// 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) }