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