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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<

                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)) }