Source file src/pkg/sort/search.go
1 // Copyright 2010 The Go Authors. All rights reserved. 2 // Use of this source code is governed by a BSD-style 3 // license that can be found in the LICENSE file. 4 5 // This file implements binary search. 6 7 package sort 8 9 // Search uses binary search to find and return the smallest index i 10 // in [0, n) at which f(i) is true, assuming that on the range [0, n), 11 // f(i) == true implies f(i+1) == true. That is, Search requires that 12 // f is false for some (possibly empty) prefix of the input range [0, n) 13 // and then true for the (possibly empty) remainder; Search returns 14 // the first true index. If there is no such index, Search returns n. 15 // Search calls f(i) only for i in the range [0, n). 16 // 17 // A common use of Search is to find the index i for a value x in 18 // a sorted, indexable data structure such as an array or slice. 19 // In this case, the argument f, typically a closure, captures the value 20 // to be searched for, and how the data structure is indexed and 21 // ordered. 22 // 23 // For instance, given a slice data sorted in ascending order, 24 // the call Search(len(data), func(i int) bool { return data[i] >= 23 }) 25 // returns the smallest index i such that data[i] >= 23. If the caller 26 // wants to find whether 23 is in the slice, it must test data[i] == 23 27 // separately. 28 // 29 // Searching data sorted in descending order would use the <= 30 // operator instead of the >= operator. 31 // 32 // To complete the example above, the following code tries to find the value 33 // x in an integer slice data sorted in ascending order: 34 // 35 // x := 23 36 // i := sort.Search(len(data), func(i int) bool { return data[i] >= x }) 37 // if i < len(data) && data[i] == x { 38 // // x is present at data[i] 39 // } else { 40 // // x is not present in data, 41 // // but i is the index where it would be inserted. 42 // } 43 // 44 // As a more whimsical example, this program guesses your number: 45 // 46 // func GuessingGame() { 47 // var s string 48 // fmt.Printf("Pick an integer from 0 to 100.\n") 49 // answer := sort.Search(100, func(i int) bool { 50 // fmt.Printf("Is your number <= %d? ", i) 51 // fmt.Scanf("%s", &s) 52 // return s != "" && s[0] == 'y' 53 // }) 54 // fmt.Printf("Your number is %d.\n", answer) 55 // } 56 // 57 func Search(n int, f func(int) bool) int { 58 // Define f(-1) == false and f(n) == true. 59 // Invariant: f(i-1) == false, f(j) == true. 60 i, j := 0, n 61 for i < j { 62 h := i + (j-i)/2 // avoid overflow when computing h 63 // i ≤ h < j 64 if !f(h) { 65 i = h + 1 // preserves f(i-1) == false 66 } else { 67 j = h // preserves f(j) == true 68 } 69 } 70 // i == j, f(i-1) == false, and f(j) (= f(i)) == true => answer is i. 71 return i 72 } 73 74 // Convenience wrappers for common cases. 75 76 // SearchInts searches for x in a sorted slice of ints and returns the index 77 // as specified by Search. The slice must be sorted in ascending order. 78 // 79 func SearchInts(a []int, x int) int { 80 return Search(len(a), func(i int) bool { return a[i] >= x }) 81 } 82 83 // SearchFloat64s searches for x in a sorted slice of float64s and returns the index 84 // as specified by Search. The slice must be sorted in ascending order. 85 // 86 func SearchFloat64s(a []float64, x float64) int { 87 return Search(len(a), func(i int) bool { return a[i] >= x }) 88 } 89 90 // SearchStrings searches for x slice a sorted slice of strings and returns the index 91 // as specified by Search. The slice must be sorted in ascending order. 92 // 93 func SearchStrings(a []string, x string) int { 94 return Search(len(a), func(i int) bool { return a[i] >= x }) 95 } 96 97 // Search returns the result of applying SearchInts to the receiver and x. 98 func (p IntSlice) Search(x int) int { return SearchInts(p, x) } 99 100 // Search returns the result of applying SearchFloat64s to the receiver and x. 101 func (p Float64Slice) Search(x float64) int { return SearchFloat64s(p, x) } 102 103 // Search returns the result of applying SearchStrings to the receiver and x. 104 func (p StringSlice) Search(x string) int { return SearchStrings(p, x) }