@@ -65,19 +65,22 @@ impl SparseIndex {
6565 }
6666}
6767
68- /// Represents a maximum (upper envelope) of a collection of linear functions of a variable,
69- /// evaluated using the convex hull trick with square root decomposition.
70- pub struct PiecewiseLinearFn {
68+ /// Represents a maximum (upper envelope) of a collection of linear functions of one
69+ /// variable, evaluated using an online version of the convex hull trick.
70+ /// It combines the offline algorithm with square root decomposition, resulting in an
71+ /// asymptotically suboptimal but simple algorithm with good amortized performnce:
72+ /// For N inserts interleaved with Q queries, a threshold of N/sqrt(Q) yields
73+ /// O(N sqrt Q + Q log N) time complexity. If all queries come after all inserts,
74+ /// any threshold less than N (e.g., 0) yields O(N + Q log N) time complexity.
75+ pub struct PiecewiseLinearConvexFn {
7176 recent_lines : Vec < ( f64 , f64 ) > ,
7277 sorted_lines : Vec < ( f64 , f64 ) > ,
7378 intersections : Vec < f64 > ,
7479 merge_threshold : usize ,
7580}
7681
77- impl PiecewiseLinearFn {
78- /// For N inserts interleaved with Q queries, a threshold of N/sqrt(Q) yields
79- /// O(N sqrt Q + Q log N) time complexity. If all queries come after all inserts,
80- /// any threshold less than N (e.g., 0) yields O(N + Q log N) time complexity.
82+ impl PiecewiseLinearConvexFn {
83+ /// Initializes with a given threshold for re-running the convex hull algorithm
8184 pub fn with_merge_threshold ( merge_threshold : usize ) -> Self {
8285 Self {
8386 recent_lines : vec ! [ ] ,
@@ -210,7 +213,7 @@ mod test {
210213 [ 1 , -1 , -2 , -1 , 0 , 1 ] ,
211214 ] ;
212215 for threshold in 0 ..=lines. len ( ) {
213- let mut func = PiecewiseLinearFn :: with_merge_threshold ( threshold) ;
216+ let mut func = PiecewiseLinearConvexFn :: with_merge_threshold ( threshold) ;
214217 assert_eq ! ( func. evaluate( 0.0 ) , -1e18 ) ;
215218 for ( & ( slope, intercept) , expected) in lines. iter ( ) . zip ( results. iter ( ) ) {
216219 func. max_with ( slope as f64 , intercept as f64 ) ;
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