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 // 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 // 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] } 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 // SortInts sorts a slice of ints in increasing order. func SortInts(a []int) { Sort(IntSlice(a)) } // SortFloat64s sorts a slice of float64s in increasing order. func SortFloat64s(a []float64) { Sort(Float64Slice(a)) } // SortStrings sorts a slice of strings in increasing order. func SortStrings(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)) }