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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

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)
                }
        }
}

// siftDown implements the heap property on data[lo, hi).
// first is an offset into the array where the root of the heap lies.
func siftDown(data Interface, lo, hi, first int) {
        root := lo
        for {
                child := 2*root + 1
                if child >= hi {
                        break
                }
                if child+1 < hi && data.Less(first+child, first+child+1) {
                        child++
                }
                if !data.Less(first+root, first+child) {
                        return
                }
                data.Swap(first+root, first+child)
                root = child
        }
}

func heapSort(data Interface, a, b int) {
        first := a
        lo := 0
        hi := b - a

        // Build heap with greatest element at top.
        for i := (hi - 1) / 2; i >= 0; i-- {
                siftDown(data, i, hi, first)
        }

        // Pop elements, largest first, into end of data.
        for i := hi - 1; i >= 0; i-- {
                data.Swap(first, first+i)
                siftDown(data, lo, i, first)
        }
}

// Quicksort, following Bentley and McIlroy,
// ``Engineering a Sort Function,'' SP&E November 1993.

// medianOfThree moves 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, maxDepth int) {
        for b-a > 7 {
                if maxDepth == 0 {
                        heapSort(data, a, b)
                        return
                }
                maxDepth--
                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, maxDepth)
                        a = mhi // i.e., quickSort(data, mhi, b)
                } else {
                        quickSort(data, mhi, b, maxDepth)
                        b = mlo // i.e., quickSort(data, a, mlo)
                }
        }
        if b-a > 1 {
                insertionSort(data, a, b)
        }
}

func Sort(data Interface) {
        // Switch to heapsort if depth of 2*ceil(lg(n)) is reached.
        n := data.Len()
        maxDepth := 0
        for 1<<uint(maxDepth) < n {
                maxDepth++
        }
        maxDepth *= 2
        quickSort(data, 0, n, maxDepth)
}

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)) }