@@ -5,23 +5,23 @@ pub fn asserting_cmp<T: PartialOrd>(a: &T, b: &T) -> std::cmp::Ordering {
55 a. partial_cmp ( b) . expect ( "Comparing incomparable elements" )
66}
77
8- /// Assuming slice is totally ordered and sorted , returns the minimum i for which
8+ /// Assuming slice is sorted and totally ordered , returns the minimum i for which
99/// slice[i] >= key, or slice.len() if no such i exists
1010pub fn slice_lower_bound < T : PartialOrd > ( slice : & [ T ] , key : & T ) -> usize {
1111 slice
1212 . binary_search_by ( |x| asserting_cmp ( x, key) . then ( std:: cmp:: Ordering :: Greater ) )
1313 . unwrap_err ( )
1414}
1515
16- /// Assuming slice is totally ordered and sorted , returns the minimum i for which
16+ /// Assuming slice is sorted and totally ordered , returns the minimum i for which
1717/// slice[i] > key, or slice.len() if no such i exists
1818pub fn slice_upper_bound < T : PartialOrd > ( slice : & [ T ] , key : & T ) -> usize {
1919 slice
2020 . binary_search_by ( |x| asserting_cmp ( x, key) . then ( std:: cmp:: Ordering :: Less ) )
2121 . unwrap_err ( )
2222}
2323
24- /// Merge two sorted collections into one
24+ /// Merge two sorted and totally ordered collections into one
2525pub fn merge_sorted < T : PartialOrd > (
2626 i1 : impl IntoIterator < Item = T > ,
2727 i2 : impl IntoIterator < Item = T > ,
@@ -35,6 +35,16 @@ pub fn merge_sorted<T: PartialOrd>(
3535 merged
3636}
3737
38+ /// A stable sort
39+ pub fn merge_sort < T : Ord > ( mut v : Vec < T > ) -> Vec < T > {
40+ if v. len ( ) < 2 {
41+ v
42+ } else {
43+ let v2 = v. split_off ( v. len ( ) / 2 ) ;
44+ merge_sorted ( merge_sort ( v) , merge_sort ( v2) )
45+ }
46+ }
47+ 3848/// A simple data structure for coordinate compression
3949pub struct SparseIndex {
4050 coords : Vec < i64 > ,
@@ -58,9 +68,9 @@ impl SparseIndex {
5868/// Represents a maximum (upper envelope) of a collection of linear functions of a variable,
5969/// evaluated using the convex hull trick with square root decomposition.
6070pub struct PiecewiseLinearFn {
71+ recent_lines : Vec < ( f64 , f64 ) > ,
6172 sorted_lines : Vec < ( f64 , f64 ) > ,
6273 intersections : Vec < f64 > ,
63- recent_lines : Vec < ( f64 , f64 ) > ,
6474 merge_threshold : usize ,
6575}
6676
@@ -70,9 +80,9 @@ impl PiecewiseLinearFn {
7080 /// any threshold less than N (e.g., 0) yields O(N + Q log N) time complexity.
7181 pub fn with_merge_threshold ( merge_threshold : usize ) -> Self {
7282 Self {
83+ recent_lines : vec ! [ ] ,
7384 sorted_lines : vec ! [ ] ,
7485 intersections : vec ! [ ] ,
75- recent_lines : vec ! [ ] ,
7686 merge_threshold,
7787 }
7888 }
@@ -155,6 +165,15 @@ mod test {
155165 assert_eq ! ( merge_sorted( vals1, vals2) , vals_merged) ;
156166 }
157167
168+ #[ test]
169+ fn test_merge_sort ( ) {
170+ let unsorted = vec ! [ 8 , -5 , 1 , 4 , -3 , 4 ] ;
171+ let sorted = vec ! [ -5 , -3 , 1 , 4 , 4 , 8 ] ;
172+ 173+ assert_eq ! ( merge_sort( unsorted) , sorted) ;
174+ assert_eq ! ( merge_sort( sorted. clone( ) ) , sorted) ;
175+ }
176+ 158177 #[ test]
159178 fn test_coord_compress ( ) {
160179 let mut coords = vec ! [ 16 , 99 , 45 , 18 ] ;
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