元老与新秀：Go sort.Search()和sort.Find()

// 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
}
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package main

import (
 "fmt"
 "sort"
)

func main() {
 // 已排序的切片
 numbers := []int{1, 2, 4, 6, 8, 10}

 // 要查找的值
 target := 5

 // 使用 sort.Search
 index := sort.Search(len(numbers), func(i int) bool {
  return numbers[i] >= target
 })

 // 输出结果
 if index < len(numbers) {
  fmt.Printf("找到了不小于 %d 的元素，索引为 %d，值为 %d\n", target, index, numbers[index])
 } else {
  fmt.Printf("没有找到不小于 %d 的元素，索引为 %d\n", target, index)
 }
}
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找到了不小于 5 的元素，索引为 3，值为 6
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// 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
}
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package main

import (
 "fmt"
 "sort"
)

func main() {

 data := []int{1, 2, 3, 5, 10}

 target0 := 4
 index0 := sort.Search(len(data), func(i int) bool {
  return data[i] >= target0
 })
 fmt.Println(index0) //3

 target1 := 5
 index1 := sort.Search(len(data), func(i int) bool {
  return data[i] >= target1
 })
 fmt.Println(index1) //3

 target2 := 6
 index2 := sort.Search(len(data), func(i int) bool {
  return data[i] >= target2
 })
 fmt.Println(index2) //4

 target3 := 11
 index3 := sort.Search(len(data), func(i int) bool {
  return data[i] >= target3
 })
 fmt.Println(index3) //5

}
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package main

import (
 "fmt"
 "sort"
 "strings"
)

func main() {

 x := []string{"a", "e", "h", "s", "v"}

 target := "e"
 i, found := sort.Find(len(x), func(i int) int {
  return strings.Compare(target, x[i])
 })
 if found {
  fmt.Printf("found %s at entry %d\n", target, i)
 } else {
  fmt.Printf("%s not found, would insert at %d\n", target, i)
 }

 target2 := "g"
 j, found2 := sort.Find(len(x), func(j int) int {
  return strings.Compare(target2, x[j])
 })
 if found2 {
  fmt.Printf("found %s at entry %d\n", target2, j)
 } else {
  fmt.Printf("%s not found, would insert at %d\n", target2, j)
 }

}
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found e at entry 1
g not found, would insert at 2
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