From a4d8a9d4c8214c5977892d3edfa18f699d365710 Mon Sep 17 00:00:00 2001
From: EFanZh <efanzh@gmail.com>
Date: Tue, 8 Oct 2024 21:35:54 +0800
Subject: [PATCH] Add problem 2188: Minimum Time to Finish the Race

---
 src/lib.rs                                    |   1 +
 .../dynamic_programming.rs                    | 103 ++++++++++++++++++
 .../mod.rs                                    |  29 +++++
 3 files changed, 133 insertions(+)
 create mode 100644 src/problem_2188_minimum_time_to_finish_the_race/dynamic_programming.rs
 create mode 100644 src/problem_2188_minimum_time_to_finish_the_race/mod.rs

diff --git a/src/lib.rs b/src/lib.rs
index 7a082f5a..0733cbf0 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -1633,6 +1633,7 @@ pub mod problem_2183_count_array_pairs_divisible_by_k;
 pub mod problem_2185_counting_words_with_a_given_prefix;
 pub mod problem_2186_minimum_number_of_steps_to_make_two_strings_anagram_ii;
 pub mod problem_2187_minimum_time_to_complete_trips;
+pub mod problem_2188_minimum_time_to_finish_the_race;
 pub mod problem_2190_most_frequent_number_following_key_in_an_array;
 pub mod problem_2191_sort_the_jumbled_numbers;
 pub mod problem_2192_all_ancestors_of_a_node_in_a_directed_acyclic_graph;
diff --git a/src/problem_2188_minimum_time_to_finish_the_race/dynamic_programming.rs b/src/problem_2188_minimum_time_to_finish_the_race/dynamic_programming.rs
new file mode 100644
index 00000000..fe5b718e
--- /dev/null
+++ b/src/problem_2188_minimum_time_to_finish_the_race/dynamic_programming.rs
@@ -0,0 +1,103 @@
+pub struct Solution;
+
+// ------------------------------------------------------ snip ------------------------------------------------------ //
+
+impl Solution {
+    pub fn minimum_finish_time(tires: Vec<Vec<i32>>, change_time: i32, num_laps: i32) -> i32 {
+        const QUEUE_BITS: u8 = 5;
+
+        let change_time = change_time as u32;
+        let num_laps = num_laps as u32 as usize;
+        let mut min_times = [u32::MAX; 16];
+
+        for tire in tires {
+            let [f, r] = <[_; 2]>::map(tire.try_into().ok().unwrap(), |x| x as u32);
+
+            let first_min_time = min_times.first_mut().unwrap();
+
+            (*first_min_time) = (*first_min_time).min(f);
+
+            let mut prev_lap_time = f;
+            let mut prev_lap_time_sum = f;
+            let mut half_lap_time = f;
+            let mut half_lap_time_sum = f;
+            let mut is_odd_lap = false;
+
+            let max_laps = min_times.len().min(num_laps);
+
+            for target in &mut min_times[1..max_laps] {
+                if let Some((lap_time, lap_time_sum)) = prev_lap_time.checked_mul(r).and_then(|lap_time| {
+                    prev_lap_time_sum
+                        .checked_add(lap_time)
+                        .map(|lap_time_sum| (lap_time, lap_time_sum))
+                }) {
+                    let saved_half_lap_time_sum = half_lap_time_sum;
+
+                    if is_odd_lap {
+                        half_lap_time *= r;
+                        half_lap_time_sum += half_lap_time;
+                    };
+
+                    let other_lap_time_sum = saved_half_lap_time_sum + half_lap_time_sum;
+
+                    if lap_time_sum - other_lap_time_sum < change_time {
+                        *target = (*target).min(lap_time_sum);
+
+                        prev_lap_time = lap_time;
+                        prev_lap_time_sum += lap_time;
+                        is_odd_lap = !is_odd_lap;
+
+                        continue;
+                    }
+                }
+
+                break;
+            }
+        }
+
+        let max_laps = min_times.iter().take_while(|&&time| time != u32::MAX).count();
+        let mut queue = [0; (1 << QUEUE_BITS)];
+        let queue_mask = queue.len() - 1;
+        let mut total_laps = 0_usize;
+
+        queue[0] = change_time.wrapping_neg();
+
+        loop {
+            total_laps += 1;
+
+            let min_time = (1..).zip(&min_times[..total_laps.min(max_laps)]).fold(
+                u32::MAX,
+                |min_time, (last_laps, &last_laps_time)| {
+                    min_time.min(
+                        queue[total_laps.wrapping_sub(last_laps as usize) & queue_mask].wrapping_add(change_time)
+                            + last_laps_time,
+                    )
+                },
+            );
+
+            queue[total_laps & queue_mask] = min_time;
+
+            if total_laps == num_laps {
+                break;
+            }
+        }
+
+        queue[total_laps & queue_mask] as _
+    }
+}
+
+// ------------------------------------------------------ snip ------------------------------------------------------ //
+
+impl super::Solution for Solution {
+    fn minimum_finish_time(tires: Vec<Vec<i32>>, change_time: i32, num_laps: i32) -> i32 {
+        Self::minimum_finish_time(tires, change_time, num_laps)
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    #[test]
+    fn test_solution() {
+        super::super::tests::run::<super::Solution>();
+    }
+}
diff --git a/src/problem_2188_minimum_time_to_finish_the_race/mod.rs b/src/problem_2188_minimum_time_to_finish_the_race/mod.rs
new file mode 100644
index 00000000..6b6a454a
--- /dev/null
+++ b/src/problem_2188_minimum_time_to_finish_the_race/mod.rs
@@ -0,0 +1,29 @@
+pub mod dynamic_programming;
+
+pub trait Solution {
+    fn minimum_finish_time(tires: Vec<Vec<i32>>, change_time: i32, num_laps: i32) -> i32;
+}
+
+#[cfg(test)]
+mod tests {
+    use super::Solution;
+
+    pub fn run<S: Solution>() {
+        let test_cases = [
+            ((&[[2, 3], [3, 4]] as &[_], 5, 4), 21),
+            ((&[[1, 10], [2, 2], [3, 4]], 6, 5), 25),
+            (
+                (&[[1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7]], 100_000, 1000),
+                8_214_040,
+            ),
+            ((&[[100_000, 100_000]], 100_000, 1000), 199_900_000),
+        ];
+
+        for ((tires, change_time, num_laps), expected) in test_cases {
+            assert_eq!(
+                S::minimum_finish_time(tires.iter().map(Vec::from).collect(), change_time, num_laps),
+                expected,
+            );
+        }
+    }
+}