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 // (Note that the "not found" return value is not -1 as in, for instance, 16 // strings.Index.) 17 // Search calls f(i) only for i in the range [0, n). 18 // 19 // A common use of Search is to find the index i for a value x in 20 // a sorted, indexable data structure such as an array or slice. 21 // In this case, the argument f, typically a closure, captures the value 22 // to be searched for, and how the data structure is indexed and 23 // ordered. 24 // 25 // For instance, given a slice data sorted in ascending order, 26 // the call Search(len(data), func(i int) bool { return data[i] >= 23 }) 27 // returns the smallest index i such that data[i] >= 23. If the caller 28 // wants to find whether 23 is in the slice, it must test data[i] == 23 29 // separately. 30 // 31 // Searching data sorted in descending order would use the <= 32 // operator instead of the >= operator. 33 // 34 // To complete the example above, the following code tries to find the value 35 // x in an integer slice data sorted in ascending order: 36 // 37 // x := 23 38 // i := sort.Search(len(data), func(i int) bool { return data[i] >= x }) 39 // if i < len(data) && data[i] == x { 40 // // x is present at data[i] 41 // } else { 42 // // x is not present in data, 43 // // but i is the index where it would be inserted. 44 // } 45 // 46 // As a more whimsical example, this program guesses your number: 47 // 48 // func GuessingGame() { 49 // var s string 50 // fmt.Printf("Pick an integer from 0 to 100.\n") 51 // answer := sort.Search(100, func(i int) bool { 52 // fmt.Printf("Is your number <= %d? ", i) 53 // fmt.Scanf("%s", &s) 54 // return s != "" && s[0] == 'y' 55 // }) 56 // fmt.Printf("Your number is %d.\n", answer) 57 // } 58 func Search(n int, f func(int) bool) int { 59 // Define f(-1) == false and f(n) == true. 60 // Invariant: f(i-1) == false, f(j) == true. 61 i, j := 0, n 62 for i < j { 63 h := int(uint(i+j) >> 1) // avoid overflow when computing h 64 // i ≤ h < j 65 if !f(h) { 66 i = h + 1 // preserves f(i-1) == false 67 } else { 68 j = h // preserves f(j) == true 69 } 70 } 71 // i == j, f(i-1) == false, and f(j) (= f(i)) == true => answer is i. 72 return i 73 } 74 75 // Find uses binary search to find and return the smallest index i in [0, n) 76 // at which cmp(i) <= 0. If there is no such index i, Find returns i = n. 77 // The found result is true if i < n and cmp(i) == 0. 78 // Find calls cmp(i) only for i in the range [0, n). 79 // 80 // To permit binary search, Find requires that cmp(i) > 0 for a leading 81 // prefix of the range, cmp(i) == 0 in the middle, and cmp(i) < 0 for 82 // the final suffix of the range. (Each subrange could be empty.) 83 // The usual way to establish this condition is to interpret cmp(i) 84 // as a comparison of a desired target value t against entry i in an 85 // underlying indexed data structure x, returning <0, 0, and >0 86 // when t < x[i], t == x[i], and t > x[i], respectively. 87 // 88 // For example, to look for a particular string in a sorted, random-access 89 // list of strings: 90 // 91 // i, found := sort.Find(x.Len(), func(i int) int { 92 // return strings.Compare(target, x.At(i)) 93 // }) 94 // if found { 95 // fmt.Printf("found %s at entry %d\n", target, i) 96 // } else { 97 // fmt.Printf("%s not found, would insert at %d", target, i) 98 // } 99 func Find(n int, cmp func(int) int) (i int, found bool) { 100 // The invariants here are similar to the ones in Search. 101 // Define cmp(-1) > 0 and cmp(n) <= 0 102 // Invariant: cmp(i-1) > 0, cmp(j) <= 0 103 i, j := 0, n 104 for i < j { 105 h := int(uint(i+j) >> 1) // avoid overflow when computing h 106 // i ≤ h < j 107 if cmp(h) > 0 { 108 i = h + 1 // preserves cmp(i-1) > 0 109 } else { 110 j = h // preserves cmp(j) <= 0 111 } 112 } 113 // i == j, cmp(i-1) > 0 and cmp(j) <= 0 114 return i, i < n && cmp(i) == 0 115 } 116 117 // Convenience wrappers for common cases. 118 119 // SearchInts searches for x in a sorted slice of ints and returns the index 120 // as specified by [Search]. The return value is the index to insert x if x is 121 // not present (it could be len(a)). 122 // The slice must be sorted in ascending order. 123 func SearchInts(a []int, x int) int { 124 return Search(len(a), func(i int) bool { return a[i] >= x }) 125 } 126 127 // SearchFloat64s searches for x in a sorted slice of float64s and returns the index 128 // as specified by [Search]. The return value is the index to insert x if x is not 129 // present (it could be len(a)). 130 // The slice must be sorted in ascending order. 131 func SearchFloat64s(a []float64, x float64) int { 132 return Search(len(a), func(i int) bool { return a[i] >= x }) 133 } 134 135 // SearchStrings searches for x in a sorted slice of strings and returns the index 136 // as specified by Search. The return value is the index to insert x if x is not 137 // present (it could be len(a)). 138 // The slice must be sorted in ascending order. 139 func SearchStrings(a []string, x string) int { 140 return Search(len(a), func(i int) bool { return a[i] >= x }) 141 } 142 143 // Search returns the result of applying [SearchInts] to the receiver and x. 144 func (p IntSlice) Search(x int) int { return SearchInts(p, x) } 145 146 // Search returns the result of applying [SearchFloat64s] to the receiver and x. 147 func (p Float64Slice) Search(x float64) int { return SearchFloat64s(p, x) } 148 149 // Search returns the result of applying [SearchStrings] to the receiver and x. 150 func (p StringSlice) Search(x string) int { return SearchStrings(p, x) } 151