From ad51ae4d80268b4704956f75c77987d08652243b Mon Sep 17 00:00:00 2001
From: EFanZh <efanzh@gmail.com>
Date: Sat, 21 Dec 2024 14:37:21 +0800
Subject: [PATCH] Add problem 2338: Count the Number of Ideal Arrays

---
 src/lib.rs                                    |   1 +
 .../dynamic_programming_and_combinations.rs   | 101 ++++++++++++++++++
 .../mod.rs                                    |  18 ++++
 3 files changed, 120 insertions(+)
 create mode 100644 src/problem_2338_count_the_number_of_ideal_arrays/dynamic_programming_and_combinations.rs
 create mode 100644 src/problem_2338_count_the_number_of_ideal_arrays/mod.rs

diff --git a/src/lib.rs b/src/lib.rs
index b7efeba8..8675c7df 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -1740,6 +1740,7 @@ pub mod problem_2333_minimum_sum_of_squared_difference;
 pub mod problem_2335_minimum_amount_of_time_to_fill_cups;
 pub mod problem_2336_smallest_number_in_infinite_set;
 pub mod problem_2337_move_pieces_to_obtain_a_string;
+pub mod problem_2338_count_the_number_of_ideal_arrays;
 pub mod problem_2341_maximum_number_of_pairs_in_array;
 pub mod problem_2342_max_sum_of_a_pair_with_equal_sum_of_digits;
 pub mod problem_2343_query_kth_smallest_trimmed_number;
diff --git a/src/problem_2338_count_the_number_of_ideal_arrays/dynamic_programming_and_combinations.rs b/src/problem_2338_count_the_number_of_ideal_arrays/dynamic_programming_and_combinations.rs
new file mode 100644
index 00000000..8c72a891
--- /dev/null
+++ b/src/problem_2338_count_the_number_of_ideal_arrays/dynamic_programming_and_combinations.rs
@@ -0,0 +1,101 @@
+pub struct Solution;
+
+// ------------------------------------------------------ snip ------------------------------------------------------ //
+
+impl Solution {
+    const MODULUS: u64 = 1_000_000_007;
+
+    fn exp_mod(mut base: u64, mut exponent: u32) -> u64 {
+        let mut result = 1;
+
+        loop {
+            if exponent & 1 != 0 {
+                result = (result * base) % Self::MODULUS;
+            }
+
+            exponent >>= 1;
+
+            if exponent == 0 {
+                break;
+            }
+
+            base = (base * base) % Self::MODULUS;
+        }
+
+        result
+    }
+
+    fn mod_inverse(x: u64) -> u64 {
+        Self::exp_mod(x, Self::MODULUS as u32 - 2)
+    }
+
+    pub fn ideal_arrays(n: i32, max_value: i32) -> i32 {
+        let n = n as u32 as usize;
+        let max_value = max_value as u32 as usize;
+        let max_unique_values = n.min((usize::BITS - max_value.leading_zeros()) as _);
+        let mut cache = vec![0_u32; max_value * max_unique_values].into_boxed_slice();
+        let mut iter = cache.chunks_exact_mut(max_value);
+        let mut prev_row = iter.next().unwrap();
+        let mut start = 1;
+
+        prev_row.fill(1);
+
+        iter.for_each(|current_row| {
+            (start..).zip(&prev_row[start - 1..]).for_each(|(value, &count)| {
+                if count != 0 {
+                    let mut index = value * 2 - 1;
+
+                    while let Some(target) = current_row.get_mut(index) {
+                        *target += count;
+
+                        index += value;
+                    }
+                }
+            });
+
+            prev_row = current_row;
+            start <<= 1;
+        });
+
+        let mut factorials = vec![0_u32; n].into_boxed_slice();
+        let mut factorial = 1;
+
+        (1..).zip(&mut *factorials).for_each(|(factor, target)| {
+            *target = factorial as _;
+            factorial = (factorial * factor) % Self::MODULUS;
+        });
+
+        let top = u64::from(*factorials.last().unwrap());
+
+        cache
+            .chunks_exact(max_value)
+            .enumerate()
+            .fold(0, |mut result, (k, row)| {
+                let count = row[(1 << k) - 1..].iter().sum::<u32>();
+
+                let combinations = (top
+                    * Self::mod_inverse((u64::from(factorials[k]) * u64::from(factorials[n - 1 - k])) % Self::MODULUS))
+                    % Self::MODULUS;
+
+                result += (combinations * u64::from(count) % Self::MODULUS) as u32;
+
+                result.checked_sub(Self::MODULUS as _).unwrap_or(result)
+            }) as _
+    }
+}
+
+// ------------------------------------------------------ snip ------------------------------------------------------ //
+
+impl super::Solution for Solution {
+    fn ideal_arrays(n: i32, max_value: i32) -> i32 {
+        Self::ideal_arrays(n, max_value)
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    #[test]
+    fn test_solution() {
+        super::super::tests::run::<super::Solution>();
+    }
+}
diff --git a/src/problem_2338_count_the_number_of_ideal_arrays/mod.rs b/src/problem_2338_count_the_number_of_ideal_arrays/mod.rs
new file mode 100644
index 00000000..30e82f0a
--- /dev/null
+++ b/src/problem_2338_count_the_number_of_ideal_arrays/mod.rs
@@ -0,0 +1,18 @@
+pub mod dynamic_programming_and_combinations;
+
+pub trait Solution {
+    fn ideal_arrays(n: i32, max_value: i32) -> i32;
+}
+
+#[cfg(test)]
+mod tests {
+    use super::Solution;
+
+    pub fn run<S: Solution>() {
+        let test_cases = [((2, 5), 10), ((5, 3), 11), ((5, 9), 111)];
+
+        for ((n, max_value), expected) in test_cases {
+            assert_eq!(S::ideal_arrays(n, max_value), expected);
+        }
+    }
+}