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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.
+
+// The sort package provides primitives for sorting arrays
+// 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 array.
+ 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
+
+// IntArray attaches the methods of Interface to []int, sorting in increasing order.
+type IntArray []int
+
+func (p IntArray) Len() int { return len(p) }
+func (p IntArray) Less(i, j int) bool { return p[i] < p[j] }
+func (p IntArray) Swap(i, j int) { p[i], p[j] = p[j], p[i] }
+
+// Sort is a convenience method.
+func (p IntArray) Sort() { Sort(p) }
+
+
+// Float64Array attaches the methods of Interface to []float64, sorting in increasing order.
+type Float64Array []float64
+
+func (p Float64Array) Len() int { return len(p) }
+func (p Float64Array) Less(i, j int) bool { return p[i] < p[j] }
+func (p Float64Array) Swap(i, j int) { p[i], p[j] = p[j], p[i] }
+
+// Sort is a convenience method.
+func (p Float64Array) Sort() { Sort(p) }
+
+
+// StringArray attaches the methods of Interface to []string, sorting in increasing order.
+type StringArray []string
+
+func (p StringArray) Len() int { return len(p) }
+func (p StringArray) Less(i, j int) bool { return p[i] < p[j] }
+func (p StringArray) Swap(i, j int) { p[i], p[j] = p[j], p[i] }
+
+// Sort is a convenience method.
+func (p StringArray) Sort() { Sort(p) }
+
+
+// Convenience wrappers for common cases
+
+// SortInts sorts an array of ints in increasing order.
+func SortInts(a []int) { Sort(IntArray(a)) }
+// SortFloat64s sorts an array of float64s in increasing order.
+func SortFloat64s(a []float64) { Sort(Float64Array(a)) }
+// SortStrings sorts an array of strings in increasing order.
+func SortStrings(a []string) { Sort(StringArray(a)) }
+
+
+// IntsAreSorted tests whether an array of ints is sorted in increasing order.
+func IntsAreSorted(a []int) bool { return IsSorted(IntArray(a)) }
+// Float64sAreSorted tests whether an array of float64s is sorted in increasing order.
+func Float64sAreSorted(a []float64) bool { return IsSorted(Float64Array(a)) }
+// StringsAreSorted tests whether an array of strings is sorted in increasing order.
+func StringsAreSorted(a []string) bool { return IsSorted(StringArray(a)) }