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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[0] == '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
+}
+
+// Find uses binary search to find and return the smallest index i in [0, n)
+// at which cmp(i) <= 0. If there is no such index i, Find returns i = n.
+// The found result is true if i < n and cmp(i) == 0.
+// Find calls cmp(i) only for i in the range [0, n).
+//
+// To permit binary search, Find requires that cmp(i) > 0 for a leading
+// prefix of the range, cmp(i) == 0 in the middle, and cmp(i) < 0 for
+// the final suffix of the range. (Each subrange could be empty.)
+// The usual way to establish this condition is to interpret cmp(i)
+// as a comparison of a desired target value t against entry i in an
+// underlying indexed data structure x, returning <0, 0, and >0
+// when t < x[i], t == x[i], and t > x[i], respectively.
+//
+// For example, to look for a particular string in a sorted, random-access
+// list of strings:
+//
+//	i, found := sort.Find(x.Len(), func(i int) int {
+//	    return strings.Compare(target, x.At(i))
+//	})
+//	if found {
+//	    fmt.Printf("found %s at entry %d\n", target, i)
+//	} else {
+//	    fmt.Printf("%s not found, would insert at %d", target, i)
+//	}
+func Find(n int, cmp func(int) int) (i int, found bool) {
+	// The invariants here are similar to the ones in Search.
+	// Define cmp(-1) > 0 and cmp(n) <= 0
+	// Invariant: cmp(i-1) > 0, cmp(j) <= 0
+	i, j := 0, n
+	for i < j {
+		h := int(uint(i+j) >> 1) // avoid overflow when computing h
+		// i ≤ h < j
+		if cmp(h) > 0 {
+			i = h + 1 // preserves cmp(i-1) > 0
+		} else {
+			j = h // preserves cmp(j) <= 0
+		}
+	}
+	// i == j, cmp(i-1) > 0 and cmp(j) <= 0
+	return i, i < n && cmp(i) == 0
+}
+
+// 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) }