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| <pre><span class="sourceLineNo">001</span>/*<a name="line.1"></a> |
| <span class="sourceLineNo">002</span> * Licensed to the Apache Software Foundation (ASF) under one<a name="line.2"></a> |
| <span class="sourceLineNo">003</span> * or more contributor license agreements. See the NOTICE file<a name="line.3"></a> |
| <span class="sourceLineNo">004</span> * distributed with this work for additional information<a name="line.4"></a> |
| <span class="sourceLineNo">005</span> * regarding copyright ownership. The ASF licenses this file<a name="line.5"></a> |
| <span class="sourceLineNo">006</span> * to you under the Apache License, Version 2.0 (the<a name="line.6"></a> |
| <span class="sourceLineNo">007</span> * "License"); you may not use this file except in compliance<a name="line.7"></a> |
| <span class="sourceLineNo">008</span> * with the License. You may obtain a copy of the License at<a name="line.8"></a> |
| <span class="sourceLineNo">009</span> *<a name="line.9"></a> |
| <span class="sourceLineNo">010</span> * http://www.apache.org/licenses/LICENSE-2.0<a name="line.10"></a> |
| <span class="sourceLineNo">011</span> *<a name="line.11"></a> |
| <span class="sourceLineNo">012</span> * Unless required by applicable law or agreed to in writing, software<a name="line.12"></a> |
| <span class="sourceLineNo">013</span> * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.13"></a> |
| <span class="sourceLineNo">014</span> * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.14"></a> |
| <span class="sourceLineNo">015</span> * See the License for the specific language governing permissions and<a name="line.15"></a> |
| <span class="sourceLineNo">016</span> * limitations under the License.<a name="line.16"></a> |
| <span class="sourceLineNo">017</span> */<a name="line.17"></a> |
| <span class="sourceLineNo">018</span>package org.apache.hadoop.hbase.util;<a name="line.18"></a> |
| <span class="sourceLineNo">019</span><a name="line.19"></a> |
| <span class="sourceLineNo">020</span>import java.util.Arrays;<a name="line.20"></a> |
| <span class="sourceLineNo">021</span>import java.util.Deque;<a name="line.21"></a> |
| <span class="sourceLineNo">022</span>import java.util.LinkedList;<a name="line.22"></a> |
| <span class="sourceLineNo">023</span>import org.apache.yetus.audience.InterfaceAudience;<a name="line.23"></a> |
| <span class="sourceLineNo">024</span><a name="line.24"></a> |
| <span class="sourceLineNo">025</span>/**<a name="line.25"></a> |
| <span class="sourceLineNo">026</span> * Computes the optimal (minimal cost) assignment of jobs to workers (or other analogous) concepts<a name="line.26"></a> |
| <span class="sourceLineNo">027</span> * given a cost matrix of each pair of job and worker, using the algorithm by James Munkres in<a name="line.27"></a> |
| <span class="sourceLineNo">028</span> * "Algorithms for the Assignment and Transportation Problems", with additional optimizations as<a name="line.28"></a> |
| <span class="sourceLineNo">029</span> * described by Jin Kue Wong in "A New Implementation of an Algorithm for the Optimal Assignment<a name="line.29"></a> |
| <span class="sourceLineNo">030</span> * Problem: An Improved Version of Munkres' Algorithm". The algorithm runs in O(n^3) time and need<a name="line.30"></a> |
| <span class="sourceLineNo">031</span> * O(n^2) auxiliary space where n is the number of jobs or workers, whichever is greater.<a name="line.31"></a> |
| <span class="sourceLineNo">032</span> */<a name="line.32"></a> |
| <span class="sourceLineNo">033</span>@InterfaceAudience.Private<a name="line.33"></a> |
| <span class="sourceLineNo">034</span>public class MunkresAssignment {<a name="line.34"></a> |
| <span class="sourceLineNo">035</span><a name="line.35"></a> |
| <span class="sourceLineNo">036</span> // The original algorithm by Munkres uses the terms STAR and PRIME to denote<a name="line.36"></a> |
| <span class="sourceLineNo">037</span> // different states of zero values in the cost matrix. These values are<a name="line.37"></a> |
| <span class="sourceLineNo">038</span> // represented as byte constants instead of enums to save space in the mask<a name="line.38"></a> |
| <span class="sourceLineNo">039</span> // matrix by a factor of 4n^2 where n is the size of the problem.<a name="line.39"></a> |
| <span class="sourceLineNo">040</span> private static final byte NONE = 0;<a name="line.40"></a> |
| <span class="sourceLineNo">041</span> private static final byte STAR = 1;<a name="line.41"></a> |
| <span class="sourceLineNo">042</span> private static final byte PRIME = 2;<a name="line.42"></a> |
| <span class="sourceLineNo">043</span><a name="line.43"></a> |
| <span class="sourceLineNo">044</span> // The algorithm requires that the number of column is at least as great as<a name="line.44"></a> |
| <span class="sourceLineNo">045</span> // the number of rows. If that is not the case, then the cost matrix should<a name="line.45"></a> |
| <span class="sourceLineNo">046</span> // be transposed before computation, and the solution matrix transposed before<a name="line.46"></a> |
| <span class="sourceLineNo">047</span> // returning to the caller.<a name="line.47"></a> |
| <span class="sourceLineNo">048</span> private final boolean transposed;<a name="line.48"></a> |
| <span class="sourceLineNo">049</span><a name="line.49"></a> |
| <span class="sourceLineNo">050</span> // The number of rows of internal matrices.<a name="line.50"></a> |
| <span class="sourceLineNo">051</span> private final int rows;<a name="line.51"></a> |
| <span class="sourceLineNo">052</span><a name="line.52"></a> |
| <span class="sourceLineNo">053</span> // The number of columns of internal matrices.<a name="line.53"></a> |
| <span class="sourceLineNo">054</span> private final int cols;<a name="line.54"></a> |
| <span class="sourceLineNo">055</span><a name="line.55"></a> |
| <span class="sourceLineNo">056</span> // The cost matrix, the cost of assigning each row index to column index.<a name="line.56"></a> |
| <span class="sourceLineNo">057</span> private float[][] cost;<a name="line.57"></a> |
| <span class="sourceLineNo">058</span><a name="line.58"></a> |
| <span class="sourceLineNo">059</span> // Mask of zero cost assignment states.<a name="line.59"></a> |
| <span class="sourceLineNo">060</span> private byte[][] mask;<a name="line.60"></a> |
| <span class="sourceLineNo">061</span><a name="line.61"></a> |
| <span class="sourceLineNo">062</span> // Covering some rows of the cost matrix.<a name="line.62"></a> |
| <span class="sourceLineNo">063</span> private boolean[] rowsCovered;<a name="line.63"></a> |
| <span class="sourceLineNo">064</span><a name="line.64"></a> |
| <span class="sourceLineNo">065</span> // Covering some columns of the cost matrix.<a name="line.65"></a> |
| <span class="sourceLineNo">066</span> private boolean[] colsCovered;<a name="line.66"></a> |
| <span class="sourceLineNo">067</span><a name="line.67"></a> |
| <span class="sourceLineNo">068</span> // The alternating path between starred zeroes and primed zeroes<a name="line.68"></a> |
| <span class="sourceLineNo">069</span> private Deque<Pair<Integer, Integer>> path;<a name="line.69"></a> |
| <span class="sourceLineNo">070</span><a name="line.70"></a> |
| <span class="sourceLineNo">071</span> // The solution, marking which rows should be assigned to which columns. The<a name="line.71"></a> |
| <span class="sourceLineNo">072</span> // positions of elements in this array correspond to the rows of the cost<a name="line.72"></a> |
| <span class="sourceLineNo">073</span> // matrix, and the value of each element correspond to the columns of the cost<a name="line.73"></a> |
| <span class="sourceLineNo">074</span> // matrix, i.e. assignments[i] = j indicates that row i should be assigned to<a name="line.74"></a> |
| <span class="sourceLineNo">075</span> // column j.<a name="line.75"></a> |
| <span class="sourceLineNo">076</span> private int[] assignments;<a name="line.76"></a> |
| <span class="sourceLineNo">077</span><a name="line.77"></a> |
| <span class="sourceLineNo">078</span> // Improvements described by Jin Kue Wong cache the least value in each row,<a name="line.78"></a> |
| <span class="sourceLineNo">079</span> // as well as the column index of the least value in each row, and the pending<a name="line.79"></a> |
| <span class="sourceLineNo">080</span> // adjustments to each row and each column.<a name="line.80"></a> |
| <span class="sourceLineNo">081</span> private float[] leastInRow;<a name="line.81"></a> |
| <span class="sourceLineNo">082</span> private int[] leastInRowIndex;<a name="line.82"></a> |
| <span class="sourceLineNo">083</span> private float[] rowAdjust;<a name="line.83"></a> |
| <span class="sourceLineNo">084</span> private float[] colAdjust;<a name="line.84"></a> |
| <span class="sourceLineNo">085</span><a name="line.85"></a> |
| <span class="sourceLineNo">086</span> /**<a name="line.86"></a> |
| <span class="sourceLineNo">087</span> * Construct a new problem instance with the specified cost matrix. The cost matrix must be<a name="line.87"></a> |
| <span class="sourceLineNo">088</span> * rectangular, though not necessarily square. If one dimension is greater than the other, some<a name="line.88"></a> |
| <span class="sourceLineNo">089</span> * elements in the greater dimension will not be assigned. The input cost matrix will not be<a name="line.89"></a> |
| <span class="sourceLineNo">090</span> * modified.<a name="line.90"></a> |
| <span class="sourceLineNo">091</span> */<a name="line.91"></a> |
| <span class="sourceLineNo">092</span> public MunkresAssignment(float[][] costMatrix) {<a name="line.92"></a> |
| <span class="sourceLineNo">093</span> // The algorithm assumes that the number of columns is at least as great as<a name="line.93"></a> |
| <span class="sourceLineNo">094</span> // the number of rows. If this is not the case of the input matrix, then<a name="line.94"></a> |
| <span class="sourceLineNo">095</span> // all internal structures must be transposed relative to the input.<a name="line.95"></a> |
| <span class="sourceLineNo">096</span> this.transposed = costMatrix.length > costMatrix[0].length;<a name="line.96"></a> |
| <span class="sourceLineNo">097</span> if (this.transposed) {<a name="line.97"></a> |
| <span class="sourceLineNo">098</span> this.rows = costMatrix[0].length;<a name="line.98"></a> |
| <span class="sourceLineNo">099</span> this.cols = costMatrix.length;<a name="line.99"></a> |
| <span class="sourceLineNo">100</span> } else {<a name="line.100"></a> |
| <span class="sourceLineNo">101</span> this.rows = costMatrix.length;<a name="line.101"></a> |
| <span class="sourceLineNo">102</span> this.cols = costMatrix[0].length;<a name="line.102"></a> |
| <span class="sourceLineNo">103</span> }<a name="line.103"></a> |
| <span class="sourceLineNo">104</span><a name="line.104"></a> |
| <span class="sourceLineNo">105</span> cost = new float[rows][cols];<a name="line.105"></a> |
| <span class="sourceLineNo">106</span> mask = new byte[rows][cols];<a name="line.106"></a> |
| <span class="sourceLineNo">107</span> rowsCovered = new boolean[rows];<a name="line.107"></a> |
| <span class="sourceLineNo">108</span> colsCovered = new boolean[cols];<a name="line.108"></a> |
| <span class="sourceLineNo">109</span> path = new LinkedList<>();<a name="line.109"></a> |
| <span class="sourceLineNo">110</span><a name="line.110"></a> |
| <span class="sourceLineNo">111</span> leastInRow = new float[rows];<a name="line.111"></a> |
| <span class="sourceLineNo">112</span> leastInRowIndex = new int[rows];<a name="line.112"></a> |
| <span class="sourceLineNo">113</span> rowAdjust = new float[rows];<a name="line.113"></a> |
| <span class="sourceLineNo">114</span> colAdjust = new float[cols];<a name="line.114"></a> |
| <span class="sourceLineNo">115</span><a name="line.115"></a> |
| <span class="sourceLineNo">116</span> assignments = null;<a name="line.116"></a> |
| <span class="sourceLineNo">117</span><a name="line.117"></a> |
| <span class="sourceLineNo">118</span> // Copy cost matrix.<a name="line.118"></a> |
| <span class="sourceLineNo">119</span> if (transposed) {<a name="line.119"></a> |
| <span class="sourceLineNo">120</span> for (int r = 0; r < rows; r++) {<a name="line.120"></a> |
| <span class="sourceLineNo">121</span> for (int c = 0; c < cols; c++) {<a name="line.121"></a> |
| <span class="sourceLineNo">122</span> cost[r][c] = costMatrix[c][r];<a name="line.122"></a> |
| <span class="sourceLineNo">123</span> }<a name="line.123"></a> |
| <span class="sourceLineNo">124</span> }<a name="line.124"></a> |
| <span class="sourceLineNo">125</span> } else {<a name="line.125"></a> |
| <span class="sourceLineNo">126</span> for (int r = 0; r < rows; r++) {<a name="line.126"></a> |
| <span class="sourceLineNo">127</span> System.arraycopy(costMatrix[r], 0, cost[r], 0, cols);<a name="line.127"></a> |
| <span class="sourceLineNo">128</span> }<a name="line.128"></a> |
| <span class="sourceLineNo">129</span> }<a name="line.129"></a> |
| <span class="sourceLineNo">130</span><a name="line.130"></a> |
| <span class="sourceLineNo">131</span> // Costs must be finite otherwise the matrix can get into a bad state where<a name="line.131"></a> |
| <span class="sourceLineNo">132</span> // no progress can be made. If your use case depends on a distinction<a name="line.132"></a> |
| <span class="sourceLineNo">133</span> // between costs of MAX_VALUE and POSITIVE_INFINITY, you're doing it wrong.<a name="line.133"></a> |
| <span class="sourceLineNo">134</span> for (int r = 0; r < rows; r++) {<a name="line.134"></a> |
| <span class="sourceLineNo">135</span> for (int c = 0; c < cols; c++) {<a name="line.135"></a> |
| <span class="sourceLineNo">136</span> if (cost[r][c] == Float.POSITIVE_INFINITY) {<a name="line.136"></a> |
| <span class="sourceLineNo">137</span> cost[r][c] = Float.MAX_VALUE;<a name="line.137"></a> |
| <span class="sourceLineNo">138</span> }<a name="line.138"></a> |
| <span class="sourceLineNo">139</span> }<a name="line.139"></a> |
| <span class="sourceLineNo">140</span> }<a name="line.140"></a> |
| <span class="sourceLineNo">141</span> }<a name="line.141"></a> |
| <span class="sourceLineNo">142</span><a name="line.142"></a> |
| <span class="sourceLineNo">143</span> /**<a name="line.143"></a> |
| <span class="sourceLineNo">144</span> * Get the optimal assignments. The returned array will have the same number of elements as the<a name="line.144"></a> |
| <span class="sourceLineNo">145</span> * number of elements as the number of rows in the input cost matrix. Each element will indicate<a name="line.145"></a> |
| <span class="sourceLineNo">146</span> * which column should be assigned to that row or -1 if no column should be assigned, i.e. if<a name="line.146"></a> |
| <span class="sourceLineNo">147</span> * result[i] = j then row i should be assigned to column j. Subsequent invocations of this method<a name="line.147"></a> |
| <span class="sourceLineNo">148</span> * will simply return the same object without additional computation.<a name="line.148"></a> |
| <span class="sourceLineNo">149</span> * @return an array with the optimal assignments<a name="line.149"></a> |
| <span class="sourceLineNo">150</span> */<a name="line.150"></a> |
| <span class="sourceLineNo">151</span> public int[] solve() {<a name="line.151"></a> |
| <span class="sourceLineNo">152</span> // If this assignment problem has already been solved, return the known<a name="line.152"></a> |
| <span class="sourceLineNo">153</span> // solution<a name="line.153"></a> |
| <span class="sourceLineNo">154</span> if (assignments != null) {<a name="line.154"></a> |
| <span class="sourceLineNo">155</span> return assignments;<a name="line.155"></a> |
| <span class="sourceLineNo">156</span> }<a name="line.156"></a> |
| <span class="sourceLineNo">157</span><a name="line.157"></a> |
| <span class="sourceLineNo">158</span> preliminaries();<a name="line.158"></a> |
| <span class="sourceLineNo">159</span><a name="line.159"></a> |
| <span class="sourceLineNo">160</span> // Find the optimal assignments.<a name="line.160"></a> |
| <span class="sourceLineNo">161</span> while (!testIsDone()) {<a name="line.161"></a> |
| <span class="sourceLineNo">162</span> while (!stepOne()) {<a name="line.162"></a> |
| <span class="sourceLineNo">163</span> stepThree();<a name="line.163"></a> |
| <span class="sourceLineNo">164</span> }<a name="line.164"></a> |
| <span class="sourceLineNo">165</span> stepTwo();<a name="line.165"></a> |
| <span class="sourceLineNo">166</span> }<a name="line.166"></a> |
| <span class="sourceLineNo">167</span><a name="line.167"></a> |
| <span class="sourceLineNo">168</span> // Extract the assignments from the mask matrix.<a name="line.168"></a> |
| <span class="sourceLineNo">169</span> if (transposed) {<a name="line.169"></a> |
| <span class="sourceLineNo">170</span> assignments = new int[cols];<a name="line.170"></a> |
| <span class="sourceLineNo">171</span> outer: for (int c = 0; c < cols; c++) {<a name="line.171"></a> |
| <span class="sourceLineNo">172</span> for (int r = 0; r < rows; r++) {<a name="line.172"></a> |
| <span class="sourceLineNo">173</span> if (mask[r][c] == STAR) {<a name="line.173"></a> |
| <span class="sourceLineNo">174</span> assignments[c] = r;<a name="line.174"></a> |
| <span class="sourceLineNo">175</span> continue outer;<a name="line.175"></a> |
| <span class="sourceLineNo">176</span> }<a name="line.176"></a> |
| <span class="sourceLineNo">177</span> }<a name="line.177"></a> |
| <span class="sourceLineNo">178</span> // There is no assignment for this row of the input/output.<a name="line.178"></a> |
| <span class="sourceLineNo">179</span> assignments[c] = -1;<a name="line.179"></a> |
| <span class="sourceLineNo">180</span> }<a name="line.180"></a> |
| <span class="sourceLineNo">181</span> } else {<a name="line.181"></a> |
| <span class="sourceLineNo">182</span> assignments = new int[rows];<a name="line.182"></a> |
| <span class="sourceLineNo">183</span> outer: for (int r = 0; r < rows; r++) {<a name="line.183"></a> |
| <span class="sourceLineNo">184</span> for (int c = 0; c < cols; c++) {<a name="line.184"></a> |
| <span class="sourceLineNo">185</span> if (mask[r][c] == STAR) {<a name="line.185"></a> |
| <span class="sourceLineNo">186</span> assignments[r] = c;<a name="line.186"></a> |
| <span class="sourceLineNo">187</span> continue outer;<a name="line.187"></a> |
| <span class="sourceLineNo">188</span> }<a name="line.188"></a> |
| <span class="sourceLineNo">189</span> }<a name="line.189"></a> |
| <span class="sourceLineNo">190</span> }<a name="line.190"></a> |
| <span class="sourceLineNo">191</span> }<a name="line.191"></a> |
| <span class="sourceLineNo">192</span><a name="line.192"></a> |
| <span class="sourceLineNo">193</span> // Once the solution has been computed, there is no need to keep any of the<a name="line.193"></a> |
| <span class="sourceLineNo">194</span> // other internal structures. Clear all unnecessary internal references so<a name="line.194"></a> |
| <span class="sourceLineNo">195</span> // the garbage collector may reclaim that memory.<a name="line.195"></a> |
| <span class="sourceLineNo">196</span> cost = null;<a name="line.196"></a> |
| <span class="sourceLineNo">197</span> mask = null;<a name="line.197"></a> |
| <span class="sourceLineNo">198</span> rowsCovered = null;<a name="line.198"></a> |
| <span class="sourceLineNo">199</span> colsCovered = null;<a name="line.199"></a> |
| <span class="sourceLineNo">200</span> path = null;<a name="line.200"></a> |
| <span class="sourceLineNo">201</span> leastInRow = null;<a name="line.201"></a> |
| <span class="sourceLineNo">202</span> leastInRowIndex = null;<a name="line.202"></a> |
| <span class="sourceLineNo">203</span> rowAdjust = null;<a name="line.203"></a> |
| <span class="sourceLineNo">204</span> colAdjust = null;<a name="line.204"></a> |
| <span class="sourceLineNo">205</span><a name="line.205"></a> |
| <span class="sourceLineNo">206</span> return assignments;<a name="line.206"></a> |
| <span class="sourceLineNo">207</span> }<a name="line.207"></a> |
| <span class="sourceLineNo">208</span><a name="line.208"></a> |
| <span class="sourceLineNo">209</span> /**<a name="line.209"></a> |
| <span class="sourceLineNo">210</span> * Corresponds to the "preliminaries" step of the original algorithm. Guarantees that the matrix<a name="line.210"></a> |
| <span class="sourceLineNo">211</span> * is an equivalent non-negative matrix with at least one zero in each row.<a name="line.211"></a> |
| <span class="sourceLineNo">212</span> */<a name="line.212"></a> |
| <span class="sourceLineNo">213</span> private void preliminaries() {<a name="line.213"></a> |
| <span class="sourceLineNo">214</span> for (int r = 0; r < rows; r++) {<a name="line.214"></a> |
| <span class="sourceLineNo">215</span> // Find the minimum cost of each row.<a name="line.215"></a> |
| <span class="sourceLineNo">216</span> float min = Float.POSITIVE_INFINITY;<a name="line.216"></a> |
| <span class="sourceLineNo">217</span> for (int c = 0; c < cols; c++) {<a name="line.217"></a> |
| <span class="sourceLineNo">218</span> min = Math.min(min, cost[r][c]);<a name="line.218"></a> |
| <span class="sourceLineNo">219</span> }<a name="line.219"></a> |
| <span class="sourceLineNo">220</span><a name="line.220"></a> |
| <span class="sourceLineNo">221</span> // Subtract that minimum cost from each element in the row.<a name="line.221"></a> |
| <span class="sourceLineNo">222</span> for (int c = 0; c < cols; c++) {<a name="line.222"></a> |
| <span class="sourceLineNo">223</span> cost[r][c] -= min;<a name="line.223"></a> |
| <span class="sourceLineNo">224</span><a name="line.224"></a> |
| <span class="sourceLineNo">225</span> // If the element is now zero and there are no zeroes in the same row<a name="line.225"></a> |
| <span class="sourceLineNo">226</span> // or column which are already starred, then star this one. There<a name="line.226"></a> |
| <span class="sourceLineNo">227</span> // must be at least one zero because of subtracting the min cost.<a name="line.227"></a> |
| <span class="sourceLineNo">228</span> if (cost[r][c] == 0 && !rowsCovered[r] && !colsCovered[c]) {<a name="line.228"></a> |
| <span class="sourceLineNo">229</span> mask[r][c] = STAR;<a name="line.229"></a> |
| <span class="sourceLineNo">230</span> // Cover this row and column so that no other zeroes in them can be<a name="line.230"></a> |
| <span class="sourceLineNo">231</span> // starred.<a name="line.231"></a> |
| <span class="sourceLineNo">232</span> rowsCovered[r] = true;<a name="line.232"></a> |
| <span class="sourceLineNo">233</span> colsCovered[c] = true;<a name="line.233"></a> |
| <span class="sourceLineNo">234</span> }<a name="line.234"></a> |
| <span class="sourceLineNo">235</span> }<a name="line.235"></a> |
| <span class="sourceLineNo">236</span> }<a name="line.236"></a> |
| <span class="sourceLineNo">237</span><a name="line.237"></a> |
| <span class="sourceLineNo">238</span> // Clear the covered rows and columns.<a name="line.238"></a> |
| <span class="sourceLineNo">239</span> Arrays.fill(rowsCovered, false);<a name="line.239"></a> |
| <span class="sourceLineNo">240</span> Arrays.fill(colsCovered, false);<a name="line.240"></a> |
| <span class="sourceLineNo">241</span> }<a name="line.241"></a> |
| <span class="sourceLineNo">242</span><a name="line.242"></a> |
| <span class="sourceLineNo">243</span> /**<a name="line.243"></a> |
| <span class="sourceLineNo">244</span> * Test whether the algorithm is done, i.e. we have the optimal assignment. This occurs when there<a name="line.244"></a> |
| <span class="sourceLineNo">245</span> * is exactly one starred zero in each row.<a name="line.245"></a> |
| <span class="sourceLineNo">246</span> * @return true if the algorithm is done<a name="line.246"></a> |
| <span class="sourceLineNo">247</span> */<a name="line.247"></a> |
| <span class="sourceLineNo">248</span> private boolean testIsDone() {<a name="line.248"></a> |
| <span class="sourceLineNo">249</span> // Cover all columns containing a starred zero. There can be at most one<a name="line.249"></a> |
| <span class="sourceLineNo">250</span> // starred zero per column. Therefore, a covered column has an optimal<a name="line.250"></a> |
| <span class="sourceLineNo">251</span> // assignment.<a name="line.251"></a> |
| <span class="sourceLineNo">252</span> for (int r = 0; r < rows; r++) {<a name="line.252"></a> |
| <span class="sourceLineNo">253</span> for (int c = 0; c < cols; c++) {<a name="line.253"></a> |
| <span class="sourceLineNo">254</span> if (mask[r][c] == STAR) {<a name="line.254"></a> |
| <span class="sourceLineNo">255</span> colsCovered[c] = true;<a name="line.255"></a> |
| <span class="sourceLineNo">256</span> }<a name="line.256"></a> |
| <span class="sourceLineNo">257</span> }<a name="line.257"></a> |
| <span class="sourceLineNo">258</span> }<a name="line.258"></a> |
| <span class="sourceLineNo">259</span><a name="line.259"></a> |
| <span class="sourceLineNo">260</span> // Count the total number of covered columns.<a name="line.260"></a> |
| <span class="sourceLineNo">261</span> int coveredCols = 0;<a name="line.261"></a> |
| <span class="sourceLineNo">262</span> for (int c = 0; c < cols; c++) {<a name="line.262"></a> |
| <span class="sourceLineNo">263</span> coveredCols += colsCovered[c] ? 1 : 0;<a name="line.263"></a> |
| <span class="sourceLineNo">264</span> }<a name="line.264"></a> |
| <span class="sourceLineNo">265</span><a name="line.265"></a> |
| <span class="sourceLineNo">266</span> // Apply an row and column adjustments that are pending.<a name="line.266"></a> |
| <span class="sourceLineNo">267</span> for (int r = 0; r < rows; r++) {<a name="line.267"></a> |
| <span class="sourceLineNo">268</span> for (int c = 0; c < cols; c++) {<a name="line.268"></a> |
| <span class="sourceLineNo">269</span> cost[r][c] += rowAdjust[r];<a name="line.269"></a> |
| <span class="sourceLineNo">270</span> cost[r][c] += colAdjust[c];<a name="line.270"></a> |
| <span class="sourceLineNo">271</span> }<a name="line.271"></a> |
| <span class="sourceLineNo">272</span> }<a name="line.272"></a> |
| <span class="sourceLineNo">273</span><a name="line.273"></a> |
| <span class="sourceLineNo">274</span> // Clear the pending row and column adjustments.<a name="line.274"></a> |
| <span class="sourceLineNo">275</span> Arrays.fill(rowAdjust, 0);<a name="line.275"></a> |
| <span class="sourceLineNo">276</span> Arrays.fill(colAdjust, 0);<a name="line.276"></a> |
| <span class="sourceLineNo">277</span><a name="line.277"></a> |
| <span class="sourceLineNo">278</span> // The covers on columns and rows may have been reset, recompute the least<a name="line.278"></a> |
| <span class="sourceLineNo">279</span> // value for each row.<a name="line.279"></a> |
| <span class="sourceLineNo">280</span> for (int r = 0; r < rows; r++) {<a name="line.280"></a> |
| <span class="sourceLineNo">281</span> leastInRow[r] = Float.POSITIVE_INFINITY;<a name="line.281"></a> |
| <span class="sourceLineNo">282</span> for (int c = 0; c < cols; c++) {<a name="line.282"></a> |
| <span class="sourceLineNo">283</span> if (!rowsCovered[r] && !colsCovered[c] && cost[r][c] < leastInRow[r]) {<a name="line.283"></a> |
| <span class="sourceLineNo">284</span> leastInRow[r] = cost[r][c];<a name="line.284"></a> |
| <span class="sourceLineNo">285</span> leastInRowIndex[r] = c;<a name="line.285"></a> |
| <span class="sourceLineNo">286</span> }<a name="line.286"></a> |
| <span class="sourceLineNo">287</span> }<a name="line.287"></a> |
| <span class="sourceLineNo">288</span> }<a name="line.288"></a> |
| <span class="sourceLineNo">289</span><a name="line.289"></a> |
| <span class="sourceLineNo">290</span> // If all columns are covered, then we are done. Since there may be more<a name="line.290"></a> |
| <span class="sourceLineNo">291</span> // columns than rows, we are also done if the number of covered columns is<a name="line.291"></a> |
| <span class="sourceLineNo">292</span> // at least as great as the number of rows.<a name="line.292"></a> |
| <span class="sourceLineNo">293</span> return (coveredCols == cols || coveredCols >= rows);<a name="line.293"></a> |
| <span class="sourceLineNo">294</span> }<a name="line.294"></a> |
| <span class="sourceLineNo">295</span><a name="line.295"></a> |
| <span class="sourceLineNo">296</span> /**<a name="line.296"></a> |
| <span class="sourceLineNo">297</span> * Corresponds to step 1 of the original algorithm.<a name="line.297"></a> |
| <span class="sourceLineNo">298</span> * @return false if all zeroes are covered<a name="line.298"></a> |
| <span class="sourceLineNo">299</span> */<a name="line.299"></a> |
| <span class="sourceLineNo">300</span> private boolean stepOne() {<a name="line.300"></a> |
| <span class="sourceLineNo">301</span> while (true) {<a name="line.301"></a> |
| <span class="sourceLineNo">302</span> Pair<Integer, Integer> zero = findUncoveredZero();<a name="line.302"></a> |
| <span class="sourceLineNo">303</span> if (zero == null) {<a name="line.303"></a> |
| <span class="sourceLineNo">304</span> // No uncovered zeroes, need to manipulate the cost matrix in step<a name="line.304"></a> |
| <span class="sourceLineNo">305</span> // three.<a name="line.305"></a> |
| <span class="sourceLineNo">306</span> return false;<a name="line.306"></a> |
| <span class="sourceLineNo">307</span> } else {<a name="line.307"></a> |
| <span class="sourceLineNo">308</span> // Prime the uncovered zero and find a starred zero in the same row.<a name="line.308"></a> |
| <span class="sourceLineNo">309</span> mask[zero.getFirst()][zero.getSecond()] = PRIME;<a name="line.309"></a> |
| <span class="sourceLineNo">310</span> Pair<Integer, Integer> star = starInRow(zero.getFirst());<a name="line.310"></a> |
| <span class="sourceLineNo">311</span> if (star != null) {<a name="line.311"></a> |
| <span class="sourceLineNo">312</span> // Cover the row with both the newly primed zero and the starred zero.<a name="line.312"></a> |
| <span class="sourceLineNo">313</span> // Since this is the only place where zeroes are primed, and we cover<a name="line.313"></a> |
| <span class="sourceLineNo">314</span> // it here, and rows are only uncovered when primes are erased, then<a name="line.314"></a> |
| <span class="sourceLineNo">315</span> // there can be at most one primed uncovered zero.<a name="line.315"></a> |
| <span class="sourceLineNo">316</span> rowsCovered[star.getFirst()] = true;<a name="line.316"></a> |
| <span class="sourceLineNo">317</span> colsCovered[star.getSecond()] = false;<a name="line.317"></a> |
| <span class="sourceLineNo">318</span> updateMin(star.getFirst(), star.getSecond());<a name="line.318"></a> |
| <span class="sourceLineNo">319</span> } else {<a name="line.319"></a> |
| <span class="sourceLineNo">320</span> // Will go to step two after, where a path will be constructed,<a name="line.320"></a> |
| <span class="sourceLineNo">321</span> // starting from the uncovered primed zero (there is only one). Since<a name="line.321"></a> |
| <span class="sourceLineNo">322</span> // we have already found it, save it as the first node in the path.<a name="line.322"></a> |
| <span class="sourceLineNo">323</span> path.clear();<a name="line.323"></a> |
| <span class="sourceLineNo">324</span> path.offerLast(new Pair<>(zero.getFirst(), zero.getSecond()));<a name="line.324"></a> |
| <span class="sourceLineNo">325</span> return true;<a name="line.325"></a> |
| <span class="sourceLineNo">326</span> }<a name="line.326"></a> |
| <span class="sourceLineNo">327</span> }<a name="line.327"></a> |
| <span class="sourceLineNo">328</span> }<a name="line.328"></a> |
| <span class="sourceLineNo">329</span> }<a name="line.329"></a> |
| <span class="sourceLineNo">330</span><a name="line.330"></a> |
| <span class="sourceLineNo">331</span> /**<a name="line.331"></a> |
| <span class="sourceLineNo">332</span> * Corresponds to step 2 of the original algorithm.<a name="line.332"></a> |
| <span class="sourceLineNo">333</span> */<a name="line.333"></a> |
| <span class="sourceLineNo">334</span> private void stepTwo() {<a name="line.334"></a> |
| <span class="sourceLineNo">335</span> // Construct a path of alternating starred zeroes and primed zeroes, where<a name="line.335"></a> |
| <span class="sourceLineNo">336</span> // each starred zero is in the same column as the previous primed zero, and<a name="line.336"></a> |
| <span class="sourceLineNo">337</span> // each primed zero is in the same row as the previous starred zero. The<a name="line.337"></a> |
| <span class="sourceLineNo">338</span> // path will always end in a primed zero.<a name="line.338"></a> |
| <span class="sourceLineNo">339</span> while (true) {<a name="line.339"></a> |
| <span class="sourceLineNo">340</span> Pair<Integer, Integer> star = starInCol(path.getLast().getSecond());<a name="line.340"></a> |
| <span class="sourceLineNo">341</span> if (star != null) {<a name="line.341"></a> |
| <span class="sourceLineNo">342</span> path.offerLast(star);<a name="line.342"></a> |
| <span class="sourceLineNo">343</span> } else {<a name="line.343"></a> |
| <span class="sourceLineNo">344</span> break;<a name="line.344"></a> |
| <span class="sourceLineNo">345</span> }<a name="line.345"></a> |
| <span class="sourceLineNo">346</span> Pair<Integer, Integer> prime = primeInRow(path.getLast().getFirst());<a name="line.346"></a> |
| <span class="sourceLineNo">347</span> path.offerLast(prime);<a name="line.347"></a> |
| <span class="sourceLineNo">348</span> }<a name="line.348"></a> |
| <span class="sourceLineNo">349</span><a name="line.349"></a> |
| <span class="sourceLineNo">350</span> // Augment path - unmask all starred zeroes and star all primed zeroes. All<a name="line.350"></a> |
| <span class="sourceLineNo">351</span> // nodes in the path will be either starred or primed zeroes. The set of<a name="line.351"></a> |
| <span class="sourceLineNo">352</span> // starred zeroes is independent and now one larger than before.<a name="line.352"></a> |
| <span class="sourceLineNo">353</span> for (Pair<Integer, Integer> p : path) {<a name="line.353"></a> |
| <span class="sourceLineNo">354</span> if (mask[p.getFirst()][p.getSecond()] == STAR) {<a name="line.354"></a> |
| <span class="sourceLineNo">355</span> mask[p.getFirst()][p.getSecond()] = NONE;<a name="line.355"></a> |
| <span class="sourceLineNo">356</span> } else {<a name="line.356"></a> |
| <span class="sourceLineNo">357</span> mask[p.getFirst()][p.getSecond()] = STAR;<a name="line.357"></a> |
| <span class="sourceLineNo">358</span> }<a name="line.358"></a> |
| <span class="sourceLineNo">359</span> }<a name="line.359"></a> |
| <span class="sourceLineNo">360</span><a name="line.360"></a> |
| <span class="sourceLineNo">361</span> // Clear all covers from rows and columns.<a name="line.361"></a> |
| <span class="sourceLineNo">362</span> Arrays.fill(rowsCovered, false);<a name="line.362"></a> |
| <span class="sourceLineNo">363</span> Arrays.fill(colsCovered, false);<a name="line.363"></a> |
| <span class="sourceLineNo">364</span><a name="line.364"></a> |
| <span class="sourceLineNo">365</span> // Remove the prime mask from all primed zeroes.<a name="line.365"></a> |
| <span class="sourceLineNo">366</span> for (int r = 0; r < rows; r++) {<a name="line.366"></a> |
| <span class="sourceLineNo">367</span> for (int c = 0; c < cols; c++) {<a name="line.367"></a> |
| <span class="sourceLineNo">368</span> if (mask[r][c] == PRIME) {<a name="line.368"></a> |
| <span class="sourceLineNo">369</span> mask[r][c] = NONE;<a name="line.369"></a> |
| <span class="sourceLineNo">370</span> }<a name="line.370"></a> |
| <span class="sourceLineNo">371</span> }<a name="line.371"></a> |
| <span class="sourceLineNo">372</span> }<a name="line.372"></a> |
| <span class="sourceLineNo">373</span> }<a name="line.373"></a> |
| <span class="sourceLineNo">374</span><a name="line.374"></a> |
| <span class="sourceLineNo">375</span> /**<a name="line.375"></a> |
| <span class="sourceLineNo">376</span> * Corresponds to step 3 of the original algorithm.<a name="line.376"></a> |
| <span class="sourceLineNo">377</span> */<a name="line.377"></a> |
| <span class="sourceLineNo">378</span> private void stepThree() {<a name="line.378"></a> |
| <span class="sourceLineNo">379</span> // Find the minimum uncovered cost.<a name="line.379"></a> |
| <span class="sourceLineNo">380</span> float min = leastInRow[0];<a name="line.380"></a> |
| <span class="sourceLineNo">381</span> for (int r = 1; r < rows; r++) {<a name="line.381"></a> |
| <span class="sourceLineNo">382</span> if (leastInRow[r] < min) {<a name="line.382"></a> |
| <span class="sourceLineNo">383</span> min = leastInRow[r];<a name="line.383"></a> |
| <span class="sourceLineNo">384</span> }<a name="line.384"></a> |
| <span class="sourceLineNo">385</span> }<a name="line.385"></a> |
| <span class="sourceLineNo">386</span><a name="line.386"></a> |
| <span class="sourceLineNo">387</span> // Add the minimum cost to each of the costs in a covered row, or subtract<a name="line.387"></a> |
| <span class="sourceLineNo">388</span> // the minimum cost from each of the costs in an uncovered column. As an<a name="line.388"></a> |
| <span class="sourceLineNo">389</span> // optimization, do not actually modify the cost matrix yet, but track the<a name="line.389"></a> |
| <span class="sourceLineNo">390</span> // adjustments that need to be made to each row and column.<a name="line.390"></a> |
| <span class="sourceLineNo">391</span> for (int r = 0; r < rows; r++) {<a name="line.391"></a> |
| <span class="sourceLineNo">392</span> if (rowsCovered[r]) {<a name="line.392"></a> |
| <span class="sourceLineNo">393</span> rowAdjust[r] += min;<a name="line.393"></a> |
| <span class="sourceLineNo">394</span> }<a name="line.394"></a> |
| <span class="sourceLineNo">395</span> }<a name="line.395"></a> |
| <span class="sourceLineNo">396</span> for (int c = 0; c < cols; c++) {<a name="line.396"></a> |
| <span class="sourceLineNo">397</span> if (!colsCovered[c]) {<a name="line.397"></a> |
| <span class="sourceLineNo">398</span> colAdjust[c] -= min;<a name="line.398"></a> |
| <span class="sourceLineNo">399</span> }<a name="line.399"></a> |
| <span class="sourceLineNo">400</span> }<a name="line.400"></a> |
| <span class="sourceLineNo">401</span><a name="line.401"></a> |
| <span class="sourceLineNo">402</span> // Since the cost matrix is not being updated yet, the minimum uncovered<a name="line.402"></a> |
| <span class="sourceLineNo">403</span> // cost per row must be updated.<a name="line.403"></a> |
| <span class="sourceLineNo">404</span> for (int r = 0; r < rows; r++) {<a name="line.404"></a> |
| <span class="sourceLineNo">405</span> if (!colsCovered[leastInRowIndex[r]]) {<a name="line.405"></a> |
| <span class="sourceLineNo">406</span> // The least value in this row was in an uncovered column, meaning that<a name="line.406"></a> |
| <span class="sourceLineNo">407</span> // it would have had the minimum value subtracted from it, and therefore<a name="line.407"></a> |
| <span class="sourceLineNo">408</span> // will still be the minimum value in that row.<a name="line.408"></a> |
| <span class="sourceLineNo">409</span> leastInRow[r] -= min;<a name="line.409"></a> |
| <span class="sourceLineNo">410</span> } else {<a name="line.410"></a> |
| <span class="sourceLineNo">411</span> // The least value in this row was in a covered column and would not<a name="line.411"></a> |
| <span class="sourceLineNo">412</span> // have had the minimum value subtracted from it, so the minimum value<a name="line.412"></a> |
| <span class="sourceLineNo">413</span> // could be some in another column.<a name="line.413"></a> |
| <span class="sourceLineNo">414</span> for (int c = 0; c < cols; c++) {<a name="line.414"></a> |
| <span class="sourceLineNo">415</span> if (cost[r][c] + colAdjust[c] + rowAdjust[r] < leastInRow[r]) {<a name="line.415"></a> |
| <span class="sourceLineNo">416</span> leastInRow[r] = cost[r][c] + colAdjust[c] + rowAdjust[r];<a name="line.416"></a> |
| <span class="sourceLineNo">417</span> leastInRowIndex[r] = c;<a name="line.417"></a> |
| <span class="sourceLineNo">418</span> }<a name="line.418"></a> |
| <span class="sourceLineNo">419</span> }<a name="line.419"></a> |
| <span class="sourceLineNo">420</span> }<a name="line.420"></a> |
| <span class="sourceLineNo">421</span> }<a name="line.421"></a> |
| <span class="sourceLineNo">422</span> }<a name="line.422"></a> |
| <span class="sourceLineNo">423</span><a name="line.423"></a> |
| <span class="sourceLineNo">424</span> /**<a name="line.424"></a> |
| <span class="sourceLineNo">425</span> * Find a zero cost assignment which is not covered. If there are no zero cost assignments which<a name="line.425"></a> |
| <span class="sourceLineNo">426</span> * are uncovered, then null will be returned.<a name="line.426"></a> |
| <span class="sourceLineNo">427</span> * @return pair of row and column indices of an uncovered zero or null<a name="line.427"></a> |
| <span class="sourceLineNo">428</span> */<a name="line.428"></a> |
| <span class="sourceLineNo">429</span> private Pair<Integer, Integer> findUncoveredZero() {<a name="line.429"></a> |
| <span class="sourceLineNo">430</span> for (int r = 0; r < rows; r++) {<a name="line.430"></a> |
| <span class="sourceLineNo">431</span> if (leastInRow[r] == 0) {<a name="line.431"></a> |
| <span class="sourceLineNo">432</span> return new Pair<>(r, leastInRowIndex[r]);<a name="line.432"></a> |
| <span class="sourceLineNo">433</span> }<a name="line.433"></a> |
| <span class="sourceLineNo">434</span> }<a name="line.434"></a> |
| <span class="sourceLineNo">435</span> return null;<a name="line.435"></a> |
| <span class="sourceLineNo">436</span> }<a name="line.436"></a> |
| <span class="sourceLineNo">437</span><a name="line.437"></a> |
| <span class="sourceLineNo">438</span> /**<a name="line.438"></a> |
| <span class="sourceLineNo">439</span> * A specified row has become covered, and a specified column has become uncovered. The least<a name="line.439"></a> |
| <span class="sourceLineNo">440</span> * value per row may need to be updated.<a name="line.440"></a> |
| <span class="sourceLineNo">441</span> * @param row the index of the row which was just covered<a name="line.441"></a> |
| <span class="sourceLineNo">442</span> * @param col the index of the column which was just uncovered<a name="line.442"></a> |
| <span class="sourceLineNo">443</span> */<a name="line.443"></a> |
| <span class="sourceLineNo">444</span> private void updateMin(int row, int col) {<a name="line.444"></a> |
| <span class="sourceLineNo">445</span> // If the row is covered we want to ignore it as far as least values go.<a name="line.445"></a> |
| <span class="sourceLineNo">446</span> leastInRow[row] = Float.POSITIVE_INFINITY;<a name="line.446"></a> |
| <span class="sourceLineNo">447</span><a name="line.447"></a> |
| <span class="sourceLineNo">448</span> for (int r = 0; r < rows; r++) {<a name="line.448"></a> |
| <span class="sourceLineNo">449</span> // Since the column has only just been uncovered, it could not have any<a name="line.449"></a> |
| <span class="sourceLineNo">450</span> // pending adjustments. Only covered rows can have pending adjustments<a name="line.450"></a> |
| <span class="sourceLineNo">451</span> // and covered costs do not count toward row minimums. Therefore, we do<a name="line.451"></a> |
| <span class="sourceLineNo">452</span> // not need to consider rowAdjust[r] or colAdjust[col].<a name="line.452"></a> |
| <span class="sourceLineNo">453</span> if (!rowsCovered[r] && cost[r][col] < leastInRow[r]) {<a name="line.453"></a> |
| <span class="sourceLineNo">454</span> leastInRow[r] = cost[r][col];<a name="line.454"></a> |
| <span class="sourceLineNo">455</span> leastInRowIndex[r] = col;<a name="line.455"></a> |
| <span class="sourceLineNo">456</span> }<a name="line.456"></a> |
| <span class="sourceLineNo">457</span> }<a name="line.457"></a> |
| <span class="sourceLineNo">458</span> }<a name="line.458"></a> |
| <span class="sourceLineNo">459</span><a name="line.459"></a> |
| <span class="sourceLineNo">460</span> /**<a name="line.460"></a> |
| <span class="sourceLineNo">461</span> * Find a starred zero in a specified row. If there are no starred zeroes in the specified row,<a name="line.461"></a> |
| <span class="sourceLineNo">462</span> * then null will be returned.<a name="line.462"></a> |
| <span class="sourceLineNo">463</span> * @param r the index of the row to be searched<a name="line.463"></a> |
| <span class="sourceLineNo">464</span> * @return pair of row and column indices of starred zero or null<a name="line.464"></a> |
| <span class="sourceLineNo">465</span> */<a name="line.465"></a> |
| <span class="sourceLineNo">466</span> private Pair<Integer, Integer> starInRow(int r) {<a name="line.466"></a> |
| <span class="sourceLineNo">467</span> for (int c = 0; c < cols; c++) {<a name="line.467"></a> |
| <span class="sourceLineNo">468</span> if (mask[r][c] == STAR) {<a name="line.468"></a> |
| <span class="sourceLineNo">469</span> return new Pair<>(r, c);<a name="line.469"></a> |
| <span class="sourceLineNo">470</span> }<a name="line.470"></a> |
| <span class="sourceLineNo">471</span> }<a name="line.471"></a> |
| <span class="sourceLineNo">472</span> return null;<a name="line.472"></a> |
| <span class="sourceLineNo">473</span> }<a name="line.473"></a> |
| <span class="sourceLineNo">474</span><a name="line.474"></a> |
| <span class="sourceLineNo">475</span> /**<a name="line.475"></a> |
| <span class="sourceLineNo">476</span> * Find a starred zero in the specified column. If there are no starred zeroes in the specified<a name="line.476"></a> |
| <span class="sourceLineNo">477</span> * row, then null will be returned.<a name="line.477"></a> |
| <span class="sourceLineNo">478</span> * @param c the index of the column to be searched<a name="line.478"></a> |
| <span class="sourceLineNo">479</span> * @return pair of row and column indices of starred zero or null<a name="line.479"></a> |
| <span class="sourceLineNo">480</span> */<a name="line.480"></a> |
| <span class="sourceLineNo">481</span> private Pair<Integer, Integer> starInCol(int c) {<a name="line.481"></a> |
| <span class="sourceLineNo">482</span> for (int r = 0; r < rows; r++) {<a name="line.482"></a> |
| <span class="sourceLineNo">483</span> if (mask[r][c] == STAR) {<a name="line.483"></a> |
| <span class="sourceLineNo">484</span> return new Pair<>(r, c);<a name="line.484"></a> |
| <span class="sourceLineNo">485</span> }<a name="line.485"></a> |
| <span class="sourceLineNo">486</span> }<a name="line.486"></a> |
| <span class="sourceLineNo">487</span> return null;<a name="line.487"></a> |
| <span class="sourceLineNo">488</span> }<a name="line.488"></a> |
| <span class="sourceLineNo">489</span><a name="line.489"></a> |
| <span class="sourceLineNo">490</span> /**<a name="line.490"></a> |
| <span class="sourceLineNo">491</span> * Find a primed zero in the specified row. If there are no primed zeroes in the specified row,<a name="line.491"></a> |
| <span class="sourceLineNo">492</span> * then null will be returned.<a name="line.492"></a> |
| <span class="sourceLineNo">493</span> * @param r the index of the row to be searched<a name="line.493"></a> |
| <span class="sourceLineNo">494</span> * @return pair of row and column indices of primed zero or null<a name="line.494"></a> |
| <span class="sourceLineNo">495</span> */<a name="line.495"></a> |
| <span class="sourceLineNo">496</span> private Pair<Integer, Integer> primeInRow(int r) {<a name="line.496"></a> |
| <span class="sourceLineNo">497</span> for (int c = 0; c < cols; c++) {<a name="line.497"></a> |
| <span class="sourceLineNo">498</span> if (mask[r][c] == PRIME) {<a name="line.498"></a> |
| <span class="sourceLineNo">499</span> return new Pair<>(r, c);<a name="line.499"></a> |
| <span class="sourceLineNo">500</span> }<a name="line.500"></a> |
| <span class="sourceLineNo">501</span> }<a name="line.501"></a> |
| <span class="sourceLineNo">502</span> return null;<a name="line.502"></a> |
| <span class="sourceLineNo">503</span> }<a name="line.503"></a> |
| <span class="sourceLineNo">504</span>}<a name="line.504"></a> |
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| </pre> |
| </div> |
| </body> |
| </html> |
