| // Copyright 2009 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 sort provides primitives for sorting slices and user-defined |
| // collections. |
| package sort |
| |
| import "math" |
| |
| // A type, typically a collection, that satisfies sort.Interface can be |
| // sorted by the routines in this package. The methods require that the |
| // elements of the collection be enumerated by an integer index. |
| type Interface interface { |
| // Len is the number of elements in the collection. |
| Len() int |
| // Less returns whether the element with index i should sort |
| // before the element with index j. |
| Less(i, j int) bool |
| // Swap swaps the elements with indexes i and j. |
| Swap(i, j int) |
| } |
| |
| func min(a, b int) int { |
| if a < b { |
| return a |
| } |
| return b |
| } |
| |
| // Insertion sort |
| func insertionSort(data Interface, a, b int) { |
| for i := a + 1; i < b; i++ { |
| for j := i; j > a && data.Less(j, j-1); j-- { |
| data.Swap(j, j-1) |
| } |
| } |
| } |
| |
| // Quicksort, following Bentley and McIlroy, |
| // ``Engineering a Sort Function,'' SP&E November 1993. |
| |
| // Move the median of the three values data[a], data[b], data[c] into data[a]. |
| func medianOfThree(data Interface, a, b, c int) { |
| m0 := b |
| m1 := a |
| m2 := c |
| // bubble sort on 3 elements |
| if data.Less(m1, m0) { |
| data.Swap(m1, m0) |
| } |
| if data.Less(m2, m1) { |
| data.Swap(m2, m1) |
| } |
| if data.Less(m1, m0) { |
| data.Swap(m1, m0) |
| } |
| // now data[m0] <= data[m1] <= data[m2] |
| } |
| |
| func swapRange(data Interface, a, b, n int) { |
| for i := 0; i < n; i++ { |
| data.Swap(a+i, b+i) |
| } |
| } |
| |
| func doPivot(data Interface, lo, hi int) (midlo, midhi int) { |
| m := lo + (hi-lo)/2 // Written like this to avoid integer overflow. |
| if hi-lo > 40 { |
| // Tukey's ``Ninther,'' median of three medians of three. |
| s := (hi - lo) / 8 |
| medianOfThree(data, lo, lo+s, lo+2*s) |
| medianOfThree(data, m, m-s, m+s) |
| medianOfThree(data, hi-1, hi-1-s, hi-1-2*s) |
| } |
| medianOfThree(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] is unexamined |
| // data[c <= i < d] > pivot |
| // data[d <= i < hi] = pivot |
| // |
| // Once b meets c, can swap the "= pivot" sections |
| // into the middle of the slice. |
| pivot := lo |
| a, b, c, d := lo+1, lo+1, hi, hi |
| for b < c { |
| if data.Less(b, pivot) { // data[b] < pivot |
| b++ |
| continue |
| } |
| if !data.Less(pivot, b) { // data[b] = pivot |
| data.Swap(a, b) |
| a++ |
| b++ |
| continue |
| } |
| if data.Less(pivot, c-1) { // data[c-1] > pivot |
| c-- |
| continue |
| } |
| if !data.Less(c-1, pivot) { // data[c-1] = pivot |
| data.Swap(c-1, d-1) |
| c-- |
| d-- |
| continue |
| } |
| // data[b] > pivot; data[c-1] < pivot |
| data.Swap(b, c-1) |
| b++ |
| c-- |
| } |
| |
| n := min(b-a, a-lo) |
| swapRange(data, lo, b-n, n) |
| |
| n = min(hi-d, d-c) |
| swapRange(data, c, hi-n, n) |
| |
| return lo + b - a, hi - (d - c) |
| } |
| |
| func quickSort(data Interface, a, b int) { |
| for b-a > 7 { |
| mlo, mhi := doPivot(data, a, b) |
| // Avoiding recursion on the larger subproblem guarantees |
| // a stack depth of at most lg(b-a). |
| if mlo-a < b-mhi { |
| quickSort(data, a, mlo) |
| a = mhi // i.e., quickSort(data, mhi, b) |
| } else { |
| quickSort(data, mhi, b) |
| b = mlo // i.e., quickSort(data, a, mlo) |
| } |
| } |
| if b-a > 1 { |
| insertionSort(data, a, b) |
| } |
| } |
| |
| func Sort(data Interface) { quickSort(data, 0, data.Len()) } |
| |
| func IsSorted(data Interface) bool { |
| n := data.Len() |
| for i := n - 1; i > 0; i-- { |
| if data.Less(i, i-1) { |
| return false |
| } |
| } |
| return true |
| } |
| |
| // Convenience types for common cases |
| |
| // IntSlice attaches the methods of Interface to []int, sorting in increasing order. |
| type IntSlice []int |
| |
| func (p IntSlice) Len() int { return len(p) } |
| func (p IntSlice) Less(i, j int) bool { return p[i] < p[j] } |
| func (p IntSlice) Swap(i, j int) { p[i], p[j] = p[j], p[i] } |
| |
| // Sort is a convenience method. |
| func (p IntSlice) Sort() { Sort(p) } |
| |
| // Float64Slice attaches the methods of Interface to []float64, sorting in increasing order. |
| type Float64Slice []float64 |
| |
| func (p Float64Slice) Len() int { return len(p) } |
| func (p Float64Slice) Less(i, j int) bool { return p[i] < p[j] || math.IsNaN(p[i]) && !math.IsNaN(p[j]) } |
| func (p Float64Slice) Swap(i, j int) { p[i], p[j] = p[j], p[i] } |
| |
| // Sort is a convenience method. |
| func (p Float64Slice) Sort() { Sort(p) } |
| |
| // StringSlice attaches the methods of Interface to []string, sorting in increasing order. |
| type StringSlice []string |
| |
| func (p StringSlice) Len() int { return len(p) } |
| func (p StringSlice) Less(i, j int) bool { return p[i] < p[j] } |
| func (p StringSlice) Swap(i, j int) { p[i], p[j] = p[j], p[i] } |
| |
| // Sort is a convenience method. |
| func (p StringSlice) Sort() { Sort(p) } |
| |
| // Convenience wrappers for common cases |
| |
| // Ints sorts a slice of ints in increasing order. |
| func Ints(a []int) { Sort(IntSlice(a)) } |
| // Float64s sorts a slice of float64s in increasing order. |
| func Float64s(a []float64) { Sort(Float64Slice(a)) } |
| // Strings sorts a slice of strings in increasing order. |
| func Strings(a []string) { Sort(StringSlice(a)) } |
| |
| // IntsAreSorted tests whether a slice of ints is sorted in increasing order. |
| func IntsAreSorted(a []int) bool { return IsSorted(IntSlice(a)) } |
| // Float64sAreSorted tests whether a slice of float64s is sorted in increasing order. |
| func Float64sAreSorted(a []float64) bool { return IsSorted(Float64Slice(a)) } |
| // StringsAreSorted tests whether a slice of strings is sorted in increasing order. |
| func StringsAreSorted(a []string) bool { return IsSorted(StringSlice(a)) } |