></a> <FONT color="green">288</FONT> return baseSequence;<a name="line.288"></a> <FONT color="green">289</FONT> }<a name="line.289"></a> <FONT color="green">290</FONT> }<a name="line.290"></a> </PRE> </BODY> </HTML>