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Commit f5c3543

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coordinate compression and ArqSpec documentation on point queries
1 parent fb0a9ed commit f5c3543

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‎README.md

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@@ -44,11 +44,11 @@ Rather than try to persuade you with words, this repository aims to show by exam
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## Contents
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- [Basic graph representations](src/graph/mod.rs): adjacency lists, disjoint set union
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- [Elementary Graph algorithms](src/graph/util.rs): minimum spanning tree, Euler path, Dijkstra's algorithm, DFS iteration
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- [Elementary graph algorithms](src/graph/util.rs): minimum spanning tree, Euler path, Dijkstra's algorithm, DFS iteration
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- [Network flows](src/graph/flow.rs): Dinic's blocking flow, Hopcroft-Karp bipartite matching, min cost max flow
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- [Connected components](src/graph/connectivity.rs): 2-edge-, 2-vertex- and strongly connected components, bridges, articulation points, topological sort, 2-SAT
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- [Associative range query](src/range_query): known colloquially as *segtrees*, and Mo's query square root decomposition
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- [GCD Math](src/math/mod.rs): canonical solution to Bezout's identity
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- [Associative range query](src/range_query): known colloquially as *segtrees*, coordinate compression, and Mo's query square root decomposition
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- [Number thery](src/math/mod.rs): canonical solution to Bezout's identity, Miller's primality test
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- [Arithmetic](src/math/num.rs): rational and complex numbers, linear algebra, safe modular arithmetic
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- [FFT](src/math/fft.rs): fast Fourier transform, number theoretic transform, convolution
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- [Scanner](src/scanner.rs): utility for reading input data ergonomically

‎src/range_query/mod.rs

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@@ -6,11 +6,53 @@ pub use dynamic_arq::{ArqView, DynamicArq};
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pub use specs::ArqSpec;
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pub use static_arq::StaticArq;
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/// A simple data structure for coordinate compression
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pub struct SparseIndex {
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coords: Vec<i64>
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}
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impl SparseIndex {
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/// Build an index, given the full set of coordinates to compress.
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pub fn new(mut coords: Vec<i64>) -> Self {
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coords.sort_unstable();
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coords.dedup();
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Self { coords }
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}
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/// Return Ok(i) if the coordinate q appears at index i
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/// Return Err(i) if q appears between indices i-1 and i
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pub fn compress(&self, q: i64) -> Result<usize, usize> {
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self.coords.binary_search(&q)
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}
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}
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#[cfg(test)]
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mod test {
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use super::specs::*;
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use super::*;
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#[test]
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fn test_coord_compress() {
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let mut coords = vec![16, 99, 45, 18];
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let index = SparseIndex::new(coords.clone());
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coords.sort_unstable();
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for (i, q) in coords.into_iter().enumerate() {
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assert_eq!(index.compress(q - 1), Err(i));
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assert_eq!(index.compress(q), Ok(i));
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assert_eq!(index.compress(q + 1), Err(i + 1));
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}
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}
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#[test]
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fn test_range_compress() {
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let queries = vec![(0, 10), (10, 19), (20, 29)];
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let coords = queries.iter().flat_map(|&(i, j)| vec![i, j + 1]).collect();
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let index = SparseIndex::new(coords);
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assert_eq!(index.coords, vec![0, 10, 11, 20, 30]);
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}
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#[test]
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fn test_rmq() {
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let mut arq = StaticArq::<AssignMin>::new(&[0; 10]);

‎src/range_query/specs.rs

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@@ -15,15 +15,23 @@ pub trait ArqSpec {
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/// Must satisfy the Identity Law:
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/// For all a, op(a, identity()) = op(identity(), a) = a
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fn identity() -> Self::S;
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/// For point query / eager updates, compose() can be unimplemented!()
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/// For range query / lazy updates, it must satisfy the Composition Law:
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/// Must satisfy the Composition Law:
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/// For all f,g,a, apply(compose(f, g), a) = apply(f, apply(g, a))
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fn compose(f: &Self::F, g: &Self::F) -> Self::F;
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/// For point query / eager updates, apply() can assume it acts on a leaf.
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/// For range query / lazy updates, it must satisfy the Distributive Law:
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/// For all f,a,b, apply(f, op(a, b)) = op(apply(f, a), apply(f, b))
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/// Must satisfy the Distributive Law:
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/// For all f,a,b, apply(f, op(a, b), s+t) = op(apply(f, a, s), apply(f, b, t))
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/// The `size` parameter makes this law easier to satisfy in certain cases.
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fn apply(f: &Self::F, a: &Self::S, size: i64) -> Self::S;
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// The following relaxations to the laws may apply.
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// If only point updates are made, the Composition and Distributive Laws
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// no longer apply.
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// - compose() is never called, so it can be left unimplemented!().
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// - apply() is only ever called on leaves, i.e., with size == 1.
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// If only point queries are made, the Associative and Distributive Laws
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// no longer apply.
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// - op()'s result only matters when identity() is an argument.
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// - apply()'s result only matters on leaves, i.e., with size == 1.
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}
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/// Range Minimum Query (RMQ), a classic application of ARQ.
@@ -109,7 +117,8 @@ impl ArqSpec for SupplyDemand {
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fn compose(_: &Self::F, _: &Self::F) -> Self::F {
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unimplemented!()
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}
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fn apply(&(p_add, o_add): &Self::F, &(p, o, _): &Self::S, _: i64) -> Self::S {
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fn apply(&(p_add, o_add): &Self::F, &(p, o, _): &Self::S, s: i64) -> Self::S {
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assert_eq!(s, 1);
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let p = p + p_add;
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let o = o + o_add;
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(p, o, p.min(o))

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