字符串相似度计算

对于编辑距离为1的字符串，我们只需要通过一次操作（添加、删除或修改）一个字符可以使得两个字符串相等。

使用递归来计算编辑距离。

package stringsimilarity;

public class SimilarityFactory {
    public static int getDistance(String a, String b){
        if(a.length()==0){
            return b.length();
        }
        if(b.length()==0){
            return a.length();
        }
        if(a.charAt(0)==b.charAt(0)){
            return getDistance(a.substring(1),b.substring(1));
        }else{
            int s1= getDistance(a,b.substring(1));
            int s2= getDistance(a.substring(1),b);
            int s3= getDistance(a.substring(1),b.substring(1));
            int min = s1;
            if(s2<min)
                min= s2;
            if(s3<min)
                min= s3;
            return min+1;
        }
    }

    public static double getSimilarity(String a, String b){
        int d = getDistance(a,b);
        return 1.0/(d+1);
    }

}

上述程序可以改进

1. 将字符串传递参数换成传递char数组指针

public static double getSimilarity2(String a, String b){
    //int d = getDistance(a,b);
    int d = getDistance(a.toCharArray(),0,b.toCharArray(),0);
    return 1.0/(d+1);
}
public static int getDistance(char[] a, int beginA, char[] b, int beginB){
    if(a.length - beginA ==0){
        return b.length - beginB;
    }
    if(b.length - beginB ==0){
        return a.length - beginA;
    }
    if(a[beginA]==b[beginB]){
        return getDistance(a, beginA+1, b, beginB+1);
    }else{
        int s1= getDistance(a, beginA, b, beginB+1);
        int s2= getDistance(a, beginA+1, b, beginB);
        int s3= getDistance(a, beginA+1, b, beginB+1);
        int min = s1;
        if(s2<min)
            min= s2;
        if(s3<min)
            min= s3;
        return min+1;
    }
}

2. 在递归过程中有些递归调用是重复的，可以通过记录中间值避免重新计算

 可以使用HashMap来保存，或使用数组

public static double getSimilarity4(String a, String b){

    int[][] dis = new int[a.length()+1][b.length()+1];
    for(int i = 0;i<dis.length;i++){
        for (int j = 0; j < dis[0].length; j++)
            dis[i][j]=-1;
    }
    int d = getDistance3(a.toCharArray(),0,b.toCharArray(),0, dis);
    return 1.0/(d+1);
}

public static int getDistance3(char[] a, int beginA, char[] b, int beginB, int[][] dis){
    if(a.length - beginA ==0){
        return b.length - beginB;
    }
    if(b.length - beginB ==0){
        return a.length - beginA;
    }
    if(a[beginA]==b[beginB]){
        int s = dis[beginA+1][beginB+1];
        if(s == -1){
            s = getDistance3(a, beginA+1, b, beginB+1,dis);
            dis[beginA+1][beginB+1] = s;
        }
        return s;
    }else{
        int s1 = dis[beginA][beginB+1];
        if(s1 == -1){
          s1= getDistance3(a, beginA, b, beginB+1,dis);
          dis[beginA][beginB+1] = s1;
        }

        int s2 = dis[beginA+1][beginB];
        if(s2 == -1){
            s2= getDistance3(a, beginA+1, b, beginB,dis);
            dis[beginA+1][beginB] = s2;
        }


        int s3 = dis[beginA+1][beginB+1];
        if(s3 == -1){
            s3= getDistance3(a, beginA+1, b, beginB+1,dis);
            dis[beginA+1][beginB+1] = s3;
        }
        int min = s1;
        if(s2<min)
            min= s2;
        if(s3<min)
            min= s3;
        return min+1;
    }
}

 测试：

package stringsimilarity;

import junit.framework.TestCase;

public class TestSimilarity extends TestCase {

    public void testSimilarity1(){//添加一个字符
        String a = "traveling";
        String b = "travelling";
        double s = SimilarityFactory.getSimilarity(a, b);
        System.out.println(s);
        assertEquals(s,0.5);
    }

    public void testSimilarity2(){//删除一个字符
        String a = "about";
        String b = "bout";
        double s = SimilarityFactory.getSimilarity(a, b);
        System.out.println(s);
        assertEquals(s,0.5);
    }

    public void testSimilarity3(){//修改一个字符
        String a = "flying";
        String b = "flyong";
        double s = SimilarityFactory.getSimilarity(a, b);
        System.out.println(s);
        assertEquals(s,0.5);
    }

    public void testSimilarity4(){//修改一个字符
        long start = System.currentTimeMillis();
        String a = "appidimiologist";
        String b = "epidemiologist";
        //double s = SimilarityFactory.getSimilarity(a, b);//传字符串作参数21.734s
        //double s = SimilarityFactory.getSimilarity2(a, b);//传char数组引用6.141s
        //double s = SimilarityFactory.getSimilarity3(a, b);//使用hashmap保持计算过的值
        double s = SimilarityFactory.getSimilarity4(a, b);//使用数组保存计算过的值0.015s
        System.out.println("result:"+s);
        assertEquals(s,0.25);

        long end = System.currentTimeMillis();

        System.out.println("Total time:"+ (end - start)/1000.0);

    }

}

改进后运行时间效率有很大的改善。