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Source file src/pkg/sort/search.go

     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	//
    59	func Search(n int, f func(int) bool) int {
    60		// Define f(-1) == false and f(n) == true.
    61		// Invariant: f(i-1) == false, f(j) == true.
    62		i, j := 0, n
    63		for i < j {
    64			h := i + (j-i)/2 // avoid overflow when computing h
    65			// i ≤ h < j
    66			if !f(h) {
    67				i = h + 1 // preserves f(i-1) == false
    68			} else {
    69				j = h // preserves f(j) == true
    70			}
    71		}
    72		// i == j, f(i-1) == false, and f(j) (= f(i)) == true  =>  answer is i.
    73		return i
    74	}
    75	
    76	// Convenience wrappers for common cases.
    77	
    78	// SearchInts searches for x in a sorted slice of ints and returns the index
    79	// as specified by Search. The return value is the index to insert x if x is
    80	// not present (it could be len(a)).
    81	// The slice must be sorted in ascending order.
    82	//
    83	func SearchInts(a []int, x int) int {
    84		return Search(len(a), func(i int) bool { return a[i] >= x })
    85	}
    86	
    87	// SearchFloat64s searches for x in a sorted slice of float64s and returns the index
    88	// as specified by Search.  The return value is the index to insert x if x is not
    89	// present (it could be len(a)).
    90	// The slice must be sorted in ascending order.
    91	//
    92	func SearchFloat64s(a []float64, x float64) int {
    93		return Search(len(a), func(i int) bool { return a[i] >= x })
    94	}
    95	
    96	// SearchStrings searches for x in a sorted slice of strings and returns the index
    97	// as specified by Search.  The return value is the index to insert x if x is not
    98	// present (it could be len(a)).
    99	// The slice must be sorted in ascending order.
   100	//
   101	func SearchStrings(a []string, x string) int {
   102		return Search(len(a), func(i int) bool { return a[i] >= x })
   103	}
   104	
   105	// Search returns the result of applying SearchInts to the receiver and x.
   106	func (p IntSlice) Search(x int) int { return SearchInts(p, x) }
   107	
   108	// Search returns the result of applying SearchFloat64s to the receiver and x.
   109	func (p Float64Slice) Search(x float64) int { return SearchFloat64s(p, x) }
   110	
   111	// Search returns the result of applying SearchStrings to the receiver and x.
   112	func (p StringSlice) Search(x string) int { return SearchStrings(p, x) }

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