feat: add Rod Cutting (rust-lang#190)

* Add Rod Cutting

* updating DIRECTORY.md

Co-authored-by: xelahi <xelahi@users.noreply.github.com>
Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>

Author: 3 people

DIRECTORY.md

@@ -28,6 +28,7 @@
     * [Longest Common Subsequence](https://github.com/TheAlgorithms/Rust/blob/master/src/dynamic_programming/longest_common_subsequence.rs)
     * [Longest Continuous Increasing Subsequence](https://github.com/TheAlgorithms/Rust/blob/master/src/dynamic_programming/longest_continuous_increasing_subsequence.rs)
     * [Maximum Subarray](https://github.com/TheAlgorithms/Rust/blob/master/src/dynamic_programming/maximum_subarray.rs)
+    * [Rod Cutting](https://github.com/TheAlgorithms/Rust/blob/master/src/dynamic_programming/rod_cutting.rs)
   * General
     * [Convex Hull](https://github.com/TheAlgorithms/Rust/blob/master/src/general/convex_hull.rs)
     * [Hanoi](https://github.com/TheAlgorithms/Rust/blob/master/src/general/hanoi.rs)

README.md

@@ -43,7 +43,7 @@ RESTART BUILD
 - [ ] Longest increasing subsequence
 - [x] [K-Means Clustering](./src/general/kmeans.rs)
 - [x] [Coin Change](./src/dynamic_programming/coin_change.rs)
-- [ ] Rod cut
+- [x] [Rod Cutting](./src/dynamic_programming/rod_cutting.rs)
 - [x] [Egg Dropping Puzzle](./src/dynamic_programming/egg_dropping.rs)
 - [x] [Maximum Subarray](./src/dynamic_programming/maximum_subarray.rs)
 

src/dynamic_programming/mod.rs

@@ -6,6 +6,7 @@ mod knapsack;
 mod longest_common_subsequence;
 mod longest_continuous_increasing_subsequence;
 mod maximum_subarray;
+mod rod_cutting;
 
 pub use self::coin_change::coin_change;
 pub use self::edit_distance::{edit_distance, edit_distance_se};
@@ -16,3 +17,4 @@ pub use self::knapsack::knapsack;
 pub use self::longest_common_subsequence::longest_common_subsequence;
 pub use self::longest_continuous_increasing_subsequence::longest_continuous_increasing_subsequence;
 pub use self::maximum_subarray::maximum_subarray;
+pub use self::rod_cutting::rod_cut;

src/dynamic_programming/rod_cutting.rs

@@ -0,0 +1,55 @@
+//! Solves the rod-cutting problem
+use std::cmp::max;
+
+/// `rod_cut(p)` returns the maximum possible profit if a rod of length `n` = `p.len()`
+/// is cut into up to `n` pieces, where the profit gained from each piece of length
+/// `l` is determined by `p[l - 1]` and the total profit is the sum of the profit
+/// gained from each piece.
+///
+/// # Arguments
+///    - `p` - profit for rods of length 1 to n inclusive
+///
+/// # Complexity
+///    - time complexity: O(n^2),
+///    - space complexity: O(n^2),
+///
+/// where n is the length of `p`.
+pub fn rod_cut(p: &[usize]) -> usize {
+    let n = p.len();
+    // f is the dynamic programming table
+    let mut f = vec![0; n];
+
+    for i in 0..n {
+        let mut max_price = p[i];
+        for j in 1..=i {
+            max_price = max(max_price, p[j - 1] + f[i - j]);
+        }
+        f[i] = max_price;
+    }
+
+    // accomodate for input with length zero
+    if n != 0 {
+        f[n - 1]
+    } else {
+        0
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::rod_cut;
+
+    #[test]
+    fn test_rod_cut() {
+        assert_eq!(0, rod_cut(&[]));
+        assert_eq!(15, rod_cut(&[5, 8, 2]));
+        assert_eq!(10, rod_cut(&[1, 5, 8, 9]));
+        assert_eq!(25, rod_cut(&[5, 8, 2, 1, 7]));
+        assert_eq!(87, rod_cut(&[0, 0, 0, 0, 0, 87]));
+        assert_eq!(49, rod_cut(&[7, 6, 5, 4, 3, 2, 1]));
+        assert_eq!(22, rod_cut(&[1, 5, 8, 9, 10, 17, 17, 20]));
+        assert_eq!(60, rod_cut(&[6, 4, 8, 2, 5, 8, 2, 3, 7, 11]));
+        assert_eq!(30, rod_cut(&[1, 5, 8, 9, 10, 17, 17, 20, 24, 30]));
+        assert_eq!(12, rod_cut(&[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]));
+    }
+}