go-sort

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Go排序实现在/src/go4.org/sort/sort.go中.

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func Sort(data Interface) {
	n := data.Len()
	if fs, ok := data.(*funcs); ok {
		quickSort_func(fs.lessSwap, 0, n, maxDepth(n))
	} else {
		quickSort(data, 0, n, maxDepth(n))
	}
}

func quickSort(data Interface, a, b, maxDepth int) {
	for b-a > 12 { // Use ShellSort for slices <= 12 elements
		if maxDepth == 0 {
			heapSort(data, a, b)
			return
		}
		maxDepth--
		mlo, mhi := doPivot(data, a, b)
		// Avoiding recursion on the larger subproblem guarantees
		// a stack depth of at most lg(b-a).
		if mlo-a < b-mhi {
			quickSort(data, a, mlo, maxDepth)
			a = mhi // i.e., quickSort(data, mhi, b)
		} else {
			quickSort(data, mhi, b, maxDepth)
			b = mlo // i.e., quickSort(data, a, mlo)
		}
	}
	if b-a > 1 {
		// Do ShellSort pass with gap 6
		// It could be written in this simplified form cause b-a <= 12
		for i := a + 6; i < b; i++ {
			if data.Less(i, i-6) {
				data.Swap(i, i-6)
			}
		}
		insertionSort(data, a, b)
	}
}
// 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)
		}
	}
}

quickSort和quickSort_func基本相同, 子不过自己定义的比较方法, 这里不在赘述.

可以看到主体是quickSort, 所以不保证稳定排序, 当数据量小于等于12时. 退化为希尔排序, 但希尔排序只做了一次gap为6, 之后再次退化为了简单插入排序. 这部分实现非常简单, i从前往后, j从i往前, 每次比较j-1和j, 将小的换到前面.

当数据量大于12时, 根据maxDepth是否为0决定使用对排序还是使用快速排序, maxDepth计算:

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// maxDepth returns a threshold at which quicksort should switch
// to heapsort. It returns 2*ceil(lg(n+1)).
func maxDepth(n int) int {
	var depth int
	for i := n; i > 0; i >>= 1 {
		depth++
	}
	return depth * 2
}

返回的是目前树高度的2倍. 每进行一轮快速排序的partition(doPivot), 这个数值就减1, 当减为0, 此时认为数据已经比较有序, 如果数据长度依然大于12, 改为堆排序效率更高.

这里先看快速排序的主体部分, 再来看堆排序的实现. partition是快排的思想核心, 他实现在doPivot中:

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func doPivot(data Interface, lo, hi int) (midlo, midhi int) {
	m := lo + (hi-lo)/2 // 避免整数溢出
	if hi-lo > 40 { 如果长度大于40, 使用Tukey ninther法
		// Tukey's ``Ninther,'' median of three medians of three.
		s := (hi - lo) / 8
		medianOfThree(data, lo, lo+s, lo+2*s)
		medianOfThree(data, m, m-s, m+s)
		medianOfThree(data, hi-1, hi-1-s, hi-1-2*s)
	}
    // medianOfThree 保证lo, m hi-1三个值是从小到大的
	medianOfThree(data, lo, m, hi-1)

	// Invariants are:
	//	data[lo] = pivot (set up by ChoosePivot)
	//	data[lo < i < a] < pivot
	//	data[a <= i < b] <= pivot
	//	data[b <= i < c] unexamined
	//	data[c <= i < hi-1] > pivot
	//	data[hi-1] >= pivot
	pivot := lo
	a, c := lo+1, hi-1

    // 找到第一个比起始值点大的Index
	for ; a < c && data.Less(a, pivot); a++ {
	}
	b := a
	for {
		for ; b < c && !data.Less(pivot, b); b++ { // data[b] <= pivot
		}
		for ; b < c && data.Less(pivot, c-1); c-- { // data[c-1] > pivot
		}
		if b >= c {
			break
		}
		// data[b] > pivot; data[c-1] <= pivot
		data.Swap(b, c-1)
		b++
		c--
	}
	// If hi-c<3 then there are duplicates (by property of median of nine).
	// Let be a bit more conservative, and set border to 5.
	protect := hi-c < 5
	if !protect && hi-c < (hi-lo)/4 {
		// Lets test some points for equality to pivot
		dups := 0
		if !data.Less(pivot, hi-1) { // data[hi-1] = pivot
			data.Swap(c, hi-1)
			c++
			dups++
		}
		if !data.Less(b-1, pivot) { // data[b-1] = pivot
			b--
			dups++
		}
		// m-lo = (hi-lo)/2 > 6
		// b-lo > (hi-lo)*3/4-1 > 8
		// ==> m < b ==> data[m] <= pivot
		if !data.Less(m, pivot) { // data[m] = pivot
			data.Swap(m, b-1)
			b--
			dups++
		}
		// if at least 2 points are equal to pivot, assume skewed distribution
		protect = dups > 1
	}
	if protect {
		// Protect against a lot of duplicates
		// Add invariant:
		//	data[a <= i < b] unexamined
		//	data[b <= i < c] = pivot
		for {
			for ; a < b && !data.Less(b-1, pivot); b-- { // data[b] == pivot
			}
			for ; a < b && data.Less(a, pivot); a++ { // data[a] < pivot
			}
			if a >= b {
				break
			}
			// data[a] == pivot; data[b-1] < pivot
			data.Swap(a, b-1)
			a++
			b--
		}
	}
	// Swap pivot into middle
	data.Swap(pivot, b-1)
	return b - 1, c
}
// medianOfThree moves the median of the three values data[m0], data[m1], data[m2] into data[m1].
func medianOfThree(data Interface, m1, m0, m2 int) {
	// sort 3 elements
	if data.Less(m1, m0) {
		data.Swap(m1, m0)
	}
	// data[m0] <= data[m1]
	if data.Less(m2, m1) {
		data.Swap(m2, m1)
		// data[m0] <= data[m2] && data[m1] < data[m2]
		if data.Less(m1, m0) {
			data.Swap(m1, m0)
		}
	}
	// 保证 data[m0] <= data[m1] <= data[m2]
}