202 lines
5.4 KiB
Go
202 lines
5.4 KiB
Go
// Copyright 2009 The Go Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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package flate
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// Sort sorts data.
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// It makes one call to data.Len to determine n, and O(n*log(n)) calls to
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// data.Less and data.Swap. The sort is not guaranteed to be stable.
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func sortByLiteral(data []literalNode) {
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n := len(data)
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quickSort(data, 0, n, maxDepth(n))
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}
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func quickSort(data []literalNode, a, b, maxDepth int) {
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for b-a > 12 { // Use ShellSort for slices <= 12 elements
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if maxDepth == 0 {
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heapSort(data, a, b)
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return
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}
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maxDepth--
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mlo, mhi := doPivot(data, a, b)
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// Avoiding recursion on the larger subproblem guarantees
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// a stack depth of at most lg(b-a).
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if mlo-a < b-mhi {
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quickSort(data, a, mlo, maxDepth)
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a = mhi // i.e., quickSort(data, mhi, b)
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} else {
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quickSort(data, mhi, b, maxDepth)
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b = mlo // i.e., quickSort(data, a, mlo)
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}
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}
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if b-a > 1 {
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// Do ShellSort pass with gap 6
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// It could be written in this simplified form cause b-a <= 12
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for i := a + 6; i < b; i++ {
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if data[i].literal < data[i-6].literal {
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data[i], data[i-6] = data[i-6], data[i]
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}
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}
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insertionSort(data, a, b)
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}
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}
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func heapSort(data []literalNode, a, b int) {
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first := a
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lo := 0
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hi := b - a
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// Build heap with greatest element at top.
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for i := (hi - 1) / 2; i >= 0; i-- {
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siftDown(data, i, hi, first)
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}
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// Pop elements, largest first, into end of data.
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for i := hi - 1; i >= 0; i-- {
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data[first], data[first+i] = data[first+i], data[first]
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siftDown(data, lo, i, first)
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}
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}
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// siftDown implements the heap property on data[lo, hi).
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// first is an offset into the array where the root of the heap lies.
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func siftDown(data []literalNode, lo, hi, first int) {
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root := lo
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for {
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child := 2*root + 1
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if child >= hi {
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break
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}
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if child+1 < hi && data[first+child].literal < data[first+child+1].literal {
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child++
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}
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if data[first+root].literal > data[first+child].literal {
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return
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}
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data[first+root], data[first+child] = data[first+child], data[first+root]
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root = child
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}
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}
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func doPivot(data []literalNode, lo, hi int) (midlo, midhi int) {
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m := int(uint(lo+hi) >> 1) // Written like this to avoid integer overflow.
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if hi-lo > 40 {
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// Tukey's ``Ninther,'' median of three medians of three.
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s := (hi - lo) / 8
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medianOfThree(data, lo, lo+s, lo+2*s)
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medianOfThree(data, m, m-s, m+s)
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medianOfThree(data, hi-1, hi-1-s, hi-1-2*s)
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}
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medianOfThree(data, lo, m, hi-1)
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// Invariants are:
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// data[lo] = pivot (set up by ChoosePivot)
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// data[lo < i < a] < pivot
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// data[a <= i < b] <= pivot
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// data[b <= i < c] unexamined
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// data[c <= i < hi-1] > pivot
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// data[hi-1] >= pivot
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pivot := lo
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a, c := lo+1, hi-1
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for ; a < c && data[a].literal < data[pivot].literal; a++ {
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}
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b := a
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for {
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for ; b < c && data[pivot].literal > data[b].literal; b++ { // data[b] <= pivot
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}
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for ; b < c && data[pivot].literal < data[c-1].literal; c-- { // data[c-1] > pivot
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}
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if b >= c {
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break
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}
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// data[b] > pivot; data[c-1] <= pivot
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data[b], data[c-1] = data[c-1], data[b]
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b++
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c--
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}
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// If hi-c<3 then there are duplicates (by property of median of nine).
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// Let's be a bit more conservative, and set border to 5.
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protect := hi-c < 5
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if !protect && hi-c < (hi-lo)/4 {
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// Lets test some points for equality to pivot
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dups := 0
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if data[pivot].literal > data[hi-1].literal { // data[hi-1] = pivot
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data[c], data[hi-1] = data[hi-1], data[c]
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c++
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dups++
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}
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if data[b-1].literal > data[pivot].literal { // data[b-1] = pivot
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b--
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dups++
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}
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// m-lo = (hi-lo)/2 > 6
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// b-lo > (hi-lo)*3/4-1 > 8
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// ==> m < b ==> data[m] <= pivot
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if data[m].literal > data[pivot].literal { // data[m] = pivot
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data[m], data[b-1] = data[b-1], data[m]
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b--
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dups++
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}
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// if at least 2 points are equal to pivot, assume skewed distribution
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protect = dups > 1
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}
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if protect {
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// Protect against a lot of duplicates
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// Add invariant:
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// data[a <= i < b] unexamined
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// data[b <= i < c] = pivot
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for {
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for ; a < b && data[b-1].literal > data[pivot].literal; b-- { // data[b] == pivot
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}
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for ; a < b && data[a].literal < data[pivot].literal; a++ { // data[a] < pivot
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}
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if a >= b {
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break
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}
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// data[a] == pivot; data[b-1] < pivot
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data[a], data[b-1] = data[b-1], data[a]
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a++
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b--
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}
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}
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// Swap pivot into middle
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data[pivot], data[b-1] = data[b-1], data[pivot]
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return b - 1, c
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}
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// Insertion sort
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func insertionSort(data []literalNode, a, b int) {
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for i := a + 1; i < b; i++ {
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for j := i; j > a && data[j].literal < data[j-1].literal; j-- {
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data[j], data[j-1] = data[j-1], data[j]
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}
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}
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}
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// maxDepth returns a threshold at which quicksort should switch
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// to heapsort. It returns 2*ceil(lg(n+1)).
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func maxDepth(n int) int {
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var depth int
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for i := n; i > 0; i >>= 1 {
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depth++
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}
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return depth * 2
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}
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// medianOfThree moves the median of the three values data[m0], data[m1], data[m2] into data[m1].
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func medianOfThree(data []literalNode, m1, m0, m2 int) {
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// sort 3 elements
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if data[m1].literal < data[m0].literal {
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data[m1], data[m0] = data[m0], data[m1]
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}
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// data[m0] <= data[m1]
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if data[m2].literal < data[m1].literal {
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data[m2], data[m1] = data[m1], data[m2]
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// data[m0] <= data[m2] && data[m1] < data[m2]
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if data[m1].literal < data[m0].literal {
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data[m1], data[m0] = data[m0], data[m1]
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}
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}
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// now data[m0] <= data[m1] <= data[m2]
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}
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