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 // 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. //go:generate go run \$GOROOT/src/sort/gen_sort_variants.go -exp package slices import ( "math/bits" "golang.org/x/exp/constraints" ) // 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 constraints.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. // // SortFunc requires that cmp is a strict weak ordering. // See https://en.wikipedia.org/wiki/Weak_ordering#Strict_weak_orderings. 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 constraints.Ordered](x S) bool { for i := len(x) - 1; i > 0; i-- { if cmpLess(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 constraints.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 constraints.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 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 constraints.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 cmpLess(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 >> 17 *r ^= *r << 5 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 constraints.Ordered](x T) bool { return x != x }