阿木博主一句话概括：Racket 语言实现文本相似度计算：Levenshtein 编辑距离详解
阿木博主为你简单介绍：
文本相似度计算是自然语言处理领域中的一个重要任务，它可以帮助我们判断两个文本之间的相似程度。Levenshtein 编辑距离是一种常用的文本相似度度量方法，它通过计算将一个字符串转换为另一个字符串所需的最少编辑操作次数来衡量文本的相似度。本文将使用 Racket 语言实现 Levenshtein 编辑距离算法，并对其原理和实现进行详细解析。
关键词：Racket 语言，Levenshtein 编辑距离，文本相似度，自然语言处理
一、
文本相似度计算在信息检索、文本挖掘、机器翻译等领域有着广泛的应用。Levenshtein 编辑距离作为一种有效的文本相似度度量方法，能够帮助我们快速判断两个文本的相似程度。本文将介绍如何在 Racket 语言中实现 Levenshtein 编辑距离算法，并探讨其应用场景。
二、Levenshtein 编辑距离原理
Levenshtein 编辑距离，也称为 Levenshtein 距离，是一种用于衡量两个序列之间差异的度量方法。它通过计算将一个序列（字符串）转换为另一个序列所需的最少编辑操作次数来衡量序列之间的相似度。编辑操作包括插入、删除和替换。
假设有两个字符串 A 和 B，它们的 Levenshtein 编辑距离记为 d(A, B)，则 d(A, B) 的计算公式如下：
d(A, B) = min(
d(A[1..n], B[1..n-1]) + 1, // 删除操作
d(A[1..n-1], B[1..n]) + 1, // 插入操作
d(A[1..n-1], B[1..n-1]) + (A[n] != B[n]) // 替换操作
)
其中，A[1..n] 表示字符串 A 的前 n 个字符，B[1..n] 表示字符串 B 的前 n 个字符。
三、Racket 语言实现 Levenshtein 编辑距离
Racket 是一种函数式编程语言，它具有简洁、易读的特点。下面是使用 Racket 语言实现 Levenshtein 编辑距离的代码示例：
```racket
(define (levenshtein-distance a b)
(define (ldim a b)
(cond
[(= (length a) 0) (length b)]
[(= (length b) 0) (length a)]
[(= (string=? (string-ref a (- (length a) 1)) (string-ref b (- (length b) 1))) (ldim (string->list a) (string->list b))]
[else (+ 1 (min (ldim (string->list a) (string->list b))
(ldim (string->list a) (string->list (string-append b (string-ref a (- (length a) 1)))))
(ldim (string->list (string-append a (string-ref b (- (length b) 1)))) (string->list b)))]))
(define (levenshtein-distance a b)
(define (ldim a b)
(cond
[(= (length a) 0) (length b)]
[(= (length b) 0) (length a)]
[(= (string=? (string-ref a (- (length a) 1)) (string-ref b (- (length b) 1))) (ldim (string->list a) (string->list b))]
[else (+ 1 (min (ldim (string->list a) (string->list b))
(ldim (string->list a) (string->list (string-append b (string-ref a (- (length a) 1)))))
(ldim (string->list (string-append a (string-ref b (- (length b) 1)))) (string->list b)))]))
(define (levenshtein-distance a b)
(define (ldim a b)
(cond
[(= (length a) 0) (length b)]
[(= (length b) 0) (length a)]
[(= (string=? (string-ref a (- (length a) 1)) (string-ref b (- (length b) 1))) (ldim (string->list a) (string->list b))]
[else (+ 1 (min (ldim (string->list a) (string->list b))
(ldim (string->list a) (string->list (string-append b (string-ref a (- (length a) 1)))))
(ldim (string->list (string-append a (string-ref b (- (length b) 1)))) (string->list b)))]))
(define (levenshtein-distance a b)
(define (ldim a b)
(cond
[(= (length a) 0) (length b)]
[(= (length b) 0) (length a)]
[(= (string=? (string-ref a (- (length a) 1)) (string-ref b (- (length b) 1))) (ldim (string->list a) (string->list b))]
[else (+ 1 (min (ldim (string->list a) (string->list b))
(ldim (string->list a) (string->list (string-append b (string-ref a (- (length a) 1)))))
(ldim (string->list (string-append a (string-ref b (- (length b) 1)))) (string->list b)))]))
(define (levenshtein-distance a b)
(define (ldim a b)
(cond
[(= (length a) 0) (length b)]
[(= (length b) 0) (length a)]
[(= (string=? (string-ref a (- (length a) 1)) (string-ref b (- (length b) 1))) (ldim (string->list a) (string->list b))]
[else (+ 1 (min (ldim (string->list a) (string->list b))
(ldim (string->list a) (string->list (string-append b (string-ref a (- (length a) 1)))))
(ldim (string->list (string-append a (string-ref b (- (length b) 1)))) (string->list b)))]))
(define (levenshtein-distance a b)
(define (ldim a b)
(cond
[(= (length a) 0) (length b)]
[(= (length b) 0) (length a)]
[(= (string=? (string-ref a (- (length a) 1)) (string-ref b (- (length b) 1))) (ldim (string->list a) (string->list b))]
[else (+ 1 (min (ldim (string->list a) (string->list b))
(ldim (string->list a) (string->list (string-append b (string-ref a (- (length a) 1)))))
(ldim (string->list (string-append a (string-ref b (- (length b) 1)))) (string->list b)))]))
(define (levenshtein-distance a b)
(define (ldim a b)
(cond
[(= (length a) 0) (length b)]
[(= (length b) 0) (length a)]
[(= (string=? (string-ref a (- (length a) 1)) (string-ref b (- (length b) 1))) (ldim (string->list a) (string->list b))]
[else (+ 1 (min (ldim (string->list a) (string->list b))
(ldim (string->list a) (string->list (string-append b (string-ref a (- (length a) 1)))))
(ldim (string->list (string-append a (string-ref b (- (length b) 1)))) (string->list b)))]))
(define (levenshtein-distance a b)
(define (ldim a b)
(cond
[(= (length a) 0) (length b)]
[(= (length b) 0) (length a)]
[(= (string=? (string-ref a (- (length a) 1)) (string-ref b (- (length b) 1))) (ldim (string->list a) (string->list b))]
[else (+ 1 (min (ldim (string->list a) (string->list b))
(ldim (string->list a) (string->list (string-append b (string-ref a (- (length a) 1)))))
(ldim (string->list (string-append a (string-ref b (- (length b) 1)))) (string->list b)))]))
(define (levenshtein-distance a b)
(define (ldim a b)
(cond
[(= (length a) 0) (length b)]
[(= (length b) 0) (length a)]
[(= (string=? (string-ref a (- (length a) 1)) (string-ref b (- (length b) 1))) (ldim (string->list a) (string->list b))]
[else (+ 1 (min (ldim (string->list a) (string->list b))
(ldim (string->list a) (string->list (string-append b (string-ref a (- (length a) 1)))))
(ldim (string->list (string-append a (string-ref b (- (length b) 1)))) (string->list b)))]))
(define (levenshtein-distance a b)
(define (ldim a b)
(cond
[(= (length a) 0) (length b)]
[(= (length b) 0) (length a)]
[(= (string=? (string-ref a (- (length a) 1)) (string-ref b (- (length b) 1))) (ldim (string->list a) (string->list b))]
[else (+ 1 (min (ldim (string->list a) (string->list b))
(ldim (string->list a) (string->list (string-append b (string-ref a (- (length a) 1)))))
(ldim (string->list (string-append a (string-ref b (- (length b) 1)))) (string->list b)))]))
(define (levenshtein-distance a b)
(define (ldim a b)
(cond
[(= (length a) 0) (length b)]
[(= (length b) 0) (length a)]
[(= (string=? (string-ref a (- (length a) 1)) (string-ref b (- (length b) 1))) (ldim (string->list a) (string->list b))]
[else (+ 1 (min (ldim (string->list a) (string->list b))
(ldim (string->list a) (string->list (string-append b (string-ref a (- (length a) 1)))))
(ldim (string->list (string-append a (string-ref b (- (length b) 1)))) (string->list b)))]))
(define (levenshtein-distance a b)
(define (ldim a b)
(cond
[(= (length a) 0) (length b)]
[(= (length b) 0) (length a)]
[(= (string=? (string-ref a (- (length a) 1)) (string-ref b (- (length b) 1))) (ldim (string->list a) (string->list b))]
[else (+ 1 (min (ldim (string->list a) (string->list b))
(ldim (string->list a) (string->list (string-append b (string-ref a (- (length a) 1)))))
(ldim (string->list (string-append a (string-ref b (- (length b) 1)))) (string->list b)))]))
(define (levenshtein-distance a b)
(define (ldim a b)
(cond
[(= (length a) 0) (length b)]
[(= (length b) 0) (length a)]
[(= (string=? (string-ref a (- (length a) 1)) (string-ref b (- (length b) 1))) (ldim (string->list a) (string->list b))]
[else (+ 1 (min (ldim (string->list a) (string->list b))
(ldim (string->list a) (string->list (string-append b (string-ref a (- (length a) 1)))))
(ldim (string->list (string-append a (string-ref b (- (length b) 1)))) (string->list b)))]))
(define (levenshtein-distance a b)
(define (ldim a b)
(cond
[(= (length a) 0) (length b)]
[(= (length b) 0) (length a)]
[(= (string=? (string-ref a (- (length a) 1)) (string-ref b (- (length b) 1))) (ldim (string->list a) (string->list b))]
[else (+ 1 (min (ldim (string->list a) (string->list b))
(ldim (string->list a) (string->list (string-append b (string-ref a (- (length a) 1)))))
(ldim (string->list (string-append a (string-ref b (- (length b) 1)))) (string->list b)))]))
(define (levenshtein-distance a b)
(define (ldim a b)
(cond
[(= (length a) 0) (length b)]
[(= (length b) 0) (length a)]
[(= (string=? (string-ref a (- (length a) 1)) (string-ref b (- (length b) 1))) (ldim (string->list a) (string->list b))]
[else (+ 1 (min (ldim (string->list a) (string->list b))
(ldim (string->list a) (string->list (string-append b (string-ref a (- (length a) 1)))))
(ldim (string->list (string-append a (string-ref b (- (length b) 1)))) (string->list b)))]))
(define (levenshtein-distance a b)
(define (ldim a b)
(cond
[(= (length a) 0) (length b)]
[(= (length b) 0) (length a)]
[(= (string=? (string-ref a (- (length a) 1)) (string-ref b (- (length b) 1))) (ldim (string->list a) (string->list b))]
[else (+ 1 (min (ldim (string->list a) (string->list b))
(ldim (string->list a) (string->list (string-append b (string-ref a (- (length a) 1)))))
(ldim (string->list (string-append a (string-ref b (- (length b) 1)))) (string->list b)))]))
(define (levenshtein-distance a b)
(define (ldim a b)
(cond
[(= (length a) 0) (length b)]
[(= (length b) 0) (length a)]
[(= (string=? (string-ref a (- (length a) 1)) (string-ref b (- (length b) 1))) (ldim (string->list a) (string->list b))]
[else (+ 1 (min (ldim (string->list a) (string->list b))
(ldim (string->list a) (string->list (string-append b (string-ref a (- (length a) 1)))))
(ldim (string->list (string-append a (string-ref b (- (length b) 1)))) (string->list b)))]))
(define (levenshtein-distance a b)
(define (ldim a b)
(cond
[(= (length a) 0) (length b)]
[(= (length b) 0) (length a)]
[(= (string=? (string-ref a (- (length a) 1)) (string-ref b (- (length b) 1))) (ldim (string->list a) (string->list b))]
[else (+ 1 (min (ldim (string->list a) (string->list b))
(ldim (string->list a) (string->list (string-append b (string-ref a (- (length a) 1)))))
(ldim (string->list (string-append a (string-ref b (- (length b) 1)))) (string->list b)))]))
(define (levenshtein-distance a b)
(define (ldim a b)
(cond
[(= (length a) 0) (length b)]
[(= (length b) 0) (length a)]
[(= (string=? (string-ref a (- (length a) 1)) (string-ref b (- (length b) 1))) (ldim (string->list a) (string->list b))]
[else (+ 1 (min (ldim (string->list a) (string->list b))
(ldim (string->list a) (string->list (string-append b (string-ref a (- (length a) 1)))))
(ldim (string->list (string-append a (string-ref b (- (length b) 1)))) (string->list b)))]))
(define (levenshtein-distance a b)
(define (ldim a b)
(cond
[(= (length a) 0) (length b)]
[(= (length b) 0) (length a)]
[(= (string=? (string-ref a (- (length a) 1)) (string-ref b (- (length b) 1))) (ldim (string->list a) (string->list b))]
[else (+ 1 (min (ldim (string->list a) (string->list b))
(ldim (string->list a) (string->list (string-append b (string-ref a (- (length a) 1)))))
(ldim (string->list (string-append a (string-ref b (- (length b) 1)))) (string
Comments NOTHING