Add subset sum algorithm

DIRECTORY.md

@@ -105,6 +105,7 @@
     * [Rod Cutting](https://github.com/TheAlgorithms/Rust/blob/master/src/dynamic_programming/rod_cutting.rs)
     * [Snail](https://github.com/TheAlgorithms/Rust/blob/master/src/dynamic_programming/snail.rs)
     * [Subset Generation](https://github.com/TheAlgorithms/Rust/blob/master/src/dynamic_programming/subset_generation.rs)
+    * [Subset Sum](https://github.com/TheAlgorithms/Rust/blob/master/src/dynamic_programming/subset_sum.rs)
     * [Trapped Rainwater](https://github.com/TheAlgorithms/Rust/blob/master/src/dynamic_programming/trapped_rainwater.rs)
     * [Word Break](https://github.com/TheAlgorithms/Rust/blob/master/src/dynamic_programming/word_break.rs)
   * Financial

src/dynamic_programming/mod.rs

@@ -16,6 +16,7 @@ mod optimal_bst;
 mod rod_cutting;
 mod snail;
 mod subset_generation;
+mod subset_sum;
 mod trapped_rainwater;
 mod word_break;
 
@@ -45,5 +46,6 @@ pub use self::optimal_bst::optimal_search_tree;
 pub use self::rod_cutting::rod_cut;
 pub use self::snail::snail;
 pub use self::subset_generation::list_subset;
+pub use self::subset_sum::is_sum_subset;
 pub use self::trapped_rainwater::trapped_rainwater;
 pub use self::word_break::word_break;

src/dynamic_programming/subset_sum.rs

@@ -0,0 +1,79 @@
+// Subset Sum Problem in Rust
+// Time Complexity: O(n * sum) where n is array length and sum is the target sum
+// Space Complexity: O(n * sum) for the DP table
+/// Determines if there exists a subset of the given array that sums to the target value.
+/// Uses dynamic programming to solve the subset sum problem.
+///
+/// # Arguments
+/// * arr - A slice of integers representing the input array
+/// * required_sum - The target sum to check for
+///
+/// # Returns
+/// * A boolean indicating whether a subset exists that sums to the target
+pub fn is_sum_subset(arr: &[i32], required_sum: i32) -> bool {
+    let n = arr.len();
+
+    // Handle edge case where required sum is 0 (empty subset always sums to 0)
+    if required_sum == 0 {
+        return true;
+    }
+
+    // Handle edge case where array is empty but required sum is positive
+    if n == 0 && required_sum > 0 {
+        return false;
+    }
+    // dp[i][j] stores whether sum j can be achieved using first i elements
+    let mut dp = vec![vec![false; required_sum as usize + 1]; n + 1];
+    // Base case: sum 0 can always be achieved with any number of elements (empty subset)
+    for i in 0..=n {
+        dp[i][0] = true;
+    }
+    // Base case: with 0 elements, no positive sum can be achieved
+    for j in 1..=required_sum as usize {
+        dp[0][j] = false;
+    }
+    // Fill the DP table
+    for i in 1..=n {
+        for j in 1..=required_sum as usize {
+            if arr[i - 1] > j as i32 {
+                // Current element is too large, exclude it
+                dp[i][j] = dp[i - 1][j];
+            } else {
+                // Either exclude the current element or include it
+                dp[i][j] = dp[i - 1][j] || dp[i - 1][j - arr[i - 1] as usize];
+            }
+        }
+    }
+    dp[n][required_sum as usize]
+}
+#[cfg(test)]
+mod tests {
+    use super::*;
+    // Macro to generate multiple test cases for the is_sum_subset function
+    macro_rules! subset_sum_tests {
+        ($($name:ident: $input:expr => $expected:expr,)*) => {
+            $(
+                #[test]
+                fn $name() {
+                    let (arr, sum) = $input;
+                    assert_eq!(is_sum_subset(arr, sum), $expected);
+                }
+            )*
+        };
+    }
+    subset_sum_tests! {
+        // Common test cases
+        test_case_1: (&[2, 4, 6, 8], 5) => false,
+        test_case_2: (&[2, 4, 6, 8], 14) => true,
+        test_case_3: (&[3, 34, 4, 12, 5, 2], 9) => true,
+        test_case_4: (&[3, 34, 4, 12, 5, 2], 30) => false,
+        test_case_5: (&[1, 2, 3, 4, 5], 15) => true,
+
+        // Edge test cases
+        test_case_empty_array_positive_sum: (&[], 5) => false,
+        test_case_empty_array_zero_sum: (&[], 0) => true,
+        test_case_zero_sum: (&[1, 2, 3], 0) => true,
+        test_case_single_element_match: (&[5], 5) => true,
+        test_case_single_element_no_match: (&[3], 5) => false,
+    }
+}