slices/zsortordered.go

// 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)
}