add dynamic programming examples in rust (#296)

Author: hackeryarn

11_dynamic_programming/rust/Cargo.lock

@@ -0,0 +1,6 @@
+[package]
+name = "longest_common"
+version = "0.1.0"
+edition = "2021"
+
+[dependencies]

11_dynamic_programming/rust/Cargo.toml

@@ -0,0 +1,65 @@
+use std::cmp;
+
+fn build_dp_table<T>(table1: &[T], table2: &[T]) -> Vec<Vec<u64>> {
+    let mut dp_table = vec![];
+    for i in 0..table1.len() {
+        dp_table.push(vec![]);
+        for _ in 0..table2.len() {
+            dp_table[i].push(0);
+        }
+    }
+
+    dp_table
+}
+
+fn longest_common_substring<T: Eq>(table1: &[T], table2: &[T]) -> Vec<Vec<u64>> {
+    let mut dp_table = build_dp_table(table1, table2);
+
+    for (i, c1) in table1.into_iter().enumerate() {
+        for (j, c2) in table2.into_iter().enumerate() {
+            if c1 == c2 {
+                dp_table[i][j] =
+                    dp_table[i.checked_sub(1).unwrap_or(0)][j.checked_sub(1).unwrap_or(0)] + 1;
+            } else {
+                dp_table[i][j] = 0;
+            }
+        }
+    }
+
+    dp_table
+}
+
+fn longest_common_subsequence<T: Eq>(table1: &[T], table2: &[T]) -> Vec<Vec<u64>> {
+    let mut dp_table = build_dp_table(table1, table2);
+
+    for (i, c1) in table1.into_iter().enumerate() {
+        for (j, c2) in table2.into_iter().enumerate() {
+            if c1 == c2 {
+                dp_table[i][j] =
+                    dp_table[i.checked_sub(1).unwrap_or(0)][j.checked_sub(1).unwrap_or(0)] + 1;
+            } else {
+                dp_table[i][j] = cmp::max(
+                    dp_table[i.checked_sub(1).unwrap_or(0)][j],
+                    dp_table[i][j.checked_sub(1).unwrap_or(0)],
+                );
+            }
+        }
+    }
+
+    dp_table
+}
+
+fn main() {
+    let dp_table_blue = ['b', 'l', 'u', 'e'];
+    let dp_table_clues = ['c', 'l', 'u', 'e', 's'];
+
+    println!("Longest substring:");
+    for line in longest_common_substring(&dp_table_blue, &dp_table_clues) {
+        println!("{:?}", line)
+    }
+
+    println!("Longest subsequence:");
+    for line in longest_common_subsequence(&dp_table_blue, &dp_table_clues) {
+        println!("{:?}", line)
+    }
+}