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26 changed files with 1376 additions and 61 deletions
213
vendor/golang.org/x/exp/slices/slices.go
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213
vendor/golang.org/x/exp/slices/slices.go
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// Copyright 2021 The Go Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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// Package slices defines various functions useful with slices of any type.
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// Unless otherwise specified, these functions all apply to the elements
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// of a slice at index 0 <= i < len(s).
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package slices
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import "golang.org/x/exp/constraints"
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// Equal reports whether two slices are equal: the same length and all
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// elements equal. If the lengths are different, Equal returns false.
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// Otherwise, the elements are compared in increasing index order, and the
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// comparison stops at the first unequal pair.
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// Floating point NaNs are not considered equal.
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func Equal[E comparable](s1, s2 []E) bool {
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if len(s1) != len(s2) {
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return false
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}
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for i := range s1 {
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if s1[i] != s2[i] {
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return false
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}
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}
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return true
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}
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// EqualFunc reports whether two slices are equal using a comparison
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// function on each pair of elements. If the lengths are different,
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// EqualFunc returns false. Otherwise, the elements are compared in
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// increasing index order, and the comparison stops at the first index
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// for which eq returns false.
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func EqualFunc[E1, E2 any](s1 []E1, s2 []E2, eq func(E1, E2) bool) bool {
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if len(s1) != len(s2) {
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return false
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}
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for i, v1 := range s1 {
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v2 := s2[i]
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if !eq(v1, v2) {
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return false
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}
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}
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return true
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}
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// Compare compares the elements of s1 and s2.
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// The elements are compared sequentially, starting at index 0,
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// until one element is not equal to the other.
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// The result of comparing the first non-matching elements is returned.
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// If both slices are equal until one of them ends, the shorter slice is
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// considered less than the longer one.
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// The result is 0 if s1 == s2, -1 if s1 < s2, and +1 if s1 > s2.
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// Comparisons involving floating point NaNs are ignored.
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func Compare[E constraints.Ordered](s1, s2 []E) int {
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s2len := len(s2)
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for i, v1 := range s1 {
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if i >= s2len {
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return +1
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}
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v2 := s2[i]
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switch {
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case v1 < v2:
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return -1
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case v1 > v2:
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return +1
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}
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}
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if len(s1) < s2len {
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return -1
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}
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return 0
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}
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// CompareFunc is like Compare but uses a comparison function
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// on each pair of elements. The elements are compared in increasing
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// index order, and the comparisons stop after the first time cmp
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// returns non-zero.
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// The result is the first non-zero result of cmp; if cmp always
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// returns 0 the result is 0 if len(s1) == len(s2), -1 if len(s1) < len(s2),
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// and +1 if len(s1) > len(s2).
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func CompareFunc[E1, E2 any](s1 []E1, s2 []E2, cmp func(E1, E2) int) int {
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s2len := len(s2)
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for i, v1 := range s1 {
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if i >= s2len {
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return +1
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}
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v2 := s2[i]
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if c := cmp(v1, v2); c != 0 {
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return c
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}
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}
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if len(s1) < s2len {
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return -1
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}
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return 0
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}
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// Index returns the index of the first occurrence of v in s,
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// or -1 if not present.
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func Index[E comparable](s []E, v E) int {
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for i, vs := range s {
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if v == vs {
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return i
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}
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}
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return -1
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}
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// IndexFunc returns the first index i satisfying f(s[i]),
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// or -1 if none do.
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func IndexFunc[E any](s []E, f func(E) bool) int {
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for i, v := range s {
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if f(v) {
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return i
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}
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}
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return -1
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}
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// Contains reports whether v is present in s.
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func Contains[E comparable](s []E, v E) bool {
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return Index(s, v) >= 0
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}
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// Insert inserts the values v... into s at index i,
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// returning the modified slice.
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// In the returned slice r, r[i] == v[0].
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// Insert panics if i is out of range.
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// This function is O(len(s) + len(v)).
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func Insert[S ~[]E, E any](s S, i int, v ...E) S {
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tot := len(s) + len(v)
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if tot <= cap(s) {
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s2 := s[:tot]
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copy(s2[i+len(v):], s[i:])
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copy(s2[i:], v)
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return s2
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}
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s2 := make(S, tot)
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copy(s2, s[:i])
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copy(s2[i:], v)
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copy(s2[i+len(v):], s[i:])
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return s2
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}
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// Delete removes the elements s[i:j] from s, returning the modified slice.
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// Delete panics if s[i:j] is not a valid slice of s.
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// Delete modifies the contents of the slice s; it does not create a new slice.
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// Delete is O(len(s)-(j-i)), so if many items must be deleted, it is better to
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// make a single call deleting them all together than to delete one at a time.
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func Delete[S ~[]E, E any](s S, i, j int) S {
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return append(s[:i], s[j:]...)
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}
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// Clone returns a copy of the slice.
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// The elements are copied using assignment, so this is a shallow clone.
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func Clone[S ~[]E, E any](s S) S {
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// Preserve nil in case it matters.
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if s == nil {
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return nil
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}
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return append(S([]E{}), s...)
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}
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// Compact replaces consecutive runs of equal elements with a single copy.
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// This is like the uniq command found on Unix.
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// Compact modifies the contents of the slice s; it does not create a new slice.
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func Compact[S ~[]E, E comparable](s S) S {
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if len(s) == 0 {
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return s
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}
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i := 1
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last := s[0]
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for _, v := range s[1:] {
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if v != last {
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s[i] = v
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i++
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last = v
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}
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}
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return s[:i]
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}
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// CompactFunc is like Compact but uses a comparison function.
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func CompactFunc[S ~[]E, E any](s S, eq func(E, E) bool) S {
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if len(s) == 0 {
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return s
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}
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i := 1
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last := s[0]
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for _, v := range s[1:] {
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if !eq(v, last) {
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s[i] = v
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i++
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last = v
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}
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}
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return s[:i]
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}
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// Grow increases the slice's capacity, if necessary, to guarantee space for
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// another n elements. After Grow(n), at least n elements can be appended
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// to the slice without another allocation. Grow may modify elements of the
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// slice between the length and the capacity. If n is negative or too large to
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// allocate the memory, Grow panics.
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func Grow[S ~[]E, E any](s S, n int) S {
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return append(s, make(S, n)...)[:len(s)]
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}
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// Clip removes unused capacity from the slice, returning s[:len(s):len(s)].
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func Clip[S ~[]E, E any](s S) S {
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return s[:len(s):len(s)]
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}
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95
vendor/golang.org/x/exp/slices/sort.go
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95
vendor/golang.org/x/exp/slices/sort.go
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// Copyright 2022 The Go Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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package slices
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import "golang.org/x/exp/constraints"
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// Sort sorts a slice of any ordered type in ascending order.
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func Sort[Elem constraints.Ordered](x []Elem) {
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n := len(x)
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quickSortOrdered(x, 0, n, maxDepth(n))
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}
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// Sort sorts the slice x in ascending order as determined by the less function.
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// This sort is not guaranteed to be stable.
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func SortFunc[Elem any](x []Elem, less func(a, b Elem) bool) {
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n := len(x)
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quickSortLessFunc(x, 0, n, maxDepth(n), less)
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}
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// SortStable sorts the slice x while keeping the original order of equal
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// elements, using less to compare elements.
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func SortStableFunc[Elem any](x []Elem, less func(a, b Elem) bool) {
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stableLessFunc(x, len(x), less)
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}
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// IsSorted reports whether x is sorted in ascending order.
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func IsSorted[Elem constraints.Ordered](x []Elem) bool {
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for i := len(x) - 1; i > 0; i-- {
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if x[i] < x[i-1] {
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return false
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}
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}
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return true
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}
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// IsSortedFunc reports whether x is sorted in ascending order, with less as the
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// comparison function.
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func IsSortedFunc[Elem any](x []Elem, less func(a, b Elem) bool) bool {
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for i := len(x) - 1; i > 0; i-- {
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if less(x[i], x[i-1]) {
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return false
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}
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}
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return true
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}
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// BinarySearch searches for target in a sorted slice and returns the smallest
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// index at which target is found. If the target is not found, the index at
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// which it could be inserted into the slice is returned; therefore, if the
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// intention is to find target itself a separate check for equality with the
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// element at the returned index is required.
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func BinarySearch[Elem constraints.Ordered](x []Elem, target Elem) int {
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return search(len(x), func(i int) bool { return x[i] >= target })
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}
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// BinarySearchFunc uses binary search to find and return the smallest index i
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// in [0, n) at which ok(i) is true, assuming that on the range [0, n),
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// ok(i) == true implies ok(i+1) == true. That is, BinarySearchFunc requires
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// that ok is false for some (possibly empty) prefix of the input range [0, n)
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// and then true for the (possibly empty) remainder; BinarySearchFunc returns
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// the first true index. If there is no such index, BinarySearchFunc returns n.
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// (Note that the "not found" return value is not -1 as in, for instance,
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// strings.Index.) Search calls ok(i) only for i in the range [0, n).
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func BinarySearchFunc[Elem any](x []Elem, ok func(Elem) bool) int {
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return search(len(x), func(i int) bool { return ok(x[i]) })
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}
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// maxDepth returns a threshold at which quicksort should switch
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// to heapsort. It returns 2*ceil(lg(n+1)).
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func maxDepth(n int) int {
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var depth int
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for i := n; i > 0; i >>= 1 {
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depth++
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}
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return depth * 2
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}
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func search(n int, f func(int) bool) int {
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// Define f(-1) == false and f(n) == true.
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// Invariant: f(i-1) == false, f(j) == true.
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i, j := 0, n
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for i < j {
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h := int(uint(i+j) >> 1) // avoid overflow when computing h
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// i ≤ h < j
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if !f(h) {
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i = h + 1 // preserves f(i-1) == false
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} else {
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j = h // preserves f(j) == true
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}
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}
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// i == j, f(i-1) == false, and f(j) (= f(i)) == true => answer is i.
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return i
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}
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342
vendor/golang.org/x/exp/slices/zsortfunc.go
generated
vendored
Normal file
342
vendor/golang.org/x/exp/slices/zsortfunc.go
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@ -0,0 +1,342 @@
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// Code generated by gen_sort_variants.go; DO NOT EDIT.
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// Copyright 2022 The Go Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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package slices
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// insertionSortLessFunc sorts data[a:b] using insertion sort.
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func insertionSortLessFunc[Elem any](data []Elem, a, b int, less func(a, b Elem) bool) {
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for i := a + 1; i < b; i++ {
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for j := i; j > a && less(data[j], data[j-1]); j-- {
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data[j], data[j-1] = data[j-1], data[j]
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}
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}
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}
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// siftDownLessFunc implements the heap property on data[lo:hi].
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// first is an offset into the array where the root of the heap lies.
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func siftDownLessFunc[Elem any](data []Elem, lo, hi, first int, less func(a, b Elem) bool) {
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root := lo
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for {
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child := 2*root + 1
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if child >= hi {
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break
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}
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if child+1 < hi && less(data[first+child], data[first+child+1]) {
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child++
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}
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if !less(data[first+root], data[first+child]) {
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return
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}
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data[first+root], data[first+child] = data[first+child], data[first+root]
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root = child
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}
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}
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func heapSortLessFunc[Elem any](data []Elem, a, b int, less func(a, b Elem) bool) {
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first := a
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lo := 0
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hi := b - a
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// Build heap with greatest element at top.
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for i := (hi - 1) / 2; i >= 0; i-- {
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siftDownLessFunc(data, i, hi, first, less)
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}
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// Pop elements, largest first, into end of data.
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for i := hi - 1; i >= 0; i-- {
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data[first], data[first+i] = data[first+i], data[first]
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siftDownLessFunc(data, lo, i, first, less)
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||||
}
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||||
}
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||||
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// Quicksort, loosely following Bentley and McIlroy,
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// "Engineering a Sort Function" SP&E November 1993.
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// medianOfThreeLessFunc moves the median of the three values data[m0], data[m1], data[m2] into data[m1].
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func medianOfThreeLessFunc[Elem any](data []Elem, m1, m0, m2 int, less func(a, b Elem) bool) {
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// sort 3 elements
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||||
if less(data[m1], data[m0]) {
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||||
data[m1], data[m0] = data[m0], data[m1]
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||||
}
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||||
// data[m0] <= data[m1]
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||||
if less(data[m2], data[m1]) {
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data[m2], data[m1] = data[m1], data[m2]
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||||
// data[m0] <= data[m2] && data[m1] < data[m2]
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||||
if less(data[m1], data[m0]) {
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||||
data[m1], data[m0] = data[m0], data[m1]
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||||
}
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||||
}
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||||
// now data[m0] <= data[m1] <= data[m2]
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||||
}
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||||
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||||
func swapRangeLessFunc[Elem any](data []Elem, a, b, n int, less func(a, b Elem) bool) {
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||||
for i := 0; i < n; i++ {
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||||
data[a+i], data[b+i] = data[b+i], data[a+i]
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||||
}
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||||
}
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||||
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func doPivotLessFunc[Elem any](data []Elem, lo, hi int, less func(a, b Elem) bool) (midlo, midhi int) {
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m := int(uint(lo+hi) >> 1) // Written like this to avoid integer overflow.
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||||
if hi-lo > 40 {
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||||
// Tukey's "Ninther" median of three medians of three.
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||||
s := (hi - lo) / 8
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medianOfThreeLessFunc(data, lo, lo+s, lo+2*s, less)
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||||
medianOfThreeLessFunc(data, m, m-s, m+s, less)
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||||
medianOfThreeLessFunc(data, hi-1, hi-1-s, hi-1-2*s, less)
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||||
}
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||||
medianOfThreeLessFunc(data, lo, m, hi-1, less)
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||||
// Invariants are:
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||||
// data[lo] = pivot (set up by ChoosePivot)
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||||
// data[lo < i < a] < pivot
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// data[a <= i < b] <= pivot
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||||
// data[b <= i < c] unexamined
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||||
// data[c <= i < hi-1] > pivot
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// data[hi-1] >= pivot
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pivot := lo
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||||
a, c := lo+1, hi-1
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||||
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||||
for ; a < c && less(data[a], data[pivot]); a++ {
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||||
}
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b := a
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for {
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for ; b < c && !less(data[pivot], data[b]); b++ { // data[b] <= pivot
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||||
}
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||||
for ; b < c && less(data[pivot], data[c-1]); c-- { // data[c-1] > pivot
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||||
}
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||||
if b >= c {
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||||
break
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||||
}
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||||
// data[b] > pivot; data[c-1] <= pivot
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||||
data[b], data[c-1] = data[c-1], data[b]
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||||
b++
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||||
c--
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||||
}
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||||
// If hi-c<3 then there are duplicates (by property of median of nine).
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||||
// Let's be a bit more conservative, and set border to 5.
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||||
protect := hi-c < 5
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||||
if !protect && hi-c < (hi-lo)/4 {
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||||
// Lets test some points for equality to pivot
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||||
dups := 0
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||||
if !less(data[pivot], data[hi-1]) { // data[hi-1] = pivot
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||||
data[c], data[hi-1] = data[hi-1], data[c]
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||||
c++
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||||
dups++
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||||
}
|
||||
if !less(data[b-1], data[pivot]) { // data[b-1] = pivot
|
||||
b--
|
||||
dups++
|
||||
}
|
||||
// m-lo = (hi-lo)/2 > 6
|
||||
// b-lo > (hi-lo)*3/4-1 > 8
|
||||
// ==> m < b ==> data[m] <= pivot
|
||||
if !less(data[m], data[pivot]) { // data[m] = pivot
|
||||
data[m], data[b-1] = data[b-1], data[m]
|
||||
b--
|
||||
dups++
|
||||
}
|
||||
// if at least 2 points are equal to pivot, assume skewed distribution
|
||||
protect = dups > 1
|
||||
}
|
||||
if protect {
|
||||
// Protect against a lot of duplicates
|
||||
// Add invariant:
|
||||
// data[a <= i < b] unexamined
|
||||
// data[b <= i < c] = pivot
|
||||
for {
|
||||
for ; a < b && !less(data[b-1], data[pivot]); b-- { // data[b] == pivot
|
||||
}
|
||||
for ; a < b && less(data[a], data[pivot]); a++ { // data[a] < pivot
|
||||
}
|
||||
if a >= b {
|
||||
break
|
||||
}
|
||||
// data[a] == pivot; data[b-1] < pivot
|
||||
data[a], data[b-1] = data[b-1], data[a]
|
||||
a++
|
||||
b--
|
||||
}
|
||||
}
|
||||
// Swap pivot into middle
|
||||
data[pivot], data[b-1] = data[b-1], data[pivot]
|
||||
return b - 1, c
|
||||
}
|
||||
|
||||
func quickSortLessFunc[Elem any](data []Elem, a, b, maxDepth int, less func(a, b Elem) bool) {
|
||||
for b-a > 12 { // Use ShellSort for slices <= 12 elements
|
||||
if maxDepth == 0 {
|
||||
heapSortLessFunc(data, a, b, less)
|
||||
return
|
||||
}
|
||||
maxDepth--
|
||||
mlo, mhi := doPivotLessFunc(data, a, b, less)
|
||||
// Avoiding recursion on the larger subproblem guarantees
|
||||
// a stack depth of at most lg(b-a).
|
||||
if mlo-a < b-mhi {
|
||||
quickSortLessFunc(data, a, mlo, maxDepth, less)
|
||||
a = mhi // i.e., quickSortLessFunc(data, mhi, b)
|
||||
} else {
|
||||
quickSortLessFunc(data, mhi, b, maxDepth, less)
|
||||
b = mlo // i.e., quickSortLessFunc(data, a, mlo)
|
||||
}
|
||||
}
|
||||
if b-a > 1 {
|
||||
// Do ShellSort pass with gap 6
|
||||
// It could be written in this simplified form cause b-a <= 12
|
||||
for i := a + 6; i < b; i++ {
|
||||
if less(data[i], data[i-6]) {
|
||||
data[i], data[i-6] = data[i-6], data[i]
|
||||
}
|
||||
}
|
||||
insertionSortLessFunc(data, a, b, less)
|
||||
}
|
||||
}
|
||||
|
||||
func stableLessFunc[Elem any](data []Elem, n int, less func(a, b Elem) bool) {
|
||||
blockSize := 20 // must be > 0
|
||||
a, b := 0, blockSize
|
||||
for b <= n {
|
||||
insertionSortLessFunc(data, a, b, less)
|
||||
a = b
|
||||
b += blockSize
|
||||
}
|
||||
insertionSortLessFunc(data, a, n, less)
|
||||
|
||||
for blockSize < n {
|
||||
a, b = 0, 2*blockSize
|
||||
for b <= n {
|
||||
symMergeLessFunc(data, a, a+blockSize, b, less)
|
||||
a = b
|
||||
b += 2 * blockSize
|
||||
}
|
||||
if m := a + blockSize; m < n {
|
||||
symMergeLessFunc(data, a, m, n, less)
|
||||
}
|
||||
blockSize *= 2
|
||||
}
|
||||
}
|
||||
|
||||
// symMergeLessFunc merges the two sorted subsequences data[a:m] and data[m:b] using
|
||||
// the SymMerge algorithm from Pok-Son Kim and Arne Kutzner, "Stable Minimum
|
||||
// Storage Merging by Symmetric Comparisons", in Susanne Albers and Tomasz
|
||||
// Radzik, editors, Algorithms - ESA 2004, volume 3221 of Lecture Notes in
|
||||
// Computer Science, pages 714-723. Springer, 2004.
|
||||
//
|
||||
// Let M = m-a and N = b-n. Wolog M < N.
|
||||
// The recursion depth is bound by ceil(log(N+M)).
|
||||
// The algorithm needs O(M*log(N/M + 1)) calls to data.Less.
|
||||
// The algorithm needs O((M+N)*log(M)) calls to data.Swap.
|
||||
//
|
||||
// The paper gives O((M+N)*log(M)) as the number of assignments assuming a
|
||||
// rotation algorithm which uses O(M+N+gcd(M+N)) assignments. The argumentation
|
||||
// in the paper carries through for Swap operations, especially as the block
|
||||
// swapping rotate uses only O(M+N) Swaps.
|
||||
//
|
||||
// symMerge assumes non-degenerate arguments: a < m && m < b.
|
||||
// Having the caller check this condition eliminates many leaf recursion calls,
|
||||
// which improves performance.
|
||||
func symMergeLessFunc[Elem any](data []Elem, a, m, b int, less func(a, b Elem) bool) {
|
||||
// Avoid unnecessary recursions of symMerge
|
||||
// by direct insertion of data[a] into data[m:b]
|
||||
// if data[a:m] only contains one element.
|
||||
if m-a == 1 {
|
||||
// Use binary search to find the lowest index i
|
||||
// such that data[i] >= data[a] for m <= i < b.
|
||||
// Exit the search loop with i == b in case no such index exists.
|
||||
i := m
|
||||
j := b
|
||||
for i < j {
|
||||
h := int(uint(i+j) >> 1)
|
||||
if less(data[h], data[a]) {
|
||||
i = h + 1
|
||||
} else {
|
||||
j = h
|
||||
}
|
||||
}
|
||||
// Swap values until data[a] reaches the position before i.
|
||||
for k := a; k < i-1; k++ {
|
||||
data[k], data[k+1] = data[k+1], data[k]
|
||||
}
|
||||
return
|
||||
}
|
||||
|
||||
// Avoid unnecessary recursions of symMerge
|
||||
// by direct insertion of data[m] into data[a:m]
|
||||
// if data[m:b] only contains one element.
|
||||
if b-m == 1 {
|
||||
// Use binary search to find the lowest index i
|
||||
// such that data[i] > data[m] for a <= i < m.
|
||||
// Exit the search loop with i == m in case no such index exists.
|
||||
i := a
|
||||
j := m
|
||||
for i < j {
|
||||
h := int(uint(i+j) >> 1)
|
||||
if !less(data[m], data[h]) {
|
||||
i = h + 1
|
||||
} else {
|
||||
j = h
|
||||
}
|
||||
}
|
||||
// Swap values until data[m] reaches the position i.
|
||||
for k := m; k > i; k-- {
|
||||
data[k], data[k-1] = data[k-1], data[k]
|
||||
}
|
||||
return
|
||||
}
|
||||
|
||||
mid := int(uint(a+b) >> 1)
|
||||
n := mid + m
|
||||
var start, r int
|
||||
if m > mid {
|
||||
start = n - b
|
||||
r = mid
|
||||
} else {
|
||||
start = a
|
||||
r = m
|
||||
}
|
||||
p := n - 1
|
||||
|
||||
for start < r {
|
||||
c := int(uint(start+r) >> 1)
|
||||
if !less(data[p-c], data[c]) {
|
||||
start = c + 1
|
||||
} else {
|
||||
r = c
|
||||
}
|
||||
}
|
||||
|
||||
end := n - start
|
||||
if start < m && m < end {
|
||||
rotateLessFunc(data, start, m, end, less)
|
||||
}
|
||||
if a < start && start < mid {
|
||||
symMergeLessFunc(data, a, start, mid, less)
|
||||
}
|
||||
if mid < end && end < b {
|
||||
symMergeLessFunc(data, mid, end, b, less)
|
||||
}
|
||||
}
|
||||
|
||||
// rotateLessFunc rotates two consecutive blocks u = data[a:m] and v = data[m:b] in data:
|
||||
// Data of the form 'x u v y' is changed to 'x v u y'.
|
||||
// rotate performs at most b-a many calls to data.Swap,
|
||||
// and it assumes non-degenerate arguments: a < m && m < b.
|
||||
func rotateLessFunc[Elem any](data []Elem, a, m, b int, less func(a, b Elem) bool) {
|
||||
i := m - a
|
||||
j := b - m
|
||||
|
||||
for i != j {
|
||||
if i > j {
|
||||
swapRangeLessFunc(data, m-i, m, j, less)
|
||||
i -= j
|
||||
} else {
|
||||
swapRangeLessFunc(data, m-i, m+j-i, i, less)
|
||||
j -= i
|
||||
}
|
||||
}
|
||||
// i == j
|
||||
swapRangeLessFunc(data, m-i, m, i, less)
|
||||
}
|
||||
344
vendor/golang.org/x/exp/slices/zsortordered.go
generated
vendored
Normal file
344
vendor/golang.org/x/exp/slices/zsortordered.go
generated
vendored
Normal file
|
|
@ -0,0 +1,344 @@
|
|||
// Code generated by gen_sort_variants.go; DO NOT EDIT.
|
||||
|
||||
// Copyright 2022 The Go Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
package slices
|
||||
|
||||
import "golang.org/x/exp/constraints"
|
||||
|
||||
// insertionSortOrdered sorts data[a:b] using insertion sort.
|
||||
func insertionSortOrdered[Elem constraints.Ordered](data []Elem, a, b int) {
|
||||
for i := a + 1; i < b; i++ {
|
||||
for j := i; j > a && (data[j] < data[j-1]); j-- {
|
||||
data[j], data[j-1] = data[j-1], data[j]
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// siftDownOrdered implements the heap property on data[lo:hi].
|
||||
// first is an offset into the array where the root of the heap lies.
|
||||
func siftDownOrdered[Elem constraints.Ordered](data []Elem, lo, hi, first int) {
|
||||
root := lo
|
||||
for {
|
||||
child := 2*root + 1
|
||||
if child >= hi {
|
||||
break
|
||||
}
|
||||
if child+1 < hi && (data[first+child] < data[first+child+1]) {
|
||||
child++
|
||||
}
|
||||
if !(data[first+root] < data[first+child]) {
|
||||
return
|
||||
}
|
||||
data[first+root], data[first+child] = data[first+child], data[first+root]
|
||||
root = child
|
||||
}
|
||||
}
|
||||
|
||||
func heapSortOrdered[Elem constraints.Ordered](data []Elem, a, b int) {
|
||||
first := a
|
||||
lo := 0
|
||||
hi := b - a
|
||||
|
||||
// Build heap with greatest element at top.
|
||||
for i := (hi - 1) / 2; i >= 0; i-- {
|
||||
siftDownOrdered(data, i, hi, first)
|
||||
}
|
||||
|
||||
// Pop elements, largest first, into end of data.
|
||||
for i := hi - 1; i >= 0; i-- {
|
||||
data[first], data[first+i] = data[first+i], data[first]
|
||||
siftDownOrdered(data, lo, i, first)
|
||||
}
|
||||
}
|
||||
|
||||
// Quicksort, loosely following Bentley and McIlroy,
|
||||
// "Engineering a Sort Function" SP&E November 1993.
|
||||
|
||||
// medianOfThreeOrdered moves the median of the three values data[m0], data[m1], data[m2] into data[m1].
|
||||
func medianOfThreeOrdered[Elem constraints.Ordered](data []Elem, m1, m0, m2 int) {
|
||||
// sort 3 elements
|
||||
if data[m1] < data[m0] {
|
||||
data[m1], data[m0] = data[m0], data[m1]
|
||||
}
|
||||
// data[m0] <= data[m1]
|
||||
if data[m2] < data[m1] {
|
||||
data[m2], data[m1] = data[m1], data[m2]
|
||||
// data[m0] <= data[m2] && data[m1] < data[m2]
|
||||
if data[m1] < data[m0] {
|
||||
data[m1], data[m0] = data[m0], data[m1]
|
||||
}
|
||||
}
|
||||
// now data[m0] <= data[m1] <= data[m2]
|
||||
}
|
||||
|
||||
func swapRangeOrdered[Elem constraints.Ordered](data []Elem, a, b, n int) {
|
||||
for i := 0; i < n; i++ {
|
||||
data[a+i], data[b+i] = data[b+i], data[a+i]
|
||||
}
|
||||
}
|
||||
|
||||
func doPivotOrdered[Elem constraints.Ordered](data []Elem, lo, hi int) (midlo, midhi int) {
|
||||
m := int(uint(lo+hi) >> 1) // Written like this to avoid integer overflow.
|
||||
if hi-lo > 40 {
|
||||
// Tukey's "Ninther" median of three medians of three.
|
||||
s := (hi - lo) / 8
|
||||
medianOfThreeOrdered(data, lo, lo+s, lo+2*s)
|
||||
medianOfThreeOrdered(data, m, m-s, m+s)
|
||||
medianOfThreeOrdered(data, hi-1, hi-1-s, hi-1-2*s)
|
||||
}
|
||||
medianOfThreeOrdered(data, lo, m, hi-1)
|
||||
|
||||
// Invariants are:
|
||||
// data[lo] = pivot (set up by ChoosePivot)
|
||||
// data[lo < i < a] < pivot
|
||||
// data[a <= i < b] <= pivot
|
||||
// data[b <= i < c] unexamined
|
||||
// data[c <= i < hi-1] > pivot
|
||||
// data[hi-1] >= pivot
|
||||
pivot := lo
|
||||
a, c := lo+1, hi-1
|
||||
|
||||
for ; a < c && (data[a] < data[pivot]); a++ {
|
||||
}
|
||||
b := a
|
||||
for {
|
||||
for ; b < c && !(data[pivot] < data[b]); b++ { // data[b] <= pivot
|
||||
}
|
||||
for ; b < c && (data[pivot] < data[c-1]); c-- { // data[c-1] > pivot
|
||||
}
|
||||
if b >= c {
|
||||
break
|
||||
}
|
||||
// data[b] > pivot; data[c-1] <= pivot
|
||||
data[b], data[c-1] = data[c-1], data[b]
|
||||
b++
|
||||
c--
|
||||
}
|
||||
// If hi-c<3 then there are duplicates (by property of median of nine).
|
||||
// Let's be a bit more conservative, and set border to 5.
|
||||
protect := hi-c < 5
|
||||
if !protect && hi-c < (hi-lo)/4 {
|
||||
// Lets test some points for equality to pivot
|
||||
dups := 0
|
||||
if !(data[pivot] < data[hi-1]) { // data[hi-1] = pivot
|
||||
data[c], data[hi-1] = data[hi-1], data[c]
|
||||
c++
|
||||
dups++
|
||||
}
|
||||
if !(data[b-1] < data[pivot]) { // data[b-1] = pivot
|
||||
b--
|
||||
dups++
|
||||
}
|
||||
// m-lo = (hi-lo)/2 > 6
|
||||
// b-lo > (hi-lo)*3/4-1 > 8
|
||||
// ==> m < b ==> data[m] <= pivot
|
||||
if !(data[m] < data[pivot]) { // data[m] = pivot
|
||||
data[m], data[b-1] = data[b-1], data[m]
|
||||
b--
|
||||
dups++
|
||||
}
|
||||
// if at least 2 points are equal to pivot, assume skewed distribution
|
||||
protect = dups > 1
|
||||
}
|
||||
if protect {
|
||||
// Protect against a lot of duplicates
|
||||
// Add invariant:
|
||||
// data[a <= i < b] unexamined
|
||||
// data[b <= i < c] = pivot
|
||||
for {
|
||||
for ; a < b && !(data[b-1] < data[pivot]); b-- { // data[b] == pivot
|
||||
}
|
||||
for ; a < b && (data[a] < data[pivot]); a++ { // data[a] < pivot
|
||||
}
|
||||
if a >= b {
|
||||
break
|
||||
}
|
||||
// data[a] == pivot; data[b-1] < pivot
|
||||
data[a], data[b-1] = data[b-1], data[a]
|
||||
a++
|
||||
b--
|
||||
}
|
||||
}
|
||||
// Swap pivot into middle
|
||||
data[pivot], data[b-1] = data[b-1], data[pivot]
|
||||
return b - 1, c
|
||||
}
|
||||
|
||||
func quickSortOrdered[Elem constraints.Ordered](data []Elem, a, b, maxDepth int) {
|
||||
for b-a > 12 { // Use ShellSort for slices <= 12 elements
|
||||
if maxDepth == 0 {
|
||||
heapSortOrdered(data, a, b)
|
||||
return
|
||||
}
|
||||
maxDepth--
|
||||
mlo, mhi := doPivotOrdered(data, a, b)
|
||||
// Avoiding recursion on the larger subproblem guarantees
|
||||
// a stack depth of at most lg(b-a).
|
||||
if mlo-a < b-mhi {
|
||||
quickSortOrdered(data, a, mlo, maxDepth)
|
||||
a = mhi // i.e., quickSortOrdered(data, mhi, b)
|
||||
} else {
|
||||
quickSortOrdered(data, mhi, b, maxDepth)
|
||||
b = mlo // i.e., quickSortOrdered(data, a, mlo)
|
||||
}
|
||||
}
|
||||
if b-a > 1 {
|
||||
// Do ShellSort pass with gap 6
|
||||
// It could be written in this simplified form cause b-a <= 12
|
||||
for i := a + 6; i < b; i++ {
|
||||
if data[i] < data[i-6] {
|
||||
data[i], data[i-6] = data[i-6], data[i]
|
||||
}
|
||||
}
|
||||
insertionSortOrdered(data, a, b)
|
||||
}
|
||||
}
|
||||
|
||||
func stableOrdered[Elem constraints.Ordered](data []Elem, n int) {
|
||||
blockSize := 20 // must be > 0
|
||||
a, b := 0, blockSize
|
||||
for b <= n {
|
||||
insertionSortOrdered(data, a, b)
|
||||
a = b
|
||||
b += blockSize
|
||||
}
|
||||
insertionSortOrdered(data, a, n)
|
||||
|
||||
for blockSize < n {
|
||||
a, b = 0, 2*blockSize
|
||||
for b <= n {
|
||||
symMergeOrdered(data, a, a+blockSize, b)
|
||||
a = b
|
||||
b += 2 * blockSize
|
||||
}
|
||||
if m := a + blockSize; m < n {
|
||||
symMergeOrdered(data, a, m, n)
|
||||
}
|
||||
blockSize *= 2
|
||||
}
|
||||
}
|
||||
|
||||
// symMergeOrdered merges the two sorted subsequences data[a:m] and data[m:b] using
|
||||
// the SymMerge algorithm from Pok-Son Kim and Arne Kutzner, "Stable Minimum
|
||||
// Storage Merging by Symmetric Comparisons", in Susanne Albers and Tomasz
|
||||
// Radzik, editors, Algorithms - ESA 2004, volume 3221 of Lecture Notes in
|
||||
// Computer Science, pages 714-723. Springer, 2004.
|
||||
//
|
||||
// Let M = m-a and N = b-n. Wolog M < N.
|
||||
// The recursion depth is bound by ceil(log(N+M)).
|
||||
// The algorithm needs O(M*log(N/M + 1)) calls to data.Less.
|
||||
// The algorithm needs O((M+N)*log(M)) calls to data.Swap.
|
||||
//
|
||||
// The paper gives O((M+N)*log(M)) as the number of assignments assuming a
|
||||
// rotation algorithm which uses O(M+N+gcd(M+N)) assignments. The argumentation
|
||||
// in the paper carries through for Swap operations, especially as the block
|
||||
// swapping rotate uses only O(M+N) Swaps.
|
||||
//
|
||||
// symMerge assumes non-degenerate arguments: a < m && m < b.
|
||||
// Having the caller check this condition eliminates many leaf recursion calls,
|
||||
// which improves performance.
|
||||
func symMergeOrdered[Elem constraints.Ordered](data []Elem, a, m, b int) {
|
||||
// Avoid unnecessary recursions of symMerge
|
||||
// by direct insertion of data[a] into data[m:b]
|
||||
// if data[a:m] only contains one element.
|
||||
if m-a == 1 {
|
||||
// Use binary search to find the lowest index i
|
||||
// such that data[i] >= data[a] for m <= i < b.
|
||||
// Exit the search loop with i == b in case no such index exists.
|
||||
i := m
|
||||
j := b
|
||||
for i < j {
|
||||
h := int(uint(i+j) >> 1)
|
||||
if data[h] < data[a] {
|
||||
i = h + 1
|
||||
} else {
|
||||
j = h
|
||||
}
|
||||
}
|
||||
// Swap values until data[a] reaches the position before i.
|
||||
for k := a; k < i-1; k++ {
|
||||
data[k], data[k+1] = data[k+1], data[k]
|
||||
}
|
||||
return
|
||||
}
|
||||
|
||||
// Avoid unnecessary recursions of symMerge
|
||||
// by direct insertion of data[m] into data[a:m]
|
||||
// if data[m:b] only contains one element.
|
||||
if b-m == 1 {
|
||||
// Use binary search to find the lowest index i
|
||||
// such that data[i] > data[m] for a <= i < m.
|
||||
// Exit the search loop with i == m in case no such index exists.
|
||||
i := a
|
||||
j := m
|
||||
for i < j {
|
||||
h := int(uint(i+j) >> 1)
|
||||
if !(data[m] < data[h]) {
|
||||
i = h + 1
|
||||
} else {
|
||||
j = h
|
||||
}
|
||||
}
|
||||
// Swap values until data[m] reaches the position i.
|
||||
for k := m; k > i; k-- {
|
||||
data[k], data[k-1] = data[k-1], data[k]
|
||||
}
|
||||
return
|
||||
}
|
||||
|
||||
mid := int(uint(a+b) >> 1)
|
||||
n := mid + m
|
||||
var start, r int
|
||||
if m > mid {
|
||||
start = n - b
|
||||
r = mid
|
||||
} else {
|
||||
start = a
|
||||
r = m
|
||||
}
|
||||
p := n - 1
|
||||
|
||||
for start < r {
|
||||
c := int(uint(start+r) >> 1)
|
||||
if !(data[p-c] < data[c]) {
|
||||
start = c + 1
|
||||
} else {
|
||||
r = c
|
||||
}
|
||||
}
|
||||
|
||||
end := n - start
|
||||
if start < m && m < end {
|
||||
rotateOrdered(data, start, m, end)
|
||||
}
|
||||
if a < start && start < mid {
|
||||
symMergeOrdered(data, a, start, mid)
|
||||
}
|
||||
if mid < end && end < b {
|
||||
symMergeOrdered(data, mid, end, b)
|
||||
}
|
||||
}
|
||||
|
||||
// rotateOrdered rotates two consecutive blocks u = data[a:m] and v = data[m:b] in data:
|
||||
// Data of the form 'x u v y' is changed to 'x v u y'.
|
||||
// rotate performs at most b-a many calls to data.Swap,
|
||||
// and it assumes non-degenerate arguments: a < m && m < b.
|
||||
func rotateOrdered[Elem constraints.Ordered](data []Elem, a, m, b int) {
|
||||
i := m - a
|
||||
j := b - m
|
||||
|
||||
for i != j {
|
||||
if i > j {
|
||||
swapRangeOrdered(data, m-i, m, j)
|
||||
i -= j
|
||||
} else {
|
||||
swapRangeOrdered(data, m-i, m+j-i, i)
|
||||
j -= i
|
||||
}
|
||||
}
|
||||
// i == j
|
||||
swapRangeOrdered(data, m-i, m, i)
|
||||
}
|
||||
Loading…
Add table
Add a link
Reference in a new issue