mirror of
https://github.com/autc04/Retro68.git
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258 lines
6.5 KiB
Go
258 lines
6.5 KiB
Go
// Copyright 2009 The Go Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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// Package sort provides primitives for sorting slices and user-defined
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// collections.
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package sort
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import "math"
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// A type, typically a collection, that satisfies sort.Interface can be
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// sorted by the routines in this package. The methods require that the
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// elements of the collection be enumerated by an integer index.
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type Interface interface {
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// Len is the number of elements in the collection.
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Len() int
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// Less returns whether the element with index i should sort
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// before the element with index j.
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Less(i, j int) bool
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// Swap swaps the elements with indexes i and j.
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Swap(i, j int)
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}
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func min(a, b int) int {
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if a < b {
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return a
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}
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return b
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}
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// Insertion sort
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func insertionSort(data Interface, a, b int) {
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for i := a + 1; i < b; i++ {
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for j := i; j > a && data.Less(j, j-1); j-- {
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data.Swap(j, j-1)
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}
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}
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}
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// siftDown implements the heap property on data[lo, hi).
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// first is an offset into the array where the root of the heap lies.
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func siftDown(data Interface, lo, hi, first int) {
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root := lo
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for {
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child := 2*root + 1
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if child >= hi {
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break
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}
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if child+1 < hi && data.Less(first+child, first+child+1) {
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child++
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}
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if !data.Less(first+root, first+child) {
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return
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}
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data.Swap(first+root, first+child)
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root = child
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}
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}
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func heapSort(data Interface, a, b int) {
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first := a
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lo := 0
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hi := b - a
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// Build heap with greatest element at top.
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for i := (hi - 1) / 2; i >= 0; i-- {
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siftDown(data, i, hi, first)
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}
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// Pop elements, largest first, into end of data.
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for i := hi - 1; i >= 0; i-- {
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data.Swap(first, first+i)
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siftDown(data, lo, i, first)
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}
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}
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// Quicksort, following Bentley and McIlroy,
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// ``Engineering a Sort Function,'' SP&E November 1993.
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// medianOfThree moves the median of the three values data[a], data[b], data[c] into data[a].
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func medianOfThree(data Interface, a, b, c int) {
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m0 := b
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m1 := a
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m2 := c
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// bubble sort on 3 elements
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if data.Less(m1, m0) {
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data.Swap(m1, m0)
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}
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if data.Less(m2, m1) {
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data.Swap(m2, m1)
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}
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if data.Less(m1, m0) {
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data.Swap(m1, m0)
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}
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// now data[m0] <= data[m1] <= data[m2]
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}
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func swapRange(data Interface, a, b, n int) {
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for i := 0; i < n; i++ {
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data.Swap(a+i, b+i)
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}
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}
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func doPivot(data Interface, lo, hi int) (midlo, midhi int) {
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m := lo + (hi-lo)/2 // Written like this to avoid integer overflow.
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if hi-lo > 40 {
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// Tukey's ``Ninther,'' median of three medians of three.
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s := (hi - lo) / 8
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medianOfThree(data, lo, lo+s, lo+2*s)
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medianOfThree(data, m, m-s, m+s)
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medianOfThree(data, hi-1, hi-1-s, hi-1-2*s)
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}
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medianOfThree(data, lo, m, hi-1)
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// Invariants are:
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// data[lo] = pivot (set up by ChoosePivot)
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// data[lo <= i < a] = pivot
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// data[a <= i < b] < pivot
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// data[b <= i < c] is unexamined
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// data[c <= i < d] > pivot
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// data[d <= i < hi] = pivot
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//
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// Once b meets c, can swap the "= pivot" sections
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// into the middle of the slice.
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pivot := lo
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a, b, c, d := lo+1, lo+1, hi, hi
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for b < c {
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if data.Less(b, pivot) { // data[b] < pivot
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b++
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continue
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}
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if !data.Less(pivot, b) { // data[b] = pivot
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data.Swap(a, b)
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a++
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b++
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continue
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}
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if data.Less(pivot, c-1) { // data[c-1] > pivot
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c--
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continue
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}
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if !data.Less(c-1, pivot) { // data[c-1] = pivot
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data.Swap(c-1, d-1)
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c--
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d--
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continue
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}
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// data[b] > pivot; data[c-1] < pivot
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data.Swap(b, c-1)
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b++
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c--
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}
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n := min(b-a, a-lo)
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swapRange(data, lo, b-n, n)
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n = min(hi-d, d-c)
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swapRange(data, c, hi-n, n)
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return lo + b - a, hi - (d - c)
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}
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func quickSort(data Interface, a, b, maxDepth int) {
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for b-a > 7 {
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if maxDepth == 0 {
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heapSort(data, a, b)
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return
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}
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maxDepth--
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mlo, mhi := doPivot(data, a, b)
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// Avoiding recursion on the larger subproblem guarantees
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// a stack depth of at most lg(b-a).
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if mlo-a < b-mhi {
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quickSort(data, a, mlo, maxDepth)
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a = mhi // i.e., quickSort(data, mhi, b)
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} else {
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quickSort(data, mhi, b, maxDepth)
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b = mlo // i.e., quickSort(data, a, mlo)
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}
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}
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if b-a > 1 {
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insertionSort(data, a, b)
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}
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}
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func Sort(data Interface) {
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// Switch to heapsort if depth of 2*ceil(lg(n)) is reached.
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n := data.Len()
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maxDepth := 0
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for 1<<uint(maxDepth) < n {
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maxDepth++
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}
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maxDepth *= 2
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quickSort(data, 0, n, maxDepth)
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}
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func IsSorted(data Interface) bool {
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n := data.Len()
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for i := n - 1; i > 0; i-- {
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if data.Less(i, i-1) {
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return false
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}
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}
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return true
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}
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// Convenience types for common cases
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// IntSlice attaches the methods of Interface to []int, sorting in increasing order.
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type IntSlice []int
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func (p IntSlice) Len() int { return len(p) }
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func (p IntSlice) Less(i, j int) bool { return p[i] < p[j] }
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func (p IntSlice) Swap(i, j int) { p[i], p[j] = p[j], p[i] }
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// Sort is a convenience method.
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func (p IntSlice) Sort() { Sort(p) }
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// Float64Slice attaches the methods of Interface to []float64, sorting in increasing order.
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type Float64Slice []float64
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func (p Float64Slice) Len() int { return len(p) }
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func (p Float64Slice) Less(i, j int) bool { return p[i] < p[j] || math.IsNaN(p[i]) && !math.IsNaN(p[j]) }
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func (p Float64Slice) Swap(i, j int) { p[i], p[j] = p[j], p[i] }
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// Sort is a convenience method.
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func (p Float64Slice) Sort() { Sort(p) }
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// StringSlice attaches the methods of Interface to []string, sorting in increasing order.
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type StringSlice []string
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func (p StringSlice) Len() int { return len(p) }
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func (p StringSlice) Less(i, j int) bool { return p[i] < p[j] }
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func (p StringSlice) Swap(i, j int) { p[i], p[j] = p[j], p[i] }
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// Sort is a convenience method.
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func (p StringSlice) Sort() { Sort(p) }
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// Convenience wrappers for common cases
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// Ints sorts a slice of ints in increasing order.
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func Ints(a []int) { Sort(IntSlice(a)) }
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// Float64s sorts a slice of float64s in increasing order.
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func Float64s(a []float64) { Sort(Float64Slice(a)) }
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// Strings sorts a slice of strings in increasing order.
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func Strings(a []string) { Sort(StringSlice(a)) }
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// IntsAreSorted tests whether a slice of ints is sorted in increasing order.
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func IntsAreSorted(a []int) bool { return IsSorted(IntSlice(a)) }
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// Float64sAreSorted tests whether a slice of float64s is sorted in increasing order.
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func Float64sAreSorted(a []float64) bool { return IsSorted(Float64Slice(a)) }
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// StringsAreSorted tests whether a slice of strings is sorted in increasing order.
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func StringsAreSorted(a []string) bool { return IsSorted(StringSlice(a)) }
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