| // 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 ( |
| "math/bits" |
| |
| "golang.org/x/exp/constraints" |
| ) |
| |
| // Sort sorts a slice of any ordered type in ascending order. |
| // Sort may fail to sort correctly when sorting slices of floating-point |
| // numbers containing Not-a-number (NaN) values. |
| // Use slices.SortFunc(x, func(a, b float64) bool {return a < b || (math.IsNaN(a) && !math.IsNaN(b))}) |
| // instead if the input may contain NaNs. |
| func Sort[E constraints.Ordered](x []E) { |
| n := len(x) |
| pdqsortOrdered(x, 0, n, bits.Len(uint(n))) |
| } |
| |
| // SortFunc sorts the slice x in ascending order as determined by the less function. |
| // This sort is not guaranteed to be stable. |
| // |
| // SortFunc requires that less is a strict weak ordering. |
| // See https://en.wikipedia.org/wiki/Weak_ordering#Strict_weak_orderings. |
| func SortFunc[E any](x []E, less func(a, b E) bool) { |
| n := len(x) |
| pdqsortLessFunc(x, 0, n, bits.Len(uint(n)), less) |
| } |
| |
| // SortStableFunc sorts the slice x while keeping the original order of equal |
| // elements, using less to compare elements. |
| func SortStableFunc[E any](x []E, less func(a, b E) bool) { |
| stableLessFunc(x, len(x), less) |
| } |
| |
| // IsSorted reports whether x is sorted in ascending order. |
| func IsSorted[E constraints.Ordered](x []E) bool { |
| for i := len(x) - 1; i > 0; i-- { |
| if x[i] < x[i-1] { |
| return false |
| } |
| } |
| return true |
| } |
| |
| // IsSortedFunc reports whether x is sorted in ascending order, with less as the |
| // comparison function. |
| func IsSortedFunc[E any](x []E, less func(a, b E) bool) bool { |
| for i := len(x) - 1; i > 0; i-- { |
| if less(x[i], x[i-1]) { |
| return false |
| } |
| } |
| return true |
| } |
| |
| // 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[E constraints.Ordered](x []E, 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 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 |
| } |
| |
| // 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(a, b) is expected to return an integer comparing the two |
| // parameters: 0 if a == b, a negative number if a < b and a positive number if |
| // a > b. |
| func BinarySearchFunc[E, T any](x []E, 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)) |
| } |