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-rw-r--r--third_party/rust/smawk/src/monge.rs121
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diff --git a/third_party/rust/smawk/src/monge.rs b/third_party/rust/smawk/src/monge.rs
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+//! 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));
+ }
+}