day11 | 数据结构与算法 | 第三届 ByteDance 青年营笔记

// 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)
}