summaryrefslogtreecommitdiffstats
path: root/src/sort/zsortinterface.go
blob: 51fa5032e9912a8d7db6005dd1d11291b422a312 (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
// Code generated by gen_sort_variants.go; DO NOT EDIT.

// Copyright 2022 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.

package sort

// insertionSort sorts data[a:b] using insertion sort.
func insertionSort(data Interface, a, b int) {
	for i := a + 1; i < b; i++ {
		for j := i; j > a && data.Less(j, j-1); j-- {
			data.Swap(j, j-1)
		}
	}
}

// siftDown implements the heap property on data[lo:hi].
// first is an offset into the array where the root of the heap lies.
func siftDown(data Interface, lo, hi, first int) {
	root := lo
	for {
		child := 2*root + 1
		if child >= hi {
			break
		}
		if child+1 < hi && data.Less(first+child, first+child+1) {
			child++
		}
		if !data.Less(first+root, first+child) {
			return
		}
		data.Swap(first+root, first+child)
		root = child
	}
}

func heapSort(data Interface, a, b int) {
	first := a
	lo := 0
	hi := b - a

	// Build heap with greatest element at top.
	for i := (hi - 1) / 2; i >= 0; i-- {
		siftDown(data, i, hi, first)
	}

	// Pop elements, largest first, into end of data.
	for i := hi - 1; i >= 0; i-- {
		data.Swap(first, first+i)
		siftDown(data, lo, i, first)
	}
}

// pdqsort sorts data[a:b].
// The algorithm based on pattern-defeating quicksort(pdqsort), but without the optimizations from BlockQuicksort.
// pdqsort paper: https://arxiv.org/pdf/2106.05123.pdf
// C++ implementation: https://github.com/orlp/pdqsort
// Rust implementation: https://docs.rs/pdqsort/latest/pdqsort/
// limit is the number of allowed bad (very unbalanced) pivots before falling back to heapsort.
func pdqsort(data Interface, a, b, limit int) {
	const maxInsertion = 12

	var (
		wasBalanced    = true // whether the last partitioning was reasonably balanced
		wasPartitioned = true // whether the slice was already partitioned
	)

	for {
		length := b - a

		if length <= maxInsertion {
			insertionSort(data, a, b)
			return
		}

		// Fall back to heapsort if too many bad choices were made.
		if limit == 0 {
			heapSort(data, a, b)
			return
		}

		// If the last partitioning was imbalanced, we need to breaking patterns.
		if !wasBalanced {
			breakPatterns(data, a, b)
			limit--
		}

		pivot, hint := choosePivot(data, a, b)
		if hint == decreasingHint {
			reverseRange(data, a, b)
			// The chosen pivot was pivot-a elements after the start of the array.
			// After reversing it is pivot-a elements before the end of the array.
			// The idea came from Rust's implementation.
			pivot = (b - 1) - (pivot - a)
			hint = increasingHint
		}

		// The slice is likely already sorted.
		if wasBalanced && wasPartitioned && hint == increasingHint {
			if partialInsertionSort(data, a, b) {
				return
			}
		}

		// Probably the slice contains many duplicate elements, partition the slice into
		// elements equal to and elements greater than the pivot.
		if a > 0 && !data.Less(a-1, pivot) {
			mid := partitionEqual(data, a, b, pivot)
			a = mid
			continue
		}

		mid, alreadyPartitioned := partition(data, a, b, pivot)
		wasPartitioned = alreadyPartitioned

		leftLen, rightLen := mid-a, b-mid
		balanceThreshold := length / 8
		if leftLen < rightLen {
			wasBalanced = leftLen >= balanceThreshold
			pdqsort(data, a, mid, limit)
			a = mid + 1
		} else {
			wasBalanced = rightLen >= balanceThreshold
			pdqsort(data, mid+1, b, limit)
			b = mid
		}
	}
}

// partition does one quicksort partition.
// Let p = data[pivot]
// Moves elements in data[a:b] around, so that data[i]<p and data[j]>=p for i<newpivot and j>newpivot.
// On return, data[newpivot] = p
func partition(data Interface, a, b, pivot int) (newpivot int, alreadyPartitioned bool) {
	data.Swap(a, pivot)
	i, j := a+1, b-1 // i and j are inclusive of the elements remaining to be partitioned

	for i <= j && data.Less(i, a) {
		i++
	}
	for i <= j && !data.Less(j, a) {
		j--
	}
	if i > j {
		data.Swap(j, a)
		return j, true
	}
	data.Swap(i, j)
	i++
	j--

	for {
		for i <= j && data.Less(i, a) {
			i++
		}
		for i <= j && !data.Less(j, a) {
			j--
		}
		if i > j {
			break
		}
		data.Swap(i, j)
		i++
		j--
	}
	data.Swap(j, a)
	return j, false
}

// partitionEqual partitions data[a:b] into elements equal to data[pivot] followed by elements greater than data[pivot].
// It assumed that data[a:b] does not contain elements smaller than the data[pivot].
func partitionEqual(data Interface, a, b, pivot int) (newpivot int) {
	data.Swap(a, pivot)
	i, j := a+1, b-1 // i and j are inclusive of the elements remaining to be partitioned

	for {
		for i <= j && !data.Less(a, i) {
			i++
		}
		for i <= j && data.Less(a, j) {
			j--
		}
		if i > j {
			break
		}
		data.Swap(i, j)
		i++
		j--
	}
	return i
}

// partialInsertionSort partially sorts a slice, returns true if the slice is sorted at the end.
func partialInsertionSort(data Interface, a, b int) bool {
	const (
		maxSteps         = 5  // maximum number of adjacent out-of-order pairs that will get shifted
		shortestShifting = 50 // don't shift any elements on short arrays
	)
	i := a + 1
	for j := 0; j < maxSteps; j++ {
		for i < b && !data.Less(i, i-1) {
			i++
		}

		if i == b {
			return true
		}

		if b-a < shortestShifting {
			return false
		}

		data.Swap(i, i-1)

		// Shift the smaller one to the left.
		if i-a >= 2 {
			for j := i - 1; j >= 1; j-- {
				if !data.Less(j, j-1) {
					break
				}
				data.Swap(j, j-1)
			}
		}
		// Shift the greater one to the right.
		if b-i >= 2 {
			for j := i + 1; j < b; j++ {
				if !data.Less(j, j-1) {
					break
				}
				data.Swap(j, j-1)
			}
		}
	}
	return false
}

// breakPatterns scatters some elements around in an attempt to break some patterns
// that might cause imbalanced partitions in quicksort.
func breakPatterns(data Interface, a, b int) {
	length := b - a
	if length >= 8 {
		random := xorshift(length)
		modulus := nextPowerOfTwo(length)

		for idx := a + (length/4)*2 - 1; idx <= a+(length/4)*2+1; idx++ {
			other := int(uint(random.Next()) & (modulus - 1))
			if other >= length {
				other -= length
			}
			data.Swap(idx, a+other)
		}
	}
}

// choosePivot chooses a pivot in data[a:b].
//
// [0,8): chooses a static pivot.
// [8,shortestNinther): uses the simple median-of-three method.
// [shortestNinther,∞): uses the Tukey ninther method.
func choosePivot(data Interface, a, b int) (pivot int, hint sortedHint) {
	const (
		shortestNinther = 50
		maxSwaps        = 4 * 3
	)

	l := b - a

	var (
		swaps int
		i     = a + l/4*1
		j     = a + l/4*2
		k     = a + l/4*3
	)

	if l >= 8 {
		if l >= shortestNinther {
			// Tukey ninther method, the idea came from Rust's implementation.
			i = medianAdjacent(data, i, &swaps)
			j = medianAdjacent(data, j, &swaps)
			k = medianAdjacent(data, k, &swaps)
		}
		// Find the median among i, j, k and stores it into j.
		j = median(data, i, j, k, &swaps)
	}

	switch swaps {
	case 0:
		return j, increasingHint
	case maxSwaps:
		return j, decreasingHint
	default:
		return j, unknownHint
	}
}

// order2 returns x,y where data[x] <= data[y], where x,y=a,b or x,y=b,a.
func order2(data Interface, a, b int, swaps *int) (int, int) {
	if data.Less(b, a) {
		*swaps++
		return b, a
	}
	return a, b
}

// median returns x where data[x] is the median of data[a],data[b],data[c], where x is a, b, or c.
func median(data Interface, a, b, c int, swaps *int) int {
	a, b = order2(data, a, b, swaps)
	b, c = order2(data, b, c, swaps)
	a, b = order2(data, a, b, swaps)
	return b
}

// medianAdjacent finds the median of data[a - 1], data[a], data[a + 1] and stores the index into a.
func medianAdjacent(data Interface, a int, swaps *int) int {
	return median(data, a-1, a, a+1, swaps)
}

func reverseRange(data Interface, a, b int) {
	i := a
	j := b - 1
	for i < j {
		data.Swap(i, j)
		i++
		j--
	}
}

func swapRange(data Interface, a, b, n int) {
	for i := 0; i < n; i++ {
		data.Swap(a+i, b+i)
	}
}

func stable(data Interface, n int) {
	blockSize := 20 // must be > 0
	a, b := 0, blockSize
	for b <= n {
		insertionSort(data, a, b)
		a = b
		b += blockSize
	}
	insertionSort(data, a, n)

	for blockSize < n {
		a, b = 0, 2*blockSize
		for b <= n {
			symMerge(data, a, a+blockSize, b)
			a = b
			b += 2 * blockSize
		}
		if m := a + blockSize; m < n {
			symMerge(data, a, m, n)
		}
		blockSize *= 2
	}
}

// symMerge merges the two sorted subsequences data[a:m] and data[m:b] using
// the SymMerge algorithm from Pok-Son Kim and Arne Kutzner, "Stable Minimum
// Storage Merging by Symmetric Comparisons", in Susanne Albers and Tomasz
// Radzik, editors, Algorithms - ESA 2004, volume 3221 of Lecture Notes in
// Computer Science, pages 714-723. Springer, 2004.
//
// Let M = m-a and N = b-n. Wolog M < N.
// The recursion depth is bound by ceil(log(N+M)).
// The algorithm needs O(M*log(N/M + 1)) calls to data.Less.
// The algorithm needs O((M+N)*log(M)) calls to data.Swap.
//
// The paper gives O((M+N)*log(M)) as the number of assignments assuming a
// rotation algorithm which uses O(M+N+gcd(M+N)) assignments. The argumentation
// in the paper carries through for Swap operations, especially as the block
// swapping rotate uses only O(M+N) Swaps.
//
// symMerge assumes non-degenerate arguments: a < m && m < b.
// Having the caller check this condition eliminates many leaf recursion calls,
// which improves performance.
func symMerge(data Interface, a, m, b int) {
	// Avoid unnecessary recursions of symMerge
	// by direct insertion of data[a] into data[m:b]
	// if data[a:m] only contains one element.
	if m-a == 1 {
		// Use binary search to find the lowest index i
		// such that data[i] >= data[a] for m <= i < b.
		// Exit the search loop with i == b in case no such index exists.
		i := m
		j := b
		for i < j {
			h := int(uint(i+j) >> 1)
			if data.Less(h, a) {
				i = h + 1
			} else {
				j = h
			}
		}
		// Swap values until data[a] reaches the position before i.
		for k := a; k < i-1; k++ {
			data.Swap(k, k+1)
		}
		return
	}

	// Avoid unnecessary recursions of symMerge
	// by direct insertion of data[m] into data[a:m]
	// if data[m:b] only contains one element.
	if b-m == 1 {
		// Use binary search to find the lowest index i
		// such that data[i] > data[m] for a <= i < m.
		// Exit the search loop with i == m in case no such index exists.
		i := a
		j := m
		for i < j {
			h := int(uint(i+j) >> 1)
			if !data.Less(m, h) {
				i = h + 1
			} else {
				j = h
			}
		}
		// Swap values until data[m] reaches the position i.
		for k := m; k > i; k-- {
			data.Swap(k, k-1)
		}
		return
	}

	mid := int(uint(a+b) >> 1)
	n := mid + m
	var start, r int
	if m > mid {
		start = n - b
		r = mid
	} else {
		start = a
		r = m
	}
	p := n - 1

	for start < r {
		c := int(uint(start+r) >> 1)
		if !data.Less(p-c, c) {
			start = c + 1
		} else {
			r = c
		}
	}

	end := n - start
	if start < m && m < end {
		rotate(data, start, m, end)
	}
	if a < start && start < mid {
		symMerge(data, a, start, mid)
	}
	if mid < end && end < b {
		symMerge(data, mid, end, b)
	}
}

// rotate rotates two consecutive blocks u = data[a:m] and v = data[m:b] in data:
// Data of the form 'x u v y' is changed to 'x v u y'.
// rotate performs at most b-a many calls to data.Swap,
// and it assumes non-degenerate arguments: a < m && m < b.
func rotate(data Interface, a, m, b int) {
	i := m - a
	j := b - m

	for i != j {
		if i > j {
			swapRange(data, m-i, m, j)
			i -= j
		} else {
			swapRange(data, m-i, m+j-i, i)
			j -= i
		}
	}
	// i == j
	swapRange(data, m-i, m, i)
}