From 1b6a04ca5504955c571d1c97504fb45ea0befee4 Mon Sep 17 00:00:00 2001
From: Valentin Popov <valentin@popov.link>
Date: Mon, 8 Jan 2024 01:21:28 +0400
Subject: Initial vendor packages

Signed-off-by: Valentin Popov <valentin@popov.link>
---
 vendor/smawk/src/monge.rs | 121 ++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 121 insertions(+)
 create mode 100644 vendor/smawk/src/monge.rs

(limited to 'vendor/smawk/src/monge.rs')

diff --git a/vendor/smawk/src/monge.rs b/vendor/smawk/src/monge.rs
new file mode 100644
index 0000000..dbc80e1
--- /dev/null
+++ b/vendor/smawk/src/monge.rs
@@ -0,0 +1,121 @@
+//! Functions for generating and checking Monge arrays.
+//!
+//! The functions here are mostly meant to be used for testing
+//! correctness of the SMAWK implementation.
+
+use crate::Matrix;
+use std::num::Wrapping;
+use std::ops::Add;
+
+/// Verify that a matrix is a Monge matrix.
+///
+/// A [Monge matrix] \(or array) is a matrix where the following
+/// inequality holds:
+///
+/// ```text
+/// M[i, j] + M[i', j'] <= M[i, j'] + M[i', j]  for all i < i', j < j'
+/// ```
+///
+/// The inequality says that the sum of the main diagonal is less than
+/// the sum of the antidiagonal. Checking this condition is done by
+/// checking *n* ✕ *m* submatrices, so the running time is O(*mn*).
+///
+/// [Monge matrix]: https://en.wikipedia.org/wiki/Monge_array
+pub fn is_monge<T: Ord + Copy, M: Matrix<T>>(matrix: &M) -> bool
+where
+    Wrapping<T>: Add<Output = Wrapping<T>>,
+{
+    /// Returns `Ok(a + b)` if the computation can be done without
+    /// overflow, otherwise `Err(a + b - T::MAX - 1)` is returned.
+    fn checked_add<T: Ord + Copy>(a: Wrapping<T>, b: Wrapping<T>) -> Result<T, T>
+    where
+        Wrapping<T>: Add<Output = Wrapping<T>>,
+    {
+        let sum = a + b;
+        if sum < a {
+            Err(sum.0)
+        } else {
+            Ok(sum.0)
+        }
+    }
+
+    (0..matrix.nrows() - 1)
+        .flat_map(|row| (0..matrix.ncols() - 1).map(move |col| (row, col)))
+        .all(|(row, col)| {
+            let top_left = Wrapping(matrix.index(row, col));
+            let top_right = Wrapping(matrix.index(row, col + 1));
+            let bot_left = Wrapping(matrix.index(row + 1, col));
+            let bot_right = Wrapping(matrix.index(row + 1, col + 1));
+
+            match (
+                checked_add(top_left, bot_right),
+                checked_add(bot_left, top_right),
+            ) {
+                (Ok(a), Ok(b)) => a <= b,   // No overflow.
+                (Err(a), Err(b)) => a <= b, // Double overflow.
+                (Ok(_), Err(_)) => true,    // Anti-diagonal overflow.
+                (Err(_), Ok(_)) => false,   // Main diagonal overflow.
+            }
+        })
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn is_monge_handles_overflow() {
+        // The x + y <= z + w computations will overflow for an u8
+        // matrix unless is_monge is careful.
+        let matrix: Vec<Vec<u8>> = vec![
+            vec![200, 200, 200, 200],
+            vec![200, 200, 200, 200],
+            vec![200, 200, 200, 200],
+        ];
+        assert!(is_monge(&matrix));
+    }
+
+    #[test]
+    fn monge_constant_rows() {
+        let matrix = vec![
+            vec![42, 42, 42, 42],
+            vec![0, 0, 0, 0],
+            vec![100, 100, 100, 100],
+            vec![1000, 1000, 1000, 1000],
+        ];
+        assert!(is_monge(&matrix));
+    }
+
+    #[test]
+    fn monge_constant_cols() {
+        let matrix = vec![
+            vec![42, 0, 100, 1000],
+            vec![42, 0, 100, 1000],
+            vec![42, 0, 100, 1000],
+            vec![42, 0, 100, 1000],
+        ];
+        assert!(is_monge(&matrix));
+    }
+
+    #[test]
+    fn monge_upper_right() {
+        let matrix = vec![
+            vec![10, 10, 42, 42, 42],
+            vec![10, 10, 42, 42, 42],
+            vec![10, 10, 10, 10, 10],
+            vec![10, 10, 10, 10, 10],
+        ];
+        assert!(is_monge(&matrix));
+    }
+
+    #[test]
+    fn monge_lower_left() {
+        let matrix = vec![
+            vec![10, 10, 10, 10, 10],
+            vec![10, 10, 10, 10, 10],
+            vec![42, 42, 42, 10, 10],
+            vec![42, 42, 42, 10, 10],
+        ];
+        assert!(is_monge(&matrix));
+    }
+}
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