From d9f7c4a147f8d212af0c5935e88802055edb20fa Mon Sep 17 00:00:00 2001
From: EFanZh <efanzh@gmail.com>
Date: Mon, 16 Oct 2023 23:16:31 +0800
Subject: [PATCH] Add problem 1802: Maximum Value at a Given Index in a Bounded
 Array

---
 src/lib.rs                                    |  1 +
 .../mathematical.rs                           | 49 +++++++++++++++++++
 .../mod.rs                                    | 18 +++++++
 3 files changed, 68 insertions(+)
 create mode 100644 src/problem_1802_maximum_value_at_a_given_index_in_a_bounded_array/mathematical.rs
 create mode 100644 src/problem_1802_maximum_value_at_a_given_index_in_a_bounded_array/mod.rs

diff --git a/src/lib.rs b/src/lib.rs
index f1134c9f..76551e22 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -1419,6 +1419,7 @@ pub mod problem_1790_check_if_one_string_swap_can_make_strings_equal;
 pub mod problem_1791_find_center_of_star_graph;
 pub mod problem_1796_second_largest_digit_in_a_string;
 pub mod problem_1800_maximum_ascending_subarray_sum;
+pub mod problem_1802_maximum_value_at_a_given_index_in_a_bounded_array;
 pub mod problem_1805_number_of_different_integers_in_a_string;
 pub mod problem_1807_evaluate_the_bracket_pairs_of_a_string;
 pub mod problem_1812_determine_color_of_a_chessboard_square;
diff --git a/src/problem_1802_maximum_value_at_a_given_index_in_a_bounded_array/mathematical.rs b/src/problem_1802_maximum_value_at_a_given_index_in_a_bounded_array/mathematical.rs
new file mode 100644
index 00000000..9b390efd
--- /dev/null
+++ b/src/problem_1802_maximum_value_at_a_given_index_in_a_bounded_array/mathematical.rs
@@ -0,0 +1,49 @@
+pub struct Solution;
+
+// ------------------------------------------------------ snip ------------------------------------------------------ //
+
+impl Solution {
+    fn get_area(start: u64, end: u64) -> u64 {
+        (start + end) * (end + 1 - start) / 2
+    }
+
+    #[allow(clippy::cast_precision_loss)]
+    pub fn max_value(n: i32, index: i32, max_sum: i32) -> i32 {
+        let n = n as u32;
+        let index = index as u32;
+        let index = index.min(n - 1 - index);
+        let max_sum = max_sum as u32 - n;
+        let n_u64 = u64::from(n);
+        let index_u64 = u64::from(index);
+        let max_sum_u64 = u64::from(max_sum);
+
+        (if max_sum_u64 <= (index_u64 + 1).pow(2) {
+            f64::from(max_sum).sqrt() as u32
+        } else {
+            let threshold =
+                Self::get_area(1, n_u64 - index_u64) + Self::get_area(n_u64 - index_u64 * 2, n_u64 - index_u64 - 1);
+
+            if max_sum_u64 <= threshold {
+                (f64::sqrt((8 * (max_sum_u64 + index_u64 * (index_u64 + 1)) + 1) as _) as u32 - index * 2 - 1) / 2
+            } else {
+                n - index + (max_sum - threshold as u32) / n
+            }
+        } + 1) as _
+    }
+}
+
+// ------------------------------------------------------ snip ------------------------------------------------------ //
+
+impl super::Solution for Solution {
+    fn max_value(n: i32, index: i32, max_sum: i32) -> i32 {
+        Self::max_value(n, index, max_sum)
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    #[test]
+    fn test_solution() {
+        super::super::tests::run::<super::Solution>();
+    }
+}
diff --git a/src/problem_1802_maximum_value_at_a_given_index_in_a_bounded_array/mod.rs b/src/problem_1802_maximum_value_at_a_given_index_in_a_bounded_array/mod.rs
new file mode 100644
index 00000000..4d3de3eb
--- /dev/null
+++ b/src/problem_1802_maximum_value_at_a_given_index_in_a_bounded_array/mod.rs
@@ -0,0 +1,18 @@
+pub mod mathematical;
+
+pub trait Solution {
+    fn max_value(n: i32, index: i32, max_sum: i32) -> i32;
+}
+
+#[cfg(test)]
+mod tests {
+    use super::Solution;
+
+    pub fn run<S: Solution>() {
+        let test_cases = [((4, 2, 6), 2), ((6, 1, 10), 3), ((4, 0, 4), 1), ((5, 0, 28), 7)];
+
+        for ((n, index, max_sum), expected) in test_cases {
+            assert_eq!(S::max_value(n, index, max_sum), expected);
+        }
+    }
+}