sort.go

     1  // Copyright 2023 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  //go:generate go run $GOROOT/src/sort/gen_sort_variants.go -generic
     6  
     7  package slices
     8  
     9  import (
    10  	"cmp"
    11  	"math/bits"
    12  )
    13  
    14  // Sort sorts a slice of any ordered type in ascending order.
    15  // When sorting floating-point numbers, NaNs are ordered before other values.
    16  func Sort[S ~[]E, E cmp.Ordered](x S) {
    17  	n := len(x)
    18  	pdqsortOrdered(x, 0, n, bits.Len(uint(n)))
    19  }
    20  
    21  // SortFunc sorts the slice x in ascending order as determined by the cmp
    22  // function. This sort is not guaranteed to be stable.
    23  // cmp(a, b) should return a negative number when a < b, a positive number when
    24  // a > b and zero when a == b.
    25  //
    26  // SortFunc requires that cmp is a strict weak ordering.
    27  // See https://en.wikipedia.org/wiki/Weak_ordering#Strict_weak_orderings.
    28  func SortFunc[S ~[]E, E any](x S, cmp func(a, b E) int) {
    29  	n := len(x)
    30  	pdqsortCmpFunc(x, 0, n, bits.Len(uint(n)), cmp)
    31  }
    32  
    33  // SortStableFunc sorts the slice x while keeping the original order of equal
    34  // elements, using cmp to compare elements in the same way as [SortFunc].
    35  func SortStableFunc[S ~[]E, E any](x S, cmp func(a, b E) int) {
    36  	stableCmpFunc(x, len(x), cmp)
    37  }
    38  
    39  // IsSorted reports whether x is sorted in ascending order.
    40  func IsSorted[S ~[]E, E cmp.Ordered](x S) bool {
    41  	for i := len(x) - 1; i > 0; i-- {
    42  		if cmp.Less(x[i], x[i-1]) {
    43  			return false
    44  		}
    45  	}
    46  	return true
    47  }
    48  
    49  // IsSortedFunc reports whether x is sorted in ascending order, with cmp as the
    50  // comparison function as defined by [SortFunc].
    51  func IsSortedFunc[S ~[]E, E any](x S, cmp func(a, b E) int) bool {
    52  	for i := len(x) - 1; i > 0; i-- {
    53  		if cmp(x[i], x[i-1]) < 0 {
    54  			return false
    55  		}
    56  	}
    57  	return true
    58  }
    59  
    60  // Min returns the minimal value in x. It panics if x is empty.
    61  // For floating-point numbers, Min propagates NaNs (any NaN value in x
    62  // forces the output to be NaN).
    63  func Min[S ~[]E, E cmp.Ordered](x S) E {
    64  	if len(x) < 1 {
    65  		panic("slices.Min: empty list")
    66  	}
    67  	m := x[0]
    68  	for i := 1; i < len(x); i++ {
    69  		m = min(m, x[i])
    70  	}
    71  	return m
    72  }
    73  
    74  // MinFunc returns the minimal value in x, using cmp to compare elements.
    75  // It panics if x is empty. If there is more than one minimal element
    76  // according to the cmp function, MinFunc returns the first one.
    77  func MinFunc[S ~[]E, E any](x S, cmp func(a, b E) int) E {
    78  	if len(x) < 1 {
    79  		panic("slices.MinFunc: empty list")
    80  	}
    81  	m := x[0]
    82  	for i := 1; i < len(x); i++ {
    83  		if cmp(x[i], m) < 0 {
    84  			m = x[i]
    85  		}
    86  	}
    87  	return m
    88  }
    89  
    90  // Max returns the maximal value in x. It panics if x is empty.
    91  // For floating-point E, Max propagates NaNs (any NaN value in x
    92  // forces the output to be NaN).
    93  func Max[S ~[]E, E cmp.Ordered](x S) E {
    94  	if len(x) < 1 {
    95  		panic("slices.Max: empty list")
    96  	}
    97  	m := x[0]
    98  	for i := 1; i < len(x); i++ {
    99  		m = max(m, x[i])
   100  	}
   101  	return m
   102  }
   103  
   104  // MaxFunc returns the maximal value in x, using cmp to compare elements.
   105  // It panics if x is empty. If there is more than one maximal element
   106  // according to the cmp function, MaxFunc returns the first one.
   107  func MaxFunc[S ~[]E, E any](x S, cmp func(a, b E) int) E {
   108  	if len(x) < 1 {
   109  		panic("slices.MaxFunc: empty list")
   110  	}
   111  	m := x[0]
   112  	for i := 1; i < len(x); i++ {
   113  		if cmp(x[i], m) > 0 {
   114  			m = x[i]
   115  		}
   116  	}
   117  	return m
   118  }
   119  
   120  // BinarySearch searches for target in a sorted slice and returns the earliest
   121  // position where target is found, or the position where target would appear
   122  // in the sort order; it also returns a bool saying whether the target is
   123  // really found in the slice. The slice must be sorted in increasing order.
   124  func BinarySearch[S ~[]E, E cmp.Ordered](x S, target E) (int, bool) {
   125  	// Inlining is faster than calling BinarySearchFunc with a lambda.
   126  	n := len(x)
   127  	// Define x[-1] < target and x[n] >= target.
   128  	// Invariant: x[i-1] < target, x[j] >= target.
   129  	i, j := 0, n
   130  	for i < j {
   131  		h := int(uint(i+j) >> 1) // avoid overflow when computing h
   132  		// i ≤ h < j
   133  		if cmp.Less(x[h], target) {
   134  			i = h + 1 // preserves x[i-1] < target
   135  		} else {
   136  			j = h // preserves x[j] >= target
   137  		}
   138  	}
   139  	// i == j, x[i-1] < target, and x[j] (= x[i]) >= target  =>  answer is i.
   140  	return i, i < n && (x[i] == target || (isNaN(x[i]) && isNaN(target)))
   141  }
   142  
   143  // BinarySearchFunc works like [BinarySearch], but uses a custom comparison
   144  // function. The slice must be sorted in increasing order, where "increasing"
   145  // is defined by cmp. cmp should return 0 if the slice element matches
   146  // the target, a negative number if the slice element precedes the target,
   147  // or a positive number if the slice element follows the target.
   148  // cmp must implement the same ordering as the slice, such that if
   149  // cmp(a, t) < 0 and cmp(b, t) >= 0, then a must precede b in the slice.
   150  func BinarySearchFunc[S ~[]E, E, T any](x S, target T, cmp func(E, T) int) (int, bool) {
   151  	n := len(x)
   152  	// Define cmp(x[-1], target) < 0 and cmp(x[n], target) >= 0 .
   153  	// Invariant: cmp(x[i - 1], target) < 0, cmp(x[j], target) >= 0.
   154  	i, j := 0, n
   155  	for i < j {
   156  		h := int(uint(i+j) >> 1) // avoid overflow when computing h
   157  		// i ≤ h < j
   158  		if cmp(x[h], target) < 0 {
   159  			i = h + 1 // preserves cmp(x[i - 1], target) < 0
   160  		} else {
   161  			j = h // preserves cmp(x[j], target) >= 0
   162  		}
   163  	}
   164  	// i == j, cmp(x[i-1], target) < 0, and cmp(x[j], target) (= cmp(x[i], target)) >= 0  =>  answer is i.
   165  	return i, i < n && cmp(x[i], target) == 0
   166  }
   167  
   168  type sortedHint int // hint for pdqsort when choosing the pivot
   169  
   170  const (
   171  	unknownHint sortedHint = iota
   172  	increasingHint
   173  	decreasingHint
   174  )
   175  
   176  // xorshift paper: https://www.jstatsoft.org/article/view/v008i14/xorshift.pdf
   177  type xorshift uint64
   178  
   179  func (r *xorshift) Next() uint64 {
   180  	*r ^= *r << 13
   181  	*r ^= *r >> 17
   182  	*r ^= *r << 5
   183  	return uint64(*r)
   184  }
   185  
   186  func nextPowerOfTwo(length int) uint {
   187  	return 1 << bits.Len(uint(length))
   188  }
   189  
   190  // isNaN reports whether x is a NaN without requiring the math package.
   191  // This will always return false if T is not floating-point.
   192  func isNaN[T cmp.Ordered](x T) bool {
   193  	return x != x
   194  }
   195
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