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// Copyright ©2019 The Gonum 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 combin_test
import (
"fmt"
"gonum.org/v1/gonum/stat/combin"
)
func ExampleCartesian() {
fmt.Println("Generate Cartesian products for given lengths:")
lens := []int{1, 2, 3}
list := combin.Cartesian(lens)
for i, v := range list {
fmt.Println(i, v)
}
// This is easy, but the number of combinations can be very large,
// and generating all at once can use a lot of memory.
// For big data sets, consider using CartesianGenerator instead.
// Output:
// Generate Cartesian products for given lengths:
// 0 [0 0 0]
// 1 [0 0 1]
// 2 [0 0 2]
// 3 [0 1 0]
// 4 [0 1 1]
// 5 [0 1 2]
}
func ExampleCartesianGenerator() {
fmt.Println("Generate products for given lengths:")
lens := []int{1, 2, 3}
gen := combin.NewCartesianGenerator(lens)
// Now loop over all products.
var i int
for gen.Next() {
fmt.Println(i, gen.Product(nil))
i++
}
// Output:
// Generate products for given lengths:
// 0 [0 0 0]
// 1 [0 0 1]
// 2 [0 0 2]
// 3 [0 1 0]
// 4 [0 1 1]
// 5 [0 1 2]
}
func ExampleCombinations() {
// combin provides several ways to work with the combinations of
// different objects. Combinations generates them directly.
fmt.Println("Generate list:")
n := 5
k := 3
list := combin.Combinations(n, k)
for i, v := range list {
fmt.Println(i, v)
}
// This is easy, but the number of combinations can be very large,
// and generating all at once can use a lot of memory.
// Output:
// Generate list:
// 0 [0 1 2]
// 1 [0 1 3]
// 2 [0 1 4]
// 3 [0 2 3]
// 4 [0 2 4]
// 5 [0 3 4]
// 6 [1 2 3]
// 7 [1 2 4]
// 8 [1 3 4]
// 9 [2 3 4]
}
func ExampleCombinations_index() {
// The integer slices returned from Combinations can be used to index
// into a data structure.
data := []string{"a", "b", "c", "d", "e"}
cs := combin.Combinations(len(data), 2)
for _, c := range cs {
fmt.Printf("%s%s\n", data[c[0]], data[c[1]])
}
// Output:
// ab
// ac
// ad
// ae
// bc
// bd
// be
// cd
// ce
// de
}
func ExampleCombinationGenerator() {
// combin provides several ways to work with the combinations of
// different objects. CombinationGenerator constructs an iterator
// for the combinations.
n := 5
k := 3
gen := combin.NewCombinationGenerator(n, k)
idx := 0
for gen.Next() {
fmt.Println(idx, gen.Combination(nil)) // can also store in-place.
idx++
}
// Output:
// 0 [0 1 2]
// 1 [0 1 3]
// 2 [0 1 4]
// 3 [0 2 3]
// 4 [0 2 4]
// 5 [0 3 4]
// 6 [1 2 3]
// 7 [1 2 4]
// 8 [1 3 4]
// 9 [2 3 4]
}
func ExampleIndexToCombination() {
// combin provides several ways to work with the combinations of
// different objects. IndexToCombination allows random access into
// the combination order. Combined with CombinationIndex this
// provides a correspondence between integers and combinations.
n := 5
k := 3
comb := make([]int, k)
for i := 0; i < combin.Binomial(n, k); i++ {
combin.IndexToCombination(comb, i, n, k) // can also use nil.
idx := combin.CombinationIndex(comb, n, k)
fmt.Println(i, comb, idx)
}
// Output:
// 0 [0 1 2] 0
// 1 [0 1 3] 1
// 2 [0 1 4] 2
// 3 [0 2 3] 3
// 4 [0 2 4] 4
// 5 [0 3 4] 5
// 6 [1 2 3] 6
// 7 [1 2 4] 7
// 8 [1 3 4] 8
// 9 [2 3 4] 9
}
func ExamplePermutations() {
// combin provides several ways to work with the permutations of
// different objects. Permutations generates them directly.
fmt.Println("Generate list:")
n := 4
k := 3
list := combin.Permutations(n, k)
for i, v := range list {
fmt.Println(i, v)
}
// This is easy, but the number of permutations can be very large,
// and generating all at once can use a lot of memory.
// Output:
// Generate list:
// 0 [0 1 2]
// 1 [0 2 1]
// 2 [1 0 2]
// 3 [1 2 0]
// 4 [2 0 1]
// 5 [2 1 0]
// 6 [0 1 3]
// 7 [0 3 1]
// 8 [1 0 3]
// 9 [1 3 0]
// 10 [3 0 1]
// 11 [3 1 0]
// 12 [0 2 3]
// 13 [0 3 2]
// 14 [2 0 3]
// 15 [2 3 0]
// 16 [3 0 2]
// 17 [3 2 0]
// 18 [1 2 3]
// 19 [1 3 2]
// 20 [2 1 3]
// 21 [2 3 1]
// 22 [3 1 2]
// 23 [3 2 1]
}
func ExamplePermutations_index() {
// The integer slices returned from Permutations can be used to index
// into a data structure.
data := []string{"a", "b", "c", "d"}
cs := combin.Permutations(len(data), 2)
for _, c := range cs {
fmt.Printf("%s%s\n", data[c[0]], data[c[1]])
}
// Output:
// ab
// ba
// ac
// ca
// ad
// da
// bc
// cb
// bd
// db
// cd
// dc
}
func ExamplePermutationGenerator() {
// combin provides several ways to work with the permutations of
// different objects. PermutationGenerator constructs an iterator
// for the permutations.
n := 4
k := 3
gen := combin.NewPermutationGenerator(n, k)
idx := 0
for gen.Next() {
fmt.Println(idx, gen.Permutation(nil)) // can also store in-place.
idx++
}
// Output:
// 0 [0 1 2]
// 1 [0 2 1]
// 2 [1 0 2]
// 3 [1 2 0]
// 4 [2 0 1]
// 5 [2 1 0]
// 6 [0 1 3]
// 7 [0 3 1]
// 8 [1 0 3]
// 9 [1 3 0]
// 10 [3 0 1]
// 11 [3 1 0]
// 12 [0 2 3]
// 13 [0 3 2]
// 14 [2 0 3]
// 15 [2 3 0]
// 16 [3 0 2]
// 17 [3 2 0]
// 18 [1 2 3]
// 19 [1 3 2]
// 20 [2 1 3]
// 21 [2 3 1]
// 22 [3 1 2]
// 23 [3 2 1]
}
func ExampleIndexToPermutation() {
// combin provides several ways to work with the permutations of
// different objects. IndexToPermutation allows random access into
// the permutation order. Combined with PermutationIndex this
// provides a correspondence between integers and permutations.
n := 4
k := 3
comb := make([]int, k)
for i := 0; i < combin.NumPermutations(n, k); i++ {
combin.IndexToPermutation(comb, i, n, k) // can also use nil.
idx := combin.PermutationIndex(comb, n, k)
fmt.Println(i, comb, idx)
}
// Output:
// 0 [0 1 2] 0
// 1 [0 2 1] 1
// 2 [1 0 2] 2
// 3 [1 2 0] 3
// 4 [2 0 1] 4
// 5 [2 1 0] 5
// 6 [0 1 3] 6
// 7 [0 3 1] 7
// 8 [1 0 3] 8
// 9 [1 3 0] 9
// 10 [3 0 1] 10
// 11 [3 1 0] 11
// 12 [0 2 3] 12
// 13 [0 3 2] 13
// 14 [2 0 3] 14
// 15 [2 3 0] 15
// 16 [3 0 2] 16
// 17 [3 2 0] 17
// 18 [1 2 3] 18
// 19 [1 3 2] 19
// 20 [2 1 3] 20
// 21 [2 3 1] 21
// 22 [3 1 2] 22
// 23 [3 2 1] 23
}
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