add choose pkg

choose/LICENSE

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+MIT License
+
+Copyright (c) 2018 Aaron Cannon
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.

choose/README.md

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+# N choose K for Go/Golang
+
+[![Go Report Card](https://goreportcard.com/badge/github.com/golang-standards/project-layout?style=flat-square)](https://goreportcard.com/report/github.com/cannona/choose)
+[![Go Doc](https://img.shields.io/badge/godoc-reference-blue.svg?style=flat-square)](http://godoc.org/github.com/cannona/choose)
+[![Release](https://img.shields.io/github/release/golang-standards/project-layout.svg?style=flat-square)](https://github.com/cannona/choose/releases/latest)
+
+package choose implements the N choose K formula, or the binomial coefficient formula. See https://en.wikipedia.org/wiki/Binomial_coefficient for more.
+
+### Installation
+
+    go get github.com/cannona/choose
+

choose/choose.go

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+// Copyright 2018, Aaron Cannon under the BSD license.
+// See the license file for details.
+
+// Package choose implements the N choose K formula, or the binomial coefficient
+// formula. See https://en.wikipedia.org/wiki/Binomial_coefficient for more.
+package choose
+
+// Choose calculates n choose k. Overflows are not detected, and Choose panics
+// if n >= k >= 0 is violated.
+func Choose(n, k int64) int64 {
+	if k > n {
+		panic("Choose: k > n")
+	}
+	if k < 0 {
+		panic("Choose: k < 0")
+	}
+	if n <= 1 || k == 0 || n == k {
+		return 1
+	}
+	if newK := n - k; newK < k {
+		k = newK
+	}
+	if k == 1 {
+		return n
+	}
+	// Our return value, and this allows us to skip the first iteration.
+	ret := int64(n - k + 1)
+	for i, j := ret+1, int64(2); j <= k; i, j = i+1, j+1 {
+		ret = ret * i / j
+	}
+	return ret
+}

choose/choose_test.go

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+package choose
+
+import "testing"
+
+func didPanic(f func()) (ret bool) {
+	defer func() {
+		if r := recover(); r != nil {
+			ret = true
+		}
+	}()
+	f()
+	return
+}
+
+func TestChoose(t *testing.T) {
+	// Let's use Pascal's triangle for the values.
+	row := append([]int64(nil), 1)
+	for n := int64(0); n < 62; n++ {
+		for k, v := range row {
+			if x := Choose(n, int64(k)); x != v {
+				t.Fatalf("%v choose %v returned %v, not %v", n, k, x, v)
+			}
+		}
+		newRow := make([]int64, len(row)+1)
+		newRow[0] = 1
+		for i := 1; i < len(row); i++ {
+			newRow[i] = row[i-1] + row[i]
+		}
+		newRow[len(row)] = 1
+		row = newRow
+	}
+	// Ensure it panics when it should.
+	if !didPanic(func() {
+		Choose(3, 4)
+	}) {
+		t.Fatal("Choose did not panic when k > n.")
+	}
+	if !didPanic(func() {
+		Choose(3, -1)
+	}) {
+		t.Fatal("Choose did not panic when k < 0")
+	}
+}
+
+func BenchmarkChoose(b *testing.B) {
+	for i := 0; i < b.N; i++ {
+		Choose(61, 30)
+	}
+}