go/src/slices/sort.go

// Copyright 2023 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.

//go:generate go run $GOROOT/src/sort/gen_sort_variants.go -generic

package slices

import (
	"cmp"
	"math/bits"
)

// Sort sorts a slice of any ordered type in ascending order.
// When sorting floating-point numbers, NaNs are ordered before other values.
func Sort[S ~[]E, E cmp.Ordered](x S) {
	n := len(x)
	pdqsortOrdered(x, 0, n, bits.Len(uint(n)))
}

// SortFunc sorts the slice x in ascending order as determined by the cmp
// function. This sort is not guaranteed to be stable.
// cmp(a, b) should return a negative number when a < b, a positive number when
// a > b and zero when a == b or a and b are incomparable in the sense of
// a strict weak ordering.
//
// SortFunc requires that cmp is a strict weak ordering.
// See https://en.wikipedia.org/wiki/Weak_ordering#Strict_weak_orderings.
// The function should return 0 for incomparable items.
func SortFunc[S ~[]E, E any](x S, cmp func(a, b E) int) {
	n := len(x)
	pdqsortCmpFunc(x, 0, n, bits.Len(uint(n)), cmp)
}

// SortStableFunc sorts the slice x while keeping the original order of equal
// elements, using cmp to compare elements in the same way as [SortFunc].
func SortStableFunc[S ~[]E, E any](x S, cmp func(a, b E) int) {
	stableCmpFunc(x, len(x), cmp)
}

// IsSorted reports whether x is sorted in ascending order.
func IsSorted[S ~[]E, E cmp.Ordered](x S) bool {
	for i := len(x) - 1; i > 0; i-- {
		if cmp.Less(x[i], x[i-1]) {
			return false
		}
	}
	return true
}

// IsSortedFunc reports whether x is sorted in ascending order, with cmp as the
// comparison function as defined by [SortFunc].
func IsSortedFunc[S ~[]E, E any](x S, cmp func(a, b E) int) bool {
	for i := len(x) - 1; i > 0; i-- {
		if cmp(x[i], x[i-1]) < 0 {
			return false
		}
	}
	return true
}

// Min returns the minimal value in x. It panics if x is empty.
// For floating-point numbers, Min propagates NaNs (any NaN value in x
// forces the output to be NaN).
func Min[S ~[]E, E cmp.Ordered](x S) E {
	if len(x) < 1 {
		panic("slices.Min: empty list")
	}
	m := x[0]
	for i := 1; i < len(x); i++ {
		m = min(m, x[i])
	}
	return m
}

// MinFunc returns the minimal value in x, using cmp to compare elements.
// It panics if x is empty. If there is more than one minimal element
// according to the cmp function, MinFunc returns the first one.
func MinFunc[S ~[]E, E any](x S, cmp func(a, b E) int) E {
	if len(x) < 1 {
		panic("slices.MinFunc: empty list")
	}
	m := x[0]
	for i := 1; i < len(x); i++ {
		if cmp(x[i], m) < 0 {
			m = x[i]
		}
	}
	return m
}

// Max returns the maximal value in x. It panics if x is empty.
// For floating-point E, Max propagates NaNs (any NaN value in x
// forces the output to be NaN).
func Max[S ~[]E, E cmp.Ordered](x S) E {
	if len(x) < 1 {
		panic("slices.Max: empty list")
	}
	m := x[0]
	for i := 1; i < len(x); i++ {
		m = max(m, x[i])
	}
	return m
}

// MaxFunc returns the maximal value in x, using cmp to compare elements.
// It panics if x is empty. If there is more than one maximal element
// according to the cmp function, MaxFunc returns the first one.
func MaxFunc[S ~[]E, E any](x S, cmp func(a, b E) int) E {
	if len(x) < 1 {
		panic("slices.MaxFunc: empty list")
	}
	m := x[0]
	for i := 1; i < len(x); i++ {
		if cmp(x[i], m) > 0 {
			m = x[i]
		}
	}
	return m
}

// BinarySearch searches for target in a sorted slice and returns the earliest
// position where target is found, or the position where target would appear
// in the sort order; it also returns a bool saying whether the target is
// really found in the slice. The slice must be sorted in increasing order.
func BinarySearch[S ~[]E, E cmp.Ordered](x S, target E) (int, bool) {
	// Inlining is faster than calling BinarySearchFunc with a lambda.
	n := len(x)
	// Define x[-1] < target and x[n] >= target.
	// Invariant: x[i-1] < target, x[j] >= target.
	i, j := 0, n
	for i < j {
		h := int(uint(i+j) >> 1) // avoid overflow when computing h
		// i ≤ h < j
		if cmp.Less(x[h], target) {
			i = h + 1 // preserves x[i-1] < target
		} else {
			j = h // preserves x[j] >= target
		}
	}
	// i == j, x[i-1] < target, and x[j] (= x[i]) >= target  =>  answer is i.
	return i, i < n && (x[i] == target || (isNaN(x[i]) && isNaN(target)))
}

// BinarySearchFunc works like [BinarySearch], but uses a custom comparison
// function. The slice must be sorted in increasing order, where "increasing"
// is defined by cmp. cmp should return 0 if the slice element matches
// the target, a negative number if the slice element precedes the target,
// or a positive number if the slice element follows the target.
// cmp must implement the same ordering as the slice, such that if
// cmp(a, t) < 0 and cmp(b, t) >= 0, then a must precede b in the slice.
func BinarySearchFunc[S ~[]E, E, T any](x S, target T, cmp func(E, T) int) (int, bool) {
	n := len(x)
	// Define cmp(x[-1], target) < 0 and cmp(x[n], target) >= 0 .
	// Invariant: cmp(x[i - 1], target) < 0, cmp(x[j], target) >= 0.
	i, j := 0, n
	for i < j {
		h := int(uint(i+j) >> 1) // avoid overflow when computing h
		// i ≤ h < j
		if cmp(x[h], target) < 0 {
			i = h + 1 // preserves cmp(x[i - 1], target) < 0
		} else {
			j = h // preserves cmp(x[j], target) >= 0
		}
	}
	// i == j, cmp(x[i-1], target) < 0, and cmp(x[j], target) (= cmp(x[i], target)) >= 0  =>  answer is i.
	return i, i < n && cmp(x[i], target) == 0
}

type sortedHint int // hint for pdqsort when choosing the pivot

const (
	unknownHint sortedHint = iota
	increasingHint
	decreasingHint
)

// xorshift paper: https://www.jstatsoft.org/article/view/v008i14/xorshift.pdf
type xorshift uint64

func (r *xorshift) Next() uint64 {
	*r ^= *r << 13
	*r ^= *r >> 7
	*r ^= *r << 17
	return uint64(*r)
}

func nextPowerOfTwo(length int) uint {
	return 1 << bits.Len(uint(length))
}

// isNaN reports whether x is a NaN without requiring the math package.
// This will always return false if T is not floating-point.
func isNaN[T cmp.Ordered](x T) bool {
	return x != x
}