Added simplicial_polytopic_number.rs and rising_factorial.rs to /src/…

DIRECTORY.md

@@ -240,9 +240,11 @@
     * [Quadratic Residue](https://github.com/TheAlgorithms/Rust/blob/master/src/math/quadratic_residue.rs)
     * [Random](https://github.com/TheAlgorithms/Rust/blob/master/src/math/random.rs)
     * [Relu](https://github.com/TheAlgorithms/Rust/blob/master/src/math/relu.rs)
+    * [Rising Factorial](https://github.com/TheAlgorithms/Rust/blob/master/rising_factorial.rs)  
     * [Sieve Of Eratosthenes](https://github.com/TheAlgorithms/Rust/blob/master/src/math/sieve_of_eratosthenes.rs)
     * [Sigmoid](https://github.com/TheAlgorithms/Rust/blob/master/src/math/sigmoid.rs)
     * [Signum](https://github.com/TheAlgorithms/Rust/blob/master/src/math/signum.rs)
+    * [Simplicial Polytopic Number](https://github.com/TheAlgorithms/Rust/blob/master/src/math/simplicial_polytopic_number)
     * [Simpsons Integration](https://github.com/TheAlgorithms/Rust/blob/master/src/math/simpsons_integration.rs)
     * [Softmax](https://github.com/TheAlgorithms/Rust/blob/master/src/math/softmax.rs)
     * [Sprague Grundy Theorem](https://github.com/TheAlgorithms/Rust/blob/master/src/math/sprague_grundy_theorem.rs)

src/math/mod.rs

@@ -63,9 +63,11 @@ mod prime_numbers;
 mod quadratic_residue;
 mod random;
 mod relu;
+mod rising_factorial;
 mod sieve_of_eratosthenes;
 mod sigmoid;
 mod signum;
+mod simplicial_polytopic_number;
 mod simpsons_integration;
 mod softmax;
 mod sprague_grundy_theorem;
@@ -155,9 +157,11 @@ pub use self::prime_numbers::prime_numbers;
 pub use self::quadratic_residue::{cipolla, tonelli_shanks};
 pub use self::random::PCG32;
 pub use self::relu::relu;
+pub use self::rising_factorial::rising_factorial;
 pub use self::sieve_of_eratosthenes::sieve_of_eratosthenes;
 pub use self::sigmoid::sigmoid;
 pub use self::signum::signum;
+pub use self::simplicial_polytopic_number::simplicial_polytopic_number;
 pub use self::simpsons_integration::simpsons_integration;
 pub use self::softmax::softmax;
 pub use self::sprague_grundy_theorem::calculate_grundy_number;

src/math/rising_factorial.rs

@@ -0,0 +1,33 @@
+use std::ops::Add;
+use std::ops::Mul;
+// Rising factorials are defined as the polynomial
+// (x)_n = x(x + 1)(x + 2) ... (x + n - 1).
+//
+// For further reading:
+// https://mathworld.wolfram.com/RisingFactorial.html
+// https://en.wikipedia.org/wiki/Falling_and_rising_factorials
+//
+// Returns the nth rising factorial.
+pub fn rising_factorial(x: u64, n: u64) -> u64 {
+    let mut result = x;
+    for i in 1..n {
+        let next_term = x.add(i);
+        result = result.mul(next_term);
+    }
+    result
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn test_rising_factorial() {
+        assert_eq!(rising_factorial(1, 0), 1);
+        assert_eq!(rising_factorial(1, 1), 1);
+        assert_eq!(rising_factorial(2, 1), 2);
+        assert_eq!(rising_factorial(1, 2), 2); // 1 * 2
+        assert_eq!(rising_factorial(2, 2), 6); // 2 * 3
+        assert_eq!(rising_factorial(3, 3), 60); // 3 * 4 * 5
+    }
+}

src/math/simplicial_polytopic_number.rs

@@ -0,0 +1,48 @@
+use crate::math::factorial;
+use crate::math::rising_factorial;
+
+use std::ops::Div;
+
+// Simplicial polytopic numbers are a family of sequences of figurate
+// numbers corresponding to the d-dimensional simplex for each
+// dimensional simplex for each dimension d, where d is a nonnegative
+// integer
+//
+// For further reading:
+// https://oeis.org/wiki/Simplicial_polytopic_numbers
+// https://en.wikipedia.org/wiki/Triangular_number
+//
+// This program returns the simplicial polytopic number for any
+// d-dimensional simplex. For example (2, 2) would return the
+// second triangular number 3.
+pub fn simplicial_polytopic_number(n: u64, d: u64) -> u64 {
+    rising_factorial(n, d).div(factorial(d))
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    macro_rules! test_simplicial_polytopic_number {
+        ($($name:ident: $inputs:expr,)*) => {
+        $(
+            #[test]
+            fn $name() {
+                let ((n, d), expected) =$inputs;
+                assert_eq!(simplicial_polytopic_number(n, d), expected);
+            }
+        )*
+        }
+    }
+
+    test_simplicial_polytopic_number! {
+        input_0: ((1, 1), 1),
+        input_1: ((2, 1), 2),
+        input_2: ((2, 2), 3),
+        input_3: ((3, 3), 10),
+        input_4: ((2, 4), 5),
+        input_5: ((5, 5), 126),
+        input_6: ((9, 6), 3003),
+        input_7: ((6, 10), 3003),
+    }
+}