From 1d5eb65ae74be546b0ad76242378c2b971064c96 Mon Sep 17 00:00:00 2001
From: EFanZh <efanzh@gmail.com>
Date: Sat, 21 Oct 2023 18:01:07 +0800
Subject: [PATCH] Add problem 1643: Kth Smallest Instructions

---
 src/lib.rs                                    |  1 +
 .../combinations.rs                           | 81 +++++++++++++++++++
 .../mod.rs                                    | 22 +++++
 3 files changed, 104 insertions(+)
 create mode 100644 src/problem_1643_kth_smallest_instructions/combinations.rs
 create mode 100644 src/problem_1643_kth_smallest_instructions/mod.rs

diff --git a/src/lib.rs b/src/lib.rs
index 31245101..19b0335f 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -1351,6 +1351,7 @@ pub mod problem_1639_number_of_ways_to_form_a_target_string_given_a_dictionary;
 pub mod problem_1640_check_array_formation_through_concatenation;
 pub mod problem_1641_count_sorted_vowel_strings;
 pub mod problem_1642_furthest_building_you_can_reach;
+pub mod problem_1643_kth_smallest_instructions;
 pub mod problem_1646_get_maximum_in_generated_array;
 pub mod problem_1647_minimum_deletions_to_make_character_frequencies_unique;
 pub mod problem_1652_defuse_the_bomb;
diff --git a/src/problem_1643_kth_smallest_instructions/combinations.rs b/src/problem_1643_kth_smallest_instructions/combinations.rs
new file mode 100644
index 00000000..9ed3d03b
--- /dev/null
+++ b/src/problem_1643_kth_smallest_instructions/combinations.rs
@@ -0,0 +1,81 @@
+pub struct Solution;
+
+// ------------------------------------------------------ snip ------------------------------------------------------ //
+
+use std::convert::TryInto;
+use std::iter;
+
+impl Solution {
+    fn combinations(n: usize) -> Box<[u32]> {
+        let mut result = vec![0; n * n].into_boxed_slice();
+        let mut iter = result.chunks_exact_mut(n);
+        let mut prev_row = iter.next().unwrap();
+
+        prev_row[0] = 1;
+
+        for row in iter {
+            let mut top_left = 0;
+
+            for (value, &mut top) in row.iter_mut().zip(prev_row) {
+                *value = top_left + top;
+                top_left = top;
+            }
+
+            prev_row = row;
+        }
+
+        result
+    }
+
+    pub fn kth_smallest_path(destination: Vec<i32>, k: i32) -> String {
+        let [row, column]: [_; 2] = destination.try_into().ok().unwrap();
+        let mut row = row as u32 as usize;
+        let mut column = column as u32 as usize;
+        let mut k = k as u32;
+        let length = row + column;
+        let combinations = Self::combinations(length);
+        let mut result = String::with_capacity(length);
+
+        let (c, count) = loop {
+            let count = combinations[length * (row + column - 1) + row];
+
+            if k <= count {
+                result.push('H');
+                column -= 1;
+
+                if column == 0 {
+                    break ('V', row);
+                }
+            } else {
+                result.push('V');
+                row -= 1;
+
+                if row == 0 {
+                    break ('H', column);
+                }
+
+                k -= count;
+            }
+        };
+
+        result.extend(iter::repeat(c).take(count));
+
+        result
+    }
+}
+
+// ------------------------------------------------------ snip ------------------------------------------------------ //
+
+impl super::Solution for Solution {
+    fn kth_smallest_path(destination: Vec<i32>, k: i32) -> String {
+        Self::kth_smallest_path(destination, k)
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    #[test]
+    fn test_solution() {
+        super::super::tests::run::<super::Solution>();
+    }
+}
diff --git a/src/problem_1643_kth_smallest_instructions/mod.rs b/src/problem_1643_kth_smallest_instructions/mod.rs
new file mode 100644
index 00000000..549a0156
--- /dev/null
+++ b/src/problem_1643_kth_smallest_instructions/mod.rs
@@ -0,0 +1,22 @@
+pub mod combinations;
+
+pub trait Solution {
+    fn kth_smallest_path(destination: Vec<i32>, k: i32) -> String;
+}
+
+#[cfg(test)]
+mod tests {
+    use super::Solution;
+
+    pub fn run<S: Solution>() {
+        let test_cases = [
+            ((&[2, 3] as &[_], 1), "HHHVV"),
+            ((&[2, 3], 2), "HHVHV"),
+            ((&[2, 3], 3), "HHVVH"),
+        ];
+
+        for ((destination, k), expected) in test_cases {
+            assert_eq!(S::kth_smallest_path(destination.to_vec(), k), expected);
+        }
+    }
+}