added least common sequence and levenshtein with no substitution

examples/lcs.rs

@@ -0,0 +1,69 @@
+use clap::Parser;
+use rmath::HMatrix;
+
+#[derive(Parser, Debug)]
+#[command(version, about, long_about = None)]
+struct CliArgs {
+    word1: String,
+    word2: String,
+}
+
+fn lcs_len(s1: &[char], s2: &[char]) -> usize {
+    let m = s1.len();
+    let n = s2.len();
+    let mut workspace = HMatrix::<usize>::new(m, n, |(_, _)| 0);
+    for i in 0..m {
+        for j in 0..n {
+            if s1[i] == s2[j] {
+                workspace[(i, j)] = if i == 0 || j == 0 {
+                    1
+                } else {
+                    workspace[(i - 1, j - 1)] + 1
+                };
+            } else {
+                let left = if j > 0 { workspace[(i, j - 1)] } else { 0 };
+                let up = if i > 0 { workspace[(i - 1, j)] } else { 0 };
+                workspace[(i, j)] = usize::max(left, up)
+            }
+        }
+    }
+    workspace[(m - 1, n - 1)]
+}
+
+fn lcs_distance(s1: &[char], s2: &[char]) -> usize {
+    let m = s1.len();
+    let n = s2.len();
+    let max_distance = m;
+    let mut workspace = HMatrix::<usize>::new(m, n, |(_, _)| 0);
+    for i in 0..m {
+        for j in 0..n {
+            if s1[i] == s2[j] {
+                workspace[(i, j)] = if i == 0 || j == 0 {
+                    max_distance - 1
+                } else {
+                    workspace[(i - 1, j - 1)] - 1
+                };
+            } else {
+                let left = if j > 0 {
+                    workspace[(i, j - 1)]
+                } else {
+                    max_distance
+                };
+                let up = if i > 0 {
+                    workspace[(i - 1, j)]
+                } else {
+                    max_distance
+                };
+                workspace[(i, j)] = usize::min(left, up)
+            }
+        }
+    }
+    workspace[(m - 1, n - 1)]
+}
+
+fn main() {
+    let args = CliArgs::parse();
+    let s1 = args.word1.chars().collect::<Vec<char>>();
+    let s2 = args.word2.chars().collect::<Vec<char>>();
+    println!("{}", lcs_distance(&s1, &s2));
+}