stat: imported stat as a subtree

stat/combin/combin.go

@@ -0,0 +1,183 @@
+// Copyright ©2016 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 implements routines involving combinatorics (permutations,
+// combinations, etc.).
+package combin
+
+import "math"
+
+const (
+	badNegInput = "combin: negative input"
+	badSetSize  = "combin: n < k"
+	badInput    = "combin: wrong input slice length"
+)
+
+// Binomial returns the binomial coefficient of (n,k), also commonly referred to
+// as "n choose k".
+//
+// The binomial coefficient, C(n,k), is the number of unordered combinations of
+// k elements in a set that is n elements big, and is defined as
+//
+//  C(n,k) = n!/((n-k)!k!)
+//
+// n and k must be non-negative with n >= k, otherwise Binomial will panic.
+// No check is made for overflow.
+func Binomial(n, k int) int {
+	if n < 0 || k < 0 {
+		panic(badNegInput)
+	}
+	if n < k {
+		panic(badSetSize)
+	}
+	// (n,k) = (n, n-k)
+	if k > n/2 {
+		k = n - k
+	}
+	b := 1
+	for i := 1; i <= k; i++ {
+		b = (n - k + i) * b / i
+	}
+	return b
+}
+
+// GeneralizedBinomial returns the generalized binomial coefficient of (n, k),
+// defined as
+//  Γ(n+1) / (Γ(k+1) Γ(n-k+1))
+// where Γ is the Gamma function. GeneralizedBinomial is useful for continuous
+// relaxations of the binomial coefficient, or when the binomial coefficient value
+// may overflow int. In the latter case, one may use math/big for an exact
+// computation.
+//
+// n and k must be non-negative with n >= k, otherwise GeneralizedBinomial will panic.
+func GeneralizedBinomial(n, k float64) float64 {
+	return math.Exp(LogGeneralizedBinomial(n, k))
+}
+
+// LogGeneralizedBinomial returns the log of the generalized binomial coefficient.
+// See GeneralizedBinomial for more information.
+func LogGeneralizedBinomial(n, k float64) float64 {
+	if n < 0 || k < 0 {
+		panic(badNegInput)
+	}
+	if n < k {
+		panic(badSetSize)
+	}
+	a, _ := math.Lgamma(n + 1)
+	b, _ := math.Lgamma(k + 1)
+	c, _ := math.Lgamma(n - k + 1)
+	return a - b - c
+}
+
+// CombinationGenerator generates combinations iteratively. Combinations may be
+// called to generate all combinations collectively.
+type CombinationGenerator struct {
+	n         int
+	k         int
+	previous  []int
+	remaining int
+}
+
+// NewCombinationGenerator returns a CombinationGenerator for generating the
+// combinations of k elements from a set of size n.
+//
+// n and k must be non-negative with n >= k, otherwise NewCombinationGenerator
+// will panic.
+func NewCombinationGenerator(n, k int) *CombinationGenerator {
+	return &CombinationGenerator{
+		n:         n,
+		k:         k,
+		remaining: Binomial(n, k),
+	}
+}
+
+// Next advances the iterator if there are combinations remaining to be generated,
+// and returns false if all combinations have been generated. Next must be called
+// to initialize the first value before calling Combination or Combination will
+// panic. The value returned by Combination is only changed during calls to Next.
+func (c *CombinationGenerator) Next() bool {
+	if c.remaining <= 0 {
+		// Next is called before combination, so c.remaining is set to zero before
+		// Combination is called. Thus, Combination cannot panic on zero, and a
+		// second sentinel value is needed.
+		c.remaining = -1
+		return false
+	}
+	if c.previous == nil {
+		c.previous = make([]int, c.k)
+		for i := range c.previous {
+			c.previous[i] = i
+		}
+	} else {
+		nextCombination(c.previous, c.n, c.k)
+	}
+	c.remaining--
+	return true
+}
+
+// Combination generates the next combination. If next is non-nil, it must have
+// length k and the result will be stored in-place into combination. If combination
+// is nil a new slice will be allocated and returned. If all of the combinations
+// have already been constructed (Next() returns false), Combination will panic.
+//
+// Next must be called to initialize the first value before calling Combination
+// or Combination will panic. The value returned by Combination is only changed
+// during calls to Next.
+func (c *CombinationGenerator) Combination(combination []int) []int {
+	if c.remaining == -1 {
+		panic("combin: all combinations have been generated")
+	}
+	if c.previous == nil {
+		panic("combin: Combination called before Next")
+	}
+	if combination == nil {
+		combination = make([]int, c.k)
+	}
+	if len(combination) != c.k {
+		panic(badInput)
+	}
+	copy(combination, c.previous)
+	return combination
+}
+
+// Combinations generates all of the combinations of k elements from a
+// set of size n. The returned slice has length Binomial(n,k) and each inner slice
+// has length k.
+//
+// n and k must be non-negative with n >= k, otherwise Combinations will panic.
+//
+// CombinationGenerator may alternatively be used to generate the combinations
+// iteratively instead of collectively.
+func Combinations(n, k int) [][]int {
+	combins := Binomial(n, k)
+	data := make([][]int, combins)
+	if len(data) == 0 {
+		return data
+	}
+	data[0] = make([]int, k)
+	for i := range data[0] {
+		data[0][i] = i
+	}
+	for i := 1; i < combins; i++ {
+		next := make([]int, k)
+		copy(next, data[i-1])
+		nextCombination(next, n, k)
+		data[i] = next
+	}
+	return data
+}
+
+// nextCombination generates the combination after s, overwriting the input value.
+func nextCombination(s []int, n, k int) {
+	for j := k - 1; j >= 0; j-- {
+		if s[j] == n+j-k {
+			continue
+		}
+		s[j]++
+		for l := j + 1; l < k; l++ {
+			s[l] = s[j] + l - j
+		}
+		break
+	}
+}