113 lines
4.1 KiB
Go
113 lines
4.1 KiB
Go
// Copyright 2010 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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// This file implements binary search.
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package sort
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// Search uses binary search to find and return the smallest index i
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// in [0, n) at which f(i) is true, assuming that on the range [0, n),
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// f(i) == true implies f(i+1) == true. That is, Search requires that
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// f is false for some (possibly empty) prefix of the input range [0, n)
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// and then true for the (possibly empty) remainder; Search returns
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// the first true index. If there is no such index, Search returns n.
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// (Note that the "not found" return value is not -1 as in, for instance,
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// strings.Index).
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// Search calls f(i) only for i in the range [0, n).
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//
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// A common use of Search is to find the index i for a value x in
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// a sorted, indexable data structure such as an array or slice.
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// In this case, the argument f, typically a closure, captures the value
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// to be searched for, and how the data structure is indexed and
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// ordered.
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//
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// For instance, given a slice data sorted in ascending order,
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// the call Search(len(data), func(i int) bool { return data[i] >= 23 })
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// returns the smallest index i such that data[i] >= 23. If the caller
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// wants to find whether 23 is in the slice, it must test data[i] == 23
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// separately.
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//
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// Searching data sorted in descending order would use the <=
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// operator instead of the >= operator.
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//
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// To complete the example above, the following code tries to find the value
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// x in an integer slice data sorted in ascending order:
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//
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// x := 23
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// i := sort.Search(len(data), func(i int) bool { return data[i] >= x })
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// if i < len(data) && data[i] == x {
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// // x is present at data[i]
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// } else {
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// // x is not present in data,
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// // but i is the index where it would be inserted.
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// }
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//
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// As a more whimsical example, this program guesses your number:
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//
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// func GuessingGame() {
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// var s string
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// fmt.Printf("Pick an integer from 0 to 100.\n")
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// answer := sort.Search(100, func(i int) bool {
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// fmt.Printf("Is your number <= %d? ", i)
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// fmt.Scanf("%s", &s)
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// return s != "" && s[0] == 'y'
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// })
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// fmt.Printf("Your number is %d.\n", answer)
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// }
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//
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func Search(n int, f func(int) bool) int {
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// Define f(-1) == false and f(n) == true.
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// Invariant: f(i-1) == false, f(j) == true.
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i, j := 0, n
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for i < j {
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h := i + (j-i)/2 // avoid overflow when computing h
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// i ≤ h < j
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if !f(h) {
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i = h + 1 // preserves f(i-1) == false
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} else {
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j = h // preserves f(j) == true
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}
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}
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// i == j, f(i-1) == false, and f(j) (= f(i)) == true => answer is i.
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return i
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}
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// Convenience wrappers for common cases.
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// SearchInts searches for x in a sorted slice of ints and returns the index
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// as specified by Search. The return value is the index to insert x if x is
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// not present (it could be len(a)).
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// The slice must be sorted in ascending order.
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//
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func SearchInts(a []int, x int) int {
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return Search(len(a), func(i int) bool { return a[i] >= x })
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}
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// SearchFloat64s searches for x in a sorted slice of float64s and returns the index
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// as specified by Search. The return value is the index to insert x if x is not
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// present (it could be len(a)).
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// The slice must be sorted in ascending order.
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//
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func SearchFloat64s(a []float64, x float64) int {
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return Search(len(a), func(i int) bool { return a[i] >= x })
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}
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// SearchStrings searches for x in a sorted slice of strings and returns the index
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// as specified by Search. The return value is the index to insert x if x is not
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// present (it could be len(a)).
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// The slice must be sorted in ascending order.
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//
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func SearchStrings(a []string, x string) int {
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return Search(len(a), func(i int) bool { return a[i] >= x })
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}
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// Search returns the result of applying SearchInts to the receiver and x.
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func (p IntSlice) Search(x int) int { return SearchInts(p, x) }
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// Search returns the result of applying SearchFloat64s to the receiver and x.
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func (p Float64Slice) Search(x float64) int { return SearchFloat64s(p, x) }
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// Search returns the result of applying SearchStrings to the receiver and x.
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func (p StringSlice) Search(x string) int { return SearchStrings(p, x) }
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