From 96c2b1a83db887822914ac3285165605125c905d Mon Sep 17 00:00:00 2001
From: EFanZh <efanzh@gmail.com>
Date: Mon, 25 Sep 2023 21:45:12 +0800
Subject: [PATCH] Add problem 1621: Number of Sets of K Non-Overlapping Line
 Segments

---
 src/lib.rs                                    |  1 +
 .../combinations.rs                           | 77 +++++++++++++++++++
 .../mod.rs                                    | 18 +++++
 3 files changed, 96 insertions(+)
 create mode 100644 src/problem_1621_number_of_sets_of_k_non_overlapping_line_segments/combinations.rs
 create mode 100644 src/problem_1621_number_of_sets_of_k_non_overlapping_line_segments/mod.rs

diff --git a/src/lib.rs b/src/lib.rs
index bd540816..9b359a7e 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -1333,6 +1333,7 @@ pub mod problem_1616_split_two_strings_to_make_palindrome;
 pub mod problem_1617_count_subtrees_with_max_distance_between_cities;
 pub mod problem_1619_mean_of_array_after_removing_some_elements;
 pub mod problem_1620_coordinate_with_maximum_network_quality;
+pub mod problem_1621_number_of_sets_of_k_non_overlapping_line_segments;
 pub mod problem_1624_largest_substring_between_two_equal_characters;
 pub mod problem_1629_slowest_key;
 pub mod problem_1630_arithmetic_subarrays;
diff --git a/src/problem_1621_number_of_sets_of_k_non_overlapping_line_segments/combinations.rs b/src/problem_1621_number_of_sets_of_k_non_overlapping_line_segments/combinations.rs
new file mode 100644
index 00000000..8698e3f9
--- /dev/null
+++ b/src/problem_1621_number_of_sets_of_k_non_overlapping_line_segments/combinations.rs
@@ -0,0 +1,77 @@
+pub struct Solution;
+
+// ------------------------------------------------------ snip ------------------------------------------------------ //
+
+impl Solution {
+    const MODULUS: u64 = 1_000_000_007;
+
+    fn exp_mod(mut base: u64, mut exponent: u64) -> u64 {
+        let mut result = 1;
+
+        while exponent != 0 {
+            if exponent & 1 != 0 {
+                result = (result * base) % Self::MODULUS;
+            }
+
+            base = (base * base) % Self::MODULUS;
+
+            exponent >>= 1;
+        }
+
+        result
+    }
+
+    // See <https://en.wikipedia.org/wiki/Modular_multiplicative_inverse#Using_Euler's_theorem>.
+    fn mod_inv(x: u64) -> u64 {
+        Self::exp_mod(x, Self::MODULUS - 2)
+    }
+
+    fn combinations(n: u64, k: u64) -> u64 {
+        let n_minus_k = n - k;
+        let (k, n_minus_k) = if n_minus_k < k { (n_minus_k, k) } else { (k, n_minus_k) };
+        let mut factorial = 1;
+
+        for i in 2..=k {
+            factorial = (factorial * i) % Self::MODULUS;
+        }
+
+        let factorial_k = factorial;
+
+        for i in k + 1..=n_minus_k {
+            factorial = (factorial * i) % Self::MODULUS;
+        }
+
+        let factorial_n_minus_k = factorial;
+
+        for i in n_minus_k + 1..=n {
+            factorial = (factorial * i) % Self::MODULUS;
+        }
+
+        let factorial_n = factorial;
+
+        (factorial_n * Self::mod_inv((factorial_k * factorial_n_minus_k) % Self::MODULUS)) % Self::MODULUS
+    }
+
+    pub fn number_of_sets(n: i32, k: i32) -> i32 {
+        let n = u64::from(n as u32);
+        let k = u64::from(k as u32);
+
+        Self::combinations(n + k - 1, k * 2) as _
+    }
+}
+
+// ------------------------------------------------------ snip ------------------------------------------------------ //
+
+impl super::Solution for Solution {
+    fn number_of_sets(n: i32, k: i32) -> i32 {
+        Self::number_of_sets(n, k)
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    #[test]
+    fn test_solution() {
+        super::super::tests::run::<super::Solution>();
+    }
+}
diff --git a/src/problem_1621_number_of_sets_of_k_non_overlapping_line_segments/mod.rs b/src/problem_1621_number_of_sets_of_k_non_overlapping_line_segments/mod.rs
new file mode 100644
index 00000000..6dddb58a
--- /dev/null
+++ b/src/problem_1621_number_of_sets_of_k_non_overlapping_line_segments/mod.rs
@@ -0,0 +1,18 @@
+pub mod combinations;
+
+pub trait Solution {
+    fn number_of_sets(n: i32, k: i32) -> i32;
+}
+
+#[cfg(test)]
+mod tests {
+    use super::Solution;
+
+    pub fn run<S: Solution>() {
+        let test_cases = [((4, 2), 5), ((3, 1), 3), ((30, 7), 796_297_179)];
+
+        for ((n, k), expected) in test_cases {
+            assert_eq!(S::number_of_sets(n, k), expected);
+        }
+    }
+}