| // 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 slices |
| |
| import "cmp" |
| |
| // insertionSortOrdered sorts data[a:b] using insertion sort. |
| func insertionSortOrdered[E cmp.Ordered](data []E, a, b int) { |
| for i := a + 1; i < b; i++ { |
| for j := i; j > a && cmp.Less(data[j], data[j-1]); j-- { |
| data[j], data[j-1] = data[j-1], data[j] |
| } |
| } |
| } |
| |
| // siftDownOrdered implements the heap property on data[lo:hi]. |
| // first is an offset into the array where the root of the heap lies. |
| func siftDownOrdered[E cmp.Ordered](data []E, lo, hi, first int) { |
| root := lo |
| for { |
| child := 2*root + 1 |
| if child >= hi { |
| break |
| } |
| if child+1 < hi && cmp.Less(data[first+child], data[first+child+1]) { |
| child++ |
| } |
| if !cmp.Less(data[first+root], data[first+child]) { |
| return |
| } |
| data[first+root], data[first+child] = data[first+child], data[first+root] |
| root = child |
| } |
| } |
| |
| func heapSortOrdered[E cmp.Ordered](data []E, 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-- { |
| siftDownOrdered(data, i, hi, first) |
| } |
| |
| // Pop elements, largest first, into end of data. |
| for i := hi - 1; i >= 0; i-- { |
| data[first], data[first+i] = data[first+i], data[first] |
| siftDownOrdered(data, lo, i, first) |
| } |
| } |
| |
| // pdqsortOrdered 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 pdqsortOrdered[E cmp.Ordered](data []E, 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 { |
| insertionSortOrdered(data, a, b) |
| return |
| } |
| |
| // Fall back to heapsort if too many bad choices were made. |
| if limit == 0 { |
| heapSortOrdered(data, a, b) |
| return |
| } |
| |
| // If the last partitioning was imbalanced, we need to breaking patterns. |
| if !wasBalanced { |
| breakPatternsOrdered(data, a, b) |
| limit-- |
| } |
| |
| pivot, hint := choosePivotOrdered(data, a, b) |
| if hint == decreasingHint { |
| reverseRangeOrdered(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 partialInsertionSortOrdered(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 && !cmp.Less(data[a-1], data[pivot]) { |
| mid := partitionEqualOrdered(data, a, b, pivot) |
| a = mid |
| continue |
| } |
| |
| mid, alreadyPartitioned := partitionOrdered(data, a, b, pivot) |
| wasPartitioned = alreadyPartitioned |
| |
| leftLen, rightLen := mid-a, b-mid |
| balanceThreshold := length / 8 |
| if leftLen < rightLen { |
| wasBalanced = leftLen >= balanceThreshold |
| pdqsortOrdered(data, a, mid, limit) |
| a = mid + 1 |
| } else { |
| wasBalanced = rightLen >= balanceThreshold |
| pdqsortOrdered(data, mid+1, b, limit) |
| b = mid |
| } |
| } |
| } |
| |
| // partitionOrdered 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 partitionOrdered[E cmp.Ordered](data []E, a, b, pivot int) (newpivot int, alreadyPartitioned bool) { |
| data[a], data[pivot] = data[pivot], data[a] |
| i, j := a+1, b-1 // i and j are inclusive of the elements remaining to be partitioned |
| |
| for i <= j && cmp.Less(data[i], data[a]) { |
| i++ |
| } |
| for i <= j && !cmp.Less(data[j], data[a]) { |
| j-- |
| } |
| if i > j { |
| data[j], data[a] = data[a], data[j] |
| return j, true |
| } |
| data[i], data[j] = data[j], data[i] |
| i++ |
| j-- |
| |
| for { |
| for i <= j && cmp.Less(data[i], data[a]) { |
| i++ |
| } |
| for i <= j && !cmp.Less(data[j], data[a]) { |
| j-- |
| } |
| if i > j { |
| break |
| } |
| data[i], data[j] = data[j], data[i] |
| i++ |
| j-- |
| } |
| data[j], data[a] = data[a], data[j] |
| return j, false |
| } |
| |
| // partitionEqualOrdered 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 partitionEqualOrdered[E cmp.Ordered](data []E, a, b, pivot int) (newpivot int) { |
| data[a], data[pivot] = data[pivot], data[a] |
| i, j := a+1, b-1 // i and j are inclusive of the elements remaining to be partitioned |
| |
| for { |
| for i <= j && !cmp.Less(data[a], data[i]) { |
| i++ |
| } |
| for i <= j && cmp.Less(data[a], data[j]) { |
| j-- |
| } |
| if i > j { |
| break |
| } |
| data[i], data[j] = data[j], data[i] |
| i++ |
| j-- |
| } |
| return i |
| } |
| |
| // partialInsertionSortOrdered partially sorts a slice, returns true if the slice is sorted at the end. |
| func partialInsertionSortOrdered[E cmp.Ordered](data []E, 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 && !cmp.Less(data[i], data[i-1]) { |
| i++ |
| } |
| |
| if i == b { |
| return true |
| } |
| |
| if b-a < shortestShifting { |
| return false |
| } |
| |
| data[i], data[i-1] = data[i-1], data[i] |
| |
| // Shift the smaller one to the left. |
| if i-a >= 2 { |
| for j := i - 1; j >= 1; j-- { |
| if !cmp.Less(data[j], data[j-1]) { |
| break |
| } |
| data[j], data[j-1] = data[j-1], data[j] |
| } |
| } |
| // Shift the greater one to the right. |
| if b-i >= 2 { |
| for j := i + 1; j < b; j++ { |
| if !cmp.Less(data[j], data[j-1]) { |
| break |
| } |
| data[j], data[j-1] = data[j-1], data[j] |
| } |
| } |
| } |
| return false |
| } |
| |
| // breakPatternsOrdered scatters some elements around in an attempt to break some patterns |
| // that might cause imbalanced partitions in quicksort. |
| func breakPatternsOrdered[E cmp.Ordered](data []E, 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[idx], data[a+other] = data[a+other], data[idx] |
| } |
| } |
| } |
| |
| // choosePivotOrdered 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 choosePivotOrdered[E cmp.Ordered](data []E, 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 = medianAdjacentOrdered(data, i, &swaps) |
| j = medianAdjacentOrdered(data, j, &swaps) |
| k = medianAdjacentOrdered(data, k, &swaps) |
| } |
| // Find the median among i, j, k and stores it into j. |
| j = medianOrdered(data, i, j, k, &swaps) |
| } |
| |
| switch swaps { |
| case 0: |
| return j, increasingHint |
| case maxSwaps: |
| return j, decreasingHint |
| default: |
| return j, unknownHint |
| } |
| } |
| |
| // order2Ordered returns x,y where data[x] <= data[y], where x,y=a,b or x,y=b,a. |
| func order2Ordered[E cmp.Ordered](data []E, a, b int, swaps *int) (int, int) { |
| if cmp.Less(data[b], data[a]) { |
| *swaps++ |
| return b, a |
| } |
| return a, b |
| } |
| |
| // medianOrdered returns x where data[x] is the median of data[a],data[b],data[c], where x is a, b, or c. |
| func medianOrdered[E cmp.Ordered](data []E, a, b, c int, swaps *int) int { |
| a, b = order2Ordered(data, a, b, swaps) |
| b, c = order2Ordered(data, b, c, swaps) |
| a, b = order2Ordered(data, a, b, swaps) |
| return b |
| } |
| |
| // medianAdjacentOrdered finds the median of data[a - 1], data[a], data[a + 1] and stores the index into a. |
| func medianAdjacentOrdered[E cmp.Ordered](data []E, a int, swaps *int) int { |
| return medianOrdered(data, a-1, a, a+1, swaps) |
| } |
| |
| func reverseRangeOrdered[E cmp.Ordered](data []E, a, b int) { |
| i := a |
| j := b - 1 |
| for i < j { |
| data[i], data[j] = data[j], data[i] |
| i++ |
| j-- |
| } |
| } |
| |
| func swapRangeOrdered[E cmp.Ordered](data []E, a, b, n int) { |
| for i := 0; i < n; i++ { |
| data[a+i], data[b+i] = data[b+i], data[a+i] |
| } |
| } |
| |
| func stableOrdered[E cmp.Ordered](data []E, n int) { |
| blockSize := 20 // must be > 0 |
| a, b := 0, blockSize |
| for b <= n { |
| insertionSortOrdered(data, a, b) |
| a = b |
| b += blockSize |
| } |
| insertionSortOrdered(data, a, n) |
| |
| for blockSize < n { |
| a, b = 0, 2*blockSize |
| for b <= n { |
| symMergeOrdered(data, a, a+blockSize, b) |
| a = b |
| b += 2 * blockSize |
| } |
| if m := a + blockSize; m < n { |
| symMergeOrdered(data, a, m, n) |
| } |
| blockSize *= 2 |
| } |
| } |
| |
| // symMergeOrdered 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 symMergeOrdered[E cmp.Ordered](data []E, 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 cmp.Less(data[h], data[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[k], data[k+1] = data[k+1], data[k] |
| } |
| 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 !cmp.Less(data[m], data[h]) { |
| i = h + 1 |
| } else { |
| j = h |
| } |
| } |
| // Swap values until data[m] reaches the position i. |
| for k := m; k > i; k-- { |
| data[k], data[k-1] = data[k-1], data[k] |
| } |
| 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 !cmp.Less(data[p-c], data[c]) { |
| start = c + 1 |
| } else { |
| r = c |
| } |
| } |
| |
| end := n - start |
| if start < m && m < end { |
| rotateOrdered(data, start, m, end) |
| } |
| if a < start && start < mid { |
| symMergeOrdered(data, a, start, mid) |
| } |
| if mid < end && end < b { |
| symMergeOrdered(data, mid, end, b) |
| } |
| } |
| |
| // rotateOrdered 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 rotateOrdered[E cmp.Ordered](data []E, a, m, b int) { |
| i := m - a |
| j := b - m |
| |
| for i != j { |
| if i > j { |
| swapRangeOrdered(data, m-i, m, j) |
| i -= j |
| } else { |
| swapRangeOrdered(data, m-i, m+j-i, i) |
| j -= i |
| } |
| } |
| // i == j |
| swapRangeOrdered(data, m-i, m, i) |
| } |