Add Abbreviation Dynamic Programming Algorithm

DIRECTORY.md

@@ -87,6 +87,7 @@
     * [Union Find](https://github.com/TheAlgorithms/Rust/blob/master/src/data_structures/union_find.rs)
     * [Veb Tree](https://github.com/TheAlgorithms/Rust/blob/master/src/data_structures/veb_tree.rs)
   * Dynamic Programming
+    * [Abbreviation](https://github.com/TheAlgorithms/Rust/blob/master/src/dynamic_programming/abbreviation.rs)
     * [Coin Change](https://github.com/TheAlgorithms/Rust/blob/master/src/dynamic_programming/coin_change.rs)
     * [Egg Dropping](https://github.com/TheAlgorithms/Rust/blob/master/src/dynamic_programming/egg_dropping.rs)
     * [Fibonacci](https://github.com/TheAlgorithms/Rust/blob/master/src/dynamic_programming/fibonacci.rs)

src/dynamic_programming/abbreviation.rs

@@ -0,0 +1,117 @@
+//! Abbreviation Problem Solution
+//!
+//! This module solves the abbreviation problem: determining if string `a` can be
+//! transformed into string `b` by capitalizing zero or more lowercase letters and
+//! deleting all remaining lowercase letters.
+
+/// Determines if string `a` can be transformed into string `b` by:
+/// 1. Capitalizing zero or more lowercase letters in `a`
+/// 2. Deleting all remaining lowercase letters
+///
+/// The solution uses dynamic programming where `dp[i][j]` represents whether
+/// the first `i` characters of `a` can form the first `j` characters of `b`.
+///
+/// # Arguments
+/// * `a` - The input string that may contain both uppercase and lowercase letters
+/// * `b` - The target string containing only uppercase letters
+///
+/// # Returns
+/// * A boolean indicating whether the transformation is possible
+///
+/// # Complexity
+/// * Time complexity: O(n * m) where n is length of string a and m is length of string b
+/// * Space complexity: O(n * m) for the DP table
+///
+/// # Examples
+/// ```
+/// use the_algorithms_rust::dynamic_programming::abbreviation;
+///
+/// assert_eq!(abbreviation("daBcd", "ABC"), true);
+/// assert_eq!(abbreviation("dBcd", "ABC"), false);
+/// ```
+pub fn abbreviation(a: &str, b: &str) -> bool {
+    let a_chars: Vec<char> = a.chars().collect();
+    let b_chars: Vec<char> = b.chars().collect();
+    let n = a_chars.len();
+    let m = b_chars.len();
+
+    // dp[i][j] represents whether first i chars of a can form first j chars of b
+    let mut dp = vec![vec![false; m + 1]; n + 1];
+
+    // Base case: empty string a can form empty string b
+    dp[0][0] = true;
+
+    // Fill the first column: we can form empty b by deleting all lowercase letters
+    for i in 0..n {
+        if a_chars[i].is_lowercase() {
+            dp[i + 1][0] = dp[i][0];
+        }
+    }
+
+    for i in 0..n {
+        for j in 0..=m {
+            if dp[i][j] {
+                // If we can match current position, check next characters
+                if j < m && a_chars[i].to_ascii_uppercase() == b_chars[j] {
+                    dp[i + 1][j + 1] = true;
+                }
+
+                // If current character in a is lowercase, we can delete it
+                if a_chars[i].is_lowercase() {
+                    dp[i + 1][j] = true;
+                }
+            }
+        }
+    }
+
+    dp[n][m]
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    macro_rules! abbreviation_tests {
+        ($($name:ident: ($a:expr, $b:expr) => $expected:expr,)*) => {
+            $(
+                #[test]
+                fn $name() {
+                    assert_eq!(abbreviation($a, $b), $expected);
+                }
+            )*
+        };
+    }
+
+    abbreviation_tests! {
+        // Original test cases from the problem
+        test_daBcd_ABC: ("daBcd", "ABC") => true,
+        test_dBcd_ABC: ("dBcd", "ABC") => false,
+
+        // Additional test cases
+        test_AbcE_ABE: ("AbcE", "ABE") => true,
+        test_AbcE_ABC: ("AbcE", "ABC") => false,
+        test_abcde_ABCDE: ("abcde", "ABCDE") => true,
+        test_abcde_ABCD: ("abcde", "ABCD") => false,
+        test_ABCDE_ABCDE: ("ABCDE", "ABCDE") => true,
+        test_ABCDE_ABCD: ("ABCDE", "ABCD") => false,
+        test_aBcDe_ABCDE: ("aBcDe", "ABCDE") => true,
+        test_aBcDe_ABCD: ("aBcDe", "ABCD") => true,
+
+        // Edge test cases
+        test_empty_both: ("", "") => true,
+        test_empty_a: ("", "ABC") => false,
+        test_empty_b: ("abc", "") => true,
+        test_only_lowercase: ("abc", "ABC") => true,
+        test_only_uppercase: ("ABC", "ABC") => true,
+        test_mismatched_uppercase: ("ABD", "ABC") => false,
+
+        // Complex cases from HackerRank
+        test_complex_1: ("LLZOSYAMQRMBTZXTQMQcKGLR", "LLZOSYAMBTZXMQKLR") => false,
+        test_complex_2: ("MGYXKOVSMAHKOLAZZKWXKS", "MGXKOVSAHKOLZKKDP") => false,
+        test_complex_3: ("bfBQZcnjXPMNWMZ", "BQZCNJXPMNWMZ") => true,
+        test_AbcDE_ABDE: ("AbcDE", "ABDE") => true,
+        test_AbcDE_AFDE: ("AbcDE", "AFDE") => false,
+        test_ABCD_ABCD: ("ABCD", "ABCD") => true,
+        test_abcdE_ABCDE: ("abcdE", "ABCDE") => true,
+    }
+}

src/dynamic_programming/mod.rs

@@ -1,3 +1,4 @@
+mod abbreviation;
 mod coin_change;
 mod egg_dropping;
 mod fibonacci;
@@ -19,6 +20,7 @@ mod subset_generation;
 mod trapped_rainwater;
 mod word_break;
 
+pub use self::abbreviation::abbreviation;
 pub use self::coin_change::coin_change;
 pub use self::egg_dropping::egg_drop;
 pub use self::fibonacci::binary_lifting_fibonacci;