code: /*
   * #%L
   * Simmetrics Core
   * %%
   * Copyright (C) 2014 - 2016 Simmetrics Authors
   * %%
   * Licensed under the Apache License, Version 2.0 (the "License");
   * you may not use this file except in compliance with the License.
   * You may obtain a copy of the License at
   * 
   *      http://www.apache.org/licenses/LICENSE-2.0
   * 
   * Unless required by applicable law or agreed to in writing, software
   * distributed under the License is distributed on an "AS IS" BASIS,
   * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
   * See the License for the specific language governing permissions and
   * limitations under the License.
   * #L%
   */
  package org.simmetrics.metrics;
  
  import static java.lang.Math.abs;
  import static org.simmetrics.metrics.Math.union;
  
  import org.simmetrics.MultisetDistance;
  import org.simmetrics.MultisetMetric;
  
  import com.google.common.collect.Multiset;
  
  /**
   * Calculates the block distance and similarity over two multisets. Also known
   * as L1 Distance or City block distance.
   * <p>
   * <code>
   * similarity(a,b) = 1 - distance(a,b) / (∣a∣ + ∣b∣)
   * <br>
   * distance(a,b) = ∣∣a - b∣∣₁
   * </code>
   * <p>
   * This class is immutable and thread-safe.
   * 
   * @see <a href="http://en.wikipedia.org/wiki/Taxicab_geometry">Wikipedia -
   *      Taxicab geometry</a>
   * @param <T>
   *            type of token
   */
  public final class BlockDistance<T> implements MultisetMetric<T>, MultisetDistance<T> {
  
  	@Override
  	public float compare(Multiset<T> a, Multiset<T> b) {
  
  		if (a.isEmpty() && b.isEmpty()) {
  			return 1.0f;
  		}
  
  		if (a.isEmpty() || b.isEmpty()) {
  			return 0.0f;
  		}
  
  		return 1.0f - distance(a, b) / (a.size() + b.size());
  	}
  
  	@Override
  	public float distance(Multiset<T> a, Multiset<T> b) {
  
  		float distance = 0;
  
  		for (T token : union(a, b).elementSet()) {
  			float frequencyInA = a.count(token);
  			float frequencyInB = b.count(token);
  
  			distance += abs(frequencyInA - frequencyInB);
  		}
  		return distance;
  	}
  
  	@Override
  	public String toString() {
  		return "BlockDistance";
  	}
  
  }
  