sort

package standard library
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Published: Jan 10, 2023 License: BSD-3-Clause Imports: 1 Imported by: 0

Documentation

Overview

Package sort provides primitives for sorting slices and user-defined collections.

Example
package main

import (
	"fmt"
	"sort"
)

type Person struct {
	Name string
	Age  int
}

func (p Person) String() string {
	return fmt.Sprintf("%s: %d", p.Name, p.Age)
}

// ByAge implements sort.Interface for []Person based on
// the Age field.
type ByAge []Person

func (a ByAge) Len() int           { return len(a) }
func (a ByAge) Swap(i, j int)      { a[i], a[j] = a[j], a[i] }
func (a ByAge) Less(i, j int) bool { return a[i].Age < a[j].Age }

func main() {
	people := []Person{
		{"Bob", 31},
		{"John", 42},
		{"Michael", 17},
		{"Jenny", 26},
	}

	fmt.Println(people)
	// There are two ways to sort a slice. First, one can define
	// a set of methods for the slice type, as with ByAge, and
	// call sort.Sort. In this first example we use that technique.
	sort.Sort(ByAge(people))
	fmt.Println(people)

	// The other way is to use sort.Slice with a custom Less
	// function, which can be provided as a closure. In this
	// case no methods are needed. (And if they exist, they
	// are ignored.) Here we re-sort in reverse order: compare
	// the closure with ByAge.Less.
	sort.Slice(people, func(i, j int) bool {
		return people[i].Age > people[j].Age
	})
	fmt.Println(people)

}
Output:

[Bob: 31 John: 42 Michael: 17 Jenny: 26]
[Michael: 17 Jenny: 26 Bob: 31 John: 42]
[John: 42 Bob: 31 Jenny: 26 Michael: 17]
Example (SortKeys)

ExampleSortKeys demonstrates a technique for sorting a struct type using programmable sort criteria.

package main

import (
	"fmt"
	"sort"
)

// A couple of type definitions to make the units clear.
type earthMass float64
type au float64

// A Planet defines the properties of a solar system object.
type Planet struct {
	name     string
	mass     earthMass
	distance au
}

// By is the type of a "less" function that defines the ordering of its Planet arguments.
type By func(p1, p2 *Planet) bool

// Sort is a method on the function type, By, that sorts the argument slice according to the function.
func (by By) Sort(planets []Planet) {
	ps := &planetSorter{
		planets: planets,
		by:      by, // The Sort method's receiver is the function (closure) that defines the sort order.
	}
	sort.Sort(ps)
}

// planetSorter joins a By function and a slice of Planets to be sorted.
type planetSorter struct {
	planets []Planet
	by      func(p1, p2 *Planet) bool // Closure used in the Less method.
}

// Len is part of sort.Interface.
func (s *planetSorter) Len() int {
	return len(s.planets)
}

// Swap is part of sort.Interface.
func (s *planetSorter) Swap(i, j int) {
	s.planets[i], s.planets[j] = s.planets[j], s.planets[i]
}

// Less is part of sort.Interface. It is implemented by calling the "by" closure in the sorter.
func (s *planetSorter) Less(i, j int) bool {
	return s.by(&s.planets[i], &s.planets[j])
}

var planets = []Planet{
	{"Mercury", 0.055, 0.4},
	{"Venus", 0.815, 0.7},
	{"Earth", 1.0, 1.0},
	{"Mars", 0.107, 1.5},
}

// ExampleSortKeys demonstrates a technique for sorting a struct type using programmable sort criteria.
func main() {
	// Closures that order the Planet structure.
	name := func(p1, p2 *Planet) bool {
		return p1.name < p2.name
	}
	mass := func(p1, p2 *Planet) bool {
		return p1.mass < p2.mass
	}
	distance := func(p1, p2 *Planet) bool {
		return p1.distance < p2.distance
	}
	decreasingDistance := func(p1, p2 *Planet) bool {
		return distance(p2, p1)
	}

	// Sort the planets by the various criteria.
	By(name).Sort(planets)
	fmt.Println("By name:", planets)

	By(mass).Sort(planets)
	fmt.Println("By mass:", planets)

	By(distance).Sort(planets)
	fmt.Println("By distance:", planets)

	By(decreasingDistance).Sort(planets)
	fmt.Println("By decreasing distance:", planets)

}
Output:

By name: [{Earth 1 1} {Mars 0.107 1.5} {Mercury 0.055 0.4} {Venus 0.815 0.7}]
By mass: [{Mercury 0.055 0.4} {Mars 0.107 1.5} {Venus 0.815 0.7} {Earth 1 1}]
By distance: [{Mercury 0.055 0.4} {Venus 0.815 0.7} {Earth 1 1} {Mars 0.107 1.5}]
By decreasing distance: [{Mars 0.107 1.5} {Earth 1 1} {Venus 0.815 0.7} {Mercury 0.055 0.4}]
Example (SortMultiKeys)

ExampleMultiKeys demonstrates a technique for sorting a struct type using different sets of multiple fields in the comparison. We chain together "Less" functions, each of which compares a single field.

package main

import (
	"fmt"
	"sort"
)

// A Change is a record of source code changes, recording user, language, and delta size.
type Change struct {
	user     string
	language string
	lines    int
}

type lessFunc func(p1, p2 *Change) bool

// multiSorter implements the Sort interface, sorting the changes within.
type multiSorter struct {
	changes []Change
	less    []lessFunc
}

// Sort sorts the argument slice according to the less functions passed to OrderedBy.
func (ms *multiSorter) Sort(changes []Change) {
	ms.changes = changes
	sort.Sort(ms)
}

// OrderedBy returns a Sorter that sorts using the less functions, in order.
// Call its Sort method to sort the data.
func OrderedBy(less ...lessFunc) *multiSorter {
	return &multiSorter{
		less: less,
	}
}

// Len is part of sort.Interface.
func (ms *multiSorter) Len() int {
	return len(ms.changes)
}

// Swap is part of sort.Interface.
func (ms *multiSorter) Swap(i, j int) {
	ms.changes[i], ms.changes[j] = ms.changes[j], ms.changes[i]
}

// Less is part of sort.Interface. It is implemented by looping along the
// less functions until it finds a comparison that discriminates between
// the two items (one is less than the other). Note that it can call the
// less functions twice per call. We could change the functions to return
// -1, 0, 1 and reduce the number of calls for greater efficiency: an
// exercise for the reader.
func (ms *multiSorter) Less(i, j int) bool {
	p, q := &ms.changes[i], &ms.changes[j]
	// Try all but the last comparison.
	var k int
	for k = 0; k < len(ms.less)-1; k++ {
		less := ms.less[k]
		switch {
		case less(p, q):
			// p < q, so we have a decision.
			return true
		case less(q, p):
			// p > q, so we have a decision.
			return false
		}
		// p == q; try the next comparison.
	}
	// All comparisons to here said "equal", so just return whatever
	// the final comparison reports.
	return ms.less[k](p, q)
}

var changes = []Change{
	{"gri", "Go", 100},
	{"ken", "C", 150},
	{"glenda", "Go", 200},
	{"rsc", "Go", 200},
	{"r", "Go", 100},
	{"ken", "Go", 200},
	{"dmr", "C", 100},
	{"r", "C", 150},
	{"gri", "Smalltalk", 80},
}

// ExampleMultiKeys demonstrates a technique for sorting a struct type using different
// sets of multiple fields in the comparison. We chain together "Less" functions, each of
// which compares a single field.
func main() {
	// Closures that order the Change structure.
	user := func(c1, c2 *Change) bool {
		return c1.user < c2.user
	}
	language := func(c1, c2 *Change) bool {
		return c1.language < c2.language
	}
	increasingLines := func(c1, c2 *Change) bool {
		return c1.lines < c2.lines
	}
	decreasingLines := func(c1, c2 *Change) bool {
		return c1.lines > c2.lines // Note: > orders downwards.
	}

	// Simple use: Sort by user.
	OrderedBy(user).Sort(changes)
	fmt.Println("By user:", changes)

	// More examples.
	OrderedBy(user, increasingLines).Sort(changes)
	fmt.Println("By user,<lines:", changes)

	OrderedBy(user, decreasingLines).Sort(changes)
	fmt.Println("By user,>lines:", changes)

	OrderedBy(language, increasingLines).Sort(changes)
	fmt.Println("By language,<lines:", changes)

	OrderedBy(language, increasingLines, user).Sort(changes)
	fmt.Println("By language,<lines,user:", changes)

}
Output:

By user: [{dmr C 100} {glenda Go 200} {gri Go 100} {gri Smalltalk 80} {ken C 150} {ken Go 200} {r Go 100} {r C 150} {rsc Go 200}]
By user,<lines: [{dmr C 100} {glenda Go 200} {gri Smalltalk 80} {gri Go 100} {ken C 150} {ken Go 200} {r Go 100} {r C 150} {rsc Go 200}]
By user,>lines: [{dmr C 100} {glenda Go 200} {gri Go 100} {gri Smalltalk 80} {ken Go 200} {ken C 150} {r C 150} {r Go 100} {rsc Go 200}]
By language,<lines: [{dmr C 100} {ken C 150} {r C 150} {r Go 100} {gri Go 100} {ken Go 200} {glenda Go 200} {rsc Go 200} {gri Smalltalk 80}]
By language,<lines,user: [{dmr C 100} {ken C 150} {r C 150} {gri Go 100} {r Go 100} {glenda Go 200} {ken Go 200} {rsc Go 200} {gri Smalltalk 80}]
Example (SortWrapper)
package main

import (
	"fmt"
	"sort"
)

type Grams int

func (g Grams) String() string { return fmt.Sprintf("%dg", int(g)) }

type Organ struct {
	Name   string
	Weight Grams
}

type Organs []*Organ

func (s Organs) Len() int      { return len(s) }
func (s Organs) Swap(i, j int) { s[i], s[j] = s[j], s[i] }

// ByName implements sort.Interface by providing Less and using the Len and
// Swap methods of the embedded Organs value.
type ByName struct{ Organs }

func (s ByName) Less(i, j int) bool { return s.Organs[i].Name < s.Organs[j].Name }

// ByWeight implements sort.Interface by providing Less and using the Len and
// Swap methods of the embedded Organs value.
type ByWeight struct{ Organs }

func (s ByWeight) Less(i, j int) bool { return s.Organs[i].Weight < s.Organs[j].Weight }

func main() {
	s := []*Organ{
		{"brain", 1340},
		{"heart", 290},
		{"liver", 1494},
		{"pancreas", 131},
		{"prostate", 62},
		{"spleen", 162},
	}

	sort.Sort(ByWeight{s})
	fmt.Println("Organs by weight:")
	printOrgans(s)

	sort.Sort(ByName{s})
	fmt.Println("Organs by name:")
	printOrgans(s)

}

func printOrgans(s []*Organ) {
	for _, o := range s {
		fmt.Printf("%-8s (%v)\n", o.Name, o.Weight)
	}
}
Output:

Organs by weight:
prostate (62g)
pancreas (131g)
spleen   (162g)
heart    (290g)
brain    (1340g)
liver    (1494g)
Organs by name:
brain    (1340g)
heart    (290g)
liver    (1494g)
pancreas (131g)
prostate (62g)
spleen   (162g)

Index

Examples

Constants

This section is empty.

Variables

This section is empty.

Functions

func Float64s

func Float64s(x []float64)

Float64s sorts a slice of float64s in increasing order. Not-a-number (NaN) values are ordered before other values.

Example
package main

import (
	"fmt"
	"math"
	"sort"
)

func main() {
	s := []float64{5.2, -1.3, 0.7, -3.8, 2.6} // unsorted
	sort.Float64s(s)
	fmt.Println(s)

	s = []float64{math.Inf(1), math.NaN(), math.Inf(-1), 0.0} // unsorted
	sort.Float64s(s)
	fmt.Println(s)

}
Output:

[-3.8 -1.3 0.7 2.6 5.2]
[NaN -Inf 0 +Inf]

func Float64sAreSorted

func Float64sAreSorted(x []float64) bool

Float64sAreSorted reports whether the slice x is sorted in increasing order, with not-a-number (NaN) values before any other values.

Example
package main

import (
	"fmt"
	"sort"
)

func main() {
	s := []float64{0.7, 1.3, 2.6, 3.8, 5.2} // sorted ascending
	fmt.Println(sort.Float64sAreSorted(s))

	s = []float64{5.2, 3.8, 2.6, 1.3, 0.7} // sorted descending
	fmt.Println(sort.Float64sAreSorted(s))

	s = []float64{5.2, 1.3, 0.7, 3.8, 2.6} // unsorted
	fmt.Println(sort.Float64sAreSorted(s))

}
Output:

true
false
false

func Ints

func Ints(x []int)

Ints sorts a slice of ints in increasing order.

Example
package main

import (
	"fmt"
	"sort"
)

func main() {
	s := []int{5, 2, 6, 3, 1, 4} // unsorted
	sort.Ints(s)
	fmt.Println(s)
}
Output:

[1 2 3 4 5 6]

func IntsAreSorted

func IntsAreSorted(x []int) bool

IntsAreSorted reports whether the slice x is sorted in increasing order.

Example
package main

import (
	"fmt"
	"sort"
)

func main() {
	s := []int{1, 2, 3, 4, 5, 6} // sorted ascending
	fmt.Println(sort.IntsAreSorted(s))

	s = []int{6, 5, 4, 3, 2, 1} // sorted descending
	fmt.Println(sort.IntsAreSorted(s))

	s = []int{3, 2, 4, 1, 5} // unsorted
	fmt.Println(sort.IntsAreSorted(s))

}
Output:

true
false
false

func IsSorted

func IsSorted(data Interface) bool

IsSorted reports whether data is sorted.

func Search(n int, f func(int) bool) int

Search uses binary search to find and return the smallest index i in [0, n) at which f(i) is true, assuming that on the range [0, n), f(i) == true implies f(i+1) == true. That is, Search requires that f is false for some (possibly empty) prefix of the input range [0, n) and then true for the (possibly empty) remainder; Search returns the first true index. If there is no such index, Search returns n. (Note that the "not found" return value is not -1 as in, for instance, strings.Index.) Search calls f(i) only for i in the range [0, n).

A common use of Search is to find the index i for a value x in a sorted, indexable data structure such as an array or slice. In this case, the argument f, typically a closure, captures the value to be searched for, and how the data structure is indexed and ordered.

For instance, given a slice data sorted in ascending order, the call Search(len(data), func(i int) bool { return data[i] >= 23 }) returns the smallest index i such that data[i] >= 23. If the caller wants to find whether 23 is in the slice, it must test data[i] == 23 separately.

Searching data sorted in descending order would use the <= operator instead of the >= operator.

To complete the example above, the following code tries to find the value x in an integer slice data sorted in ascending order:

x := 23
i := sort.Search(len(data), func(i int) bool { return data[i] >= x })
if i < len(data) && data[i] == x {
	// x is present at data[i]
} else {
	// x is not present in data,
	// but i is the index where it would be inserted.
}

As a more whimsical example, this program guesses your number:

func GuessingGame() {
	var s string
	fmt.Printf("Pick an integer from 0 to 100.\n")
	answer := sort.Search(100, func(i int) bool {
		fmt.Printf("Is your number <= %d? ", i)
		fmt.Scanf("%s", &s)
		return s != "" && s[0] == 'y'
	})
	fmt.Printf("Your number is %d.\n", answer)
}
Example (DescendingOrder)

This example demonstrates searching a list sorted in descending order. The approach is the same as searching a list in ascending order, but with the condition inverted.

package main

import (
	"fmt"
	"sort"
)

func main() {
	a := []int{55, 45, 36, 28, 21, 15, 10, 6, 3, 1}
	x := 6

	i := sort.Search(len(a), func(i int) bool { return a[i] <= x })
	if i < len(a) && a[i] == x {
		fmt.Printf("found %d at index %d in %v\n", x, i, a)
	} else {
		fmt.Printf("%d not found in %v\n", x, a)
	}
}
Output:

found 6 at index 7 in [55 45 36 28 21 15 10 6 3 1]

func SearchFloat64s

func SearchFloat64s(a []float64, x float64) int

SearchFloat64s searches for x in a sorted slice of float64s and returns the index as specified by Search. The return value is the index to insert x if x is not present (it could be len(a)). The slice must be sorted in ascending order.

Example

This example demonstrates searching for float64 in a list sorted in ascending order.

package main

import (
	"fmt"
	"sort"
)

func main() {
	a := []float64{1.0, 2.0, 3.3, 4.6, 6.1, 7.2, 8.0}

	x := 2.0
	i := sort.SearchFloat64s(a, x)
	fmt.Printf("found %g at index %d in %v\n", x, i, a)

	x = 0.5
	i = sort.SearchFloat64s(a, x)
	fmt.Printf("%g not found, can be inserted at index %d in %v\n", x, i, a)
}
Output:

found 2 at index 1 in [1 2 3.3 4.6 6.1 7.2 8]
0.5 not found, can be inserted at index 0 in [1 2 3.3 4.6 6.1 7.2 8]

func SearchInts

func SearchInts(a []int, x int) int

SearchInts searches for x in a sorted slice of ints and returns the index as specified by Search. The return value is the index to insert x if x is not present (it could be len(a)). The slice must be sorted in ascending order.

Example

This example demonstrates searching for int in a list sorted in ascending order.

package main

import (
	"fmt"
	"sort"
)

func main() {
	a := []int{1, 2, 3, 4, 6, 7, 8}

	x := 2
	i := sort.SearchInts(a, x)
	fmt.Printf("found %d at index %d in %v\n", x, i, a)

	x = 5
	i = sort.SearchInts(a, x)
	fmt.Printf("%d not found, can be inserted at index %d in %v\n", x, i, a)
}
Output:

found 2 at index 1 in [1 2 3 4 6 7 8]
5 not found, can be inserted at index 4 in [1 2 3 4 6 7 8]

func SearchStrings

func SearchStrings(a []string, x string) int

SearchStrings searches for x in a sorted slice of strings and returns the index as specified by Search. The return value is the index to insert x if x is not present (it could be len(a)). The slice must be sorted in ascending order.

func Slice

func Slice(x any, less func(i, j int) bool)

Slice sorts the slice x given the provided less function. It panics if x is not a slice.

The sort is not guaranteed to be stable: equal elements may be reversed from their original order. For a stable sort, use SliceStable.

The less function must satisfy the same requirements as the Interface type's Less method.

Example
package main

import (
	"fmt"
	"sort"
)

func main() {
	people := []struct {
		Name string
		Age  int
	}{
		{"Gopher", 7},
		{"Alice", 55},
		{"Vera", 24},
		{"Bob", 75},
	}
	sort.Slice(people, func(i, j int) bool { return people[i].Name < people[j].Name })
	fmt.Println("By name:", people)

	sort.Slice(people, func(i, j int) bool { return people[i].Age < people[j].Age })
	fmt.Println("By age:", people)
}
Output:

By name: [{Alice 55} {Bob 75} {Gopher 7} {Vera 24}]
By age: [{Gopher 7} {Vera 24} {Alice 55} {Bob 75}]

func SliceIsSorted

func SliceIsSorted(x any, less func(i, j int) bool) bool

SliceIsSorted reports whether the slice x is sorted according to the provided less function. It panics if x is not a slice.

func SliceStable

func SliceStable(x any, less func(i, j int) bool)

SliceStable sorts the slice x using the provided less function, keeping equal elements in their original order. It panics if x is not a slice.

The less function must satisfy the same requirements as the Interface type's Less method.

Example
package main

import (
	"fmt"
	"sort"
)

func main() {

	people := []struct {
		Name string
		Age  int
	}{
		{"Alice", 25},
		{"Elizabeth", 75},
		{"Alice", 75},
		{"Bob", 75},
		{"Alice", 75},
		{"Bob", 25},
		{"Colin", 25},
		{"Elizabeth", 25},
	}

	// Sort by name, preserving original order
	sort.SliceStable(people, func(i, j int) bool { return people[i].Name < people[j].Name })
	fmt.Println("By name:", people)

	// Sort by age preserving name order
	sort.SliceStable(people, func(i, j int) bool { return people[i].Age < people[j].Age })
	fmt.Println("By age,name:", people)

}
Output:

By name: [{Alice 25} {Alice 75} {Alice 75} {Bob 75} {Bob 25} {Colin 25} {Elizabeth 75} {Elizabeth 25}]
By age,name: [{Alice 25} {Bob 25} {Colin 25} {Elizabeth 25} {Alice 75} {Alice 75} {Bob 75} {Elizabeth 75}]

func Sort

func Sort(data Interface)

Sort sorts data in ascending order as determined by the Less method. It makes one call to data.Len to determine n and O(n*log(n)) calls to data.Less and data.Swap. The sort is not guaranteed to be stable.

func Stable

func Stable(data Interface)

Stable sorts data in ascending order as determined by the Less method, while keeping the original order of equal elements.

It makes one call to data.Len to determine n, O(n*log(n)) calls to data.Less and O(n*log(n)*log(n)) calls to data.Swap.

func Strings

func Strings(x []string)

Strings sorts a slice of strings in increasing order.

Example
package main

import (
	"fmt"
	"sort"
)

func main() {
	s := []string{"Go", "Bravo", "Gopher", "Alpha", "Grin", "Delta"}
	sort.Strings(s)
	fmt.Println(s)
}
Output:

[Alpha Bravo Delta Go Gopher Grin]

func StringsAreSorted

func StringsAreSorted(x []string) bool

StringsAreSorted reports whether the slice x is sorted in increasing order.

Types

type Float64Slice

type Float64Slice []float64

Float64Slice implements Interface for a []float64, sorting in increasing order, with not-a-number (NaN) values ordered before other values.

func (Float64Slice) Len

func (x Float64Slice) Len() int

func (Float64Slice) Less

func (x Float64Slice) Less(i, j int) bool

Less reports whether x[i] should be ordered before x[j], as required by the sort Interface. Note that floating-point comparison by itself is not a transitive relation: it does not report a consistent ordering for not-a-number (NaN) values. This implementation of Less places NaN values before any others, by using:

x[i] < x[j] || (math.IsNaN(x[i]) && !math.IsNaN(x[j]))

func (Float64Slice) Search

func (p Float64Slice) Search(x float64) int

Search returns the result of applying SearchFloat64s to the receiver and x.

func (Float64Slice) Sort

func (x Float64Slice) Sort()

Sort is a convenience method: x.Sort() calls Sort(x).

func (Float64Slice) Swap

func (x Float64Slice) Swap(i, j int)

type IntSlice

type IntSlice []int

IntSlice attaches the methods of Interface to []int, sorting in increasing order.

func (IntSlice) Len

func (x IntSlice) Len() int

func (IntSlice) Less

func (x IntSlice) Less(i, j int) bool

func (IntSlice) Search

func (p IntSlice) Search(x int) int

Search returns the result of applying SearchInts to the receiver and x.

func (IntSlice) Sort

func (x IntSlice) Sort()

Sort is a convenience method: x.Sort() calls Sort(x).

func (IntSlice) Swap

func (x IntSlice) Swap(i, j int)

type Interface

type Interface interface {
	// Len is the number of elements in the collection.
	Len() int

	// Less reports whether the element with index i
	// must sort before the element with index j.
	//
	// If both Less(i, j) and Less(j, i) are false,
	// then the elements at index i and j are considered equal.
	// Sort may place equal elements in any order in the final result,
	// while Stable preserves the original input order of equal elements.
	//
	// Less must describe a transitive ordering:
	//  - if both Less(i, j) and Less(j, k) are true, then Less(i, k) must be true as well.
	//  - if both Less(i, j) and Less(j, k) are false, then Less(i, k) must be false as well.
	//
	// Note that floating-point comparison (the < operator on float32 or float64 values)
	// is not a transitive ordering when not-a-number (NaN) values are involved.
	// See Float64Slice.Less for a correct implementation for floating-point values.
	Less(i, j int) bool

	// Swap swaps the elements with indexes i and j.
	Swap(i, j int)
}

An implementation of Interface can be sorted by the routines in this package. The methods refer to elements of the underlying collection by integer index.

func Reverse

func Reverse(data Interface) Interface

Reverse returns the reverse order for data.

Example
package main

import (
	"fmt"
	"sort"
)

func main() {
	s := []int{5, 2, 6, 3, 1, 4} // unsorted
	sort.Sort(sort.Reverse(sort.IntSlice(s)))
	fmt.Println(s)
}
Output:

[6 5 4 3 2 1]

type StringSlice

type StringSlice []string

StringSlice attaches the methods of Interface to []string, sorting in increasing order.

func (StringSlice) Len

func (x StringSlice) Len() int

func (StringSlice) Less

func (x StringSlice) Less(i, j int) bool

func (StringSlice) Search

func (p StringSlice) Search(x string) int

Search returns the result of applying SearchStrings to the receiver and x.

func (StringSlice) Sort

func (x StringSlice) Sort()

Sort is a convenience method: x.Sort() calls Sort(x).

func (StringSlice) Swap

func (x StringSlice) Swap(i, j int)

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