最长公共子序列

  1. /// Longest common subsequence via Dynamic Programming
  3. /// longest_common_subsequence(a, b) returns the longest common subsequence
  4. /// between the strings a and b.
  5. pub fn longest_common_subsequence(a: &str, b: &str) -> String {
  6.     let a: Vec<_> = a.chars().collect();
  7.     let b: Vec<_> = b.chars().collect();
  8.     let (na, nb) = (a.len(), b.len());
  10.     // solutions[i][j] is the length of the longest common subsequence
  11.     // between a[0..i-1] and b[0..j-1]
  12.     let mut solutions = vec![vec![0; nb + 1]; na + 1];
  14.     for (i, ci) in a.iter().enumerate() {
  15.         for (j, cj) in b.iter().enumerate() {
  16.             // if ci == cj, there is a new common character;
  17.             // otherwise, take the best of the two solutions
  18.             // at (i-1,j) and (i,j-1)
  19.             solutions[i + 1][j + 1] = if ci == cj {
  20.                 solutions[i][j] + 1
  21.             } else {
  22.                 solutions[i][j + 1].max(solutions[i + 1][j])
  23.             }
  24.         }
  25.     }
  27.     // reconstitute the solution string from the lengths
  28.     let mut result: Vec<char> = Vec::new();
  29.     let (mut i, mut j) = (na, nb);
  30.     while i > 0 && j > 0 {
  31.         if a[i - 1] == b[j - 1] {
  32.             result.push(a[i - 1]);
  33.             i -= 1;
  34.             j -= 1;
  35.         } else if solutions[i - 1][j] > solutions[i][j - 1] {
  36.             i -= 1;
  37.         } else {
  38.             j -= 1;
  39.         }
  40.     }
  42.     result.reverse();
  43.     result.iter().collect()
  44. }
  46. #[cfg(test)]
  47. mod tests {
  48.     use super::longest_common_subsequence;
  50.     #[test]
  51.     fn test_longest_common_subsequence() {
  52.         // empty case
  53.         assert_eq!(&longest_common_subsequence("", ""), "");
  54.         assert_eq!(&longest_common_subsequence("", "abcd"), "");
  55.         assert_eq!(&longest_common_subsequence("abcd", ""), "");
  57.         // simple cases
  58.         assert_eq!(&longest_common_subsequence("abcd", "c"), "c");
  59.         assert_eq!(&longest_common_subsequence("abcd", "d"), "d");
  60.         assert_eq!(&longest_common_subsequence("abcd", "e"), "");
  61.         assert_eq!(&longest_common_subsequence("abcdefghi", "acegi"), "acegi");
  63.         // less simple cases
  64.         assert_eq!(&longest_common_subsequence("abcdgh", "aedfhr"), "adh");
  65.         assert_eq!(&longest_common_subsequence("aggtab", "gxtxayb"), "gtab");
  67.         // unicode
  68.         assert_eq!(
  69.             &longest_common_subsequence("你好，世界", "再见世界"),
  70.             "世界"
  71.         );
  72.     }
  73. }