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