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@@ -6,28 +6,28 @@
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package slices
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-// insertionSortLessFunc sorts data[a:b] using insertion sort.
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-func insertionSortLessFunc[E any](data []E, a, b int, less func(a, b E) bool) {
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+// insertionSortCmpFunc sorts data[a:b] using insertion sort.
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+func insertionSortCmpFunc[E any](data []E, a, b int, cmp func(a, b E) int) {
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for i := a + 1; i < b; i++ {
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- for j := i; j > a && less(data[j], data[j-1]); j-- {
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+ for j := i; j > a && (cmp(data[j], data[j-1]) < 0); 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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-// siftDownLessFunc implements the heap property on data[lo:hi].
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+// siftDownCmpFunc 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 siftDownLessFunc[E any](data []E, lo, hi, first int, less func(a, b E) bool) {
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+func siftDownCmpFunc[E any](data []E, lo, hi, first int, cmp func(a, b E) 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 && less(data[first+child], data[first+child+1]) {
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+ if child+1 < hi && (cmp(data[first+child], data[first+child+1]) < 0) {
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child++
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}
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- if !less(data[first+root], data[first+child]) {
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+ if !(cmp(data[first+root], data[first+child]) < 0) {
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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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@@ -35,30 +35,30 @@ func siftDownLessFunc[E any](data []E, lo, hi, first int, less func(a, b E) bool
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}
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}
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-func heapSortLessFunc[E any](data []E, a, b int, less func(a, b E) bool) {
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+func heapSortCmpFunc[E any](data []E, a, b int, cmp func(a, b E) 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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- siftDownLessFunc(data, i, hi, first, less)
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+ siftDownCmpFunc(data, i, hi, first, cmp)
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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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- siftDownLessFunc(data, lo, i, first, less)
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+ siftDownCmpFunc(data, lo, i, first, cmp)
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}
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}
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-// pdqsortLessFunc sorts data[a:b].
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+// pdqsortCmpFunc sorts data[a:b].
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// The algorithm based on pattern-defeating quicksort(pdqsort), but without the optimizations from BlockQuicksort.
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// pdqsort paper: https://arxiv.org/pdf/2106.05123.pdf
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// C++ implementation: https://github.com/orlp/pdqsort
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// Rust implementation: https://docs.rs/pdqsort/latest/pdqsort/
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// limit is the number of allowed bad (very unbalanced) pivots before falling back to heapsort.
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-func pdqsortLessFunc[E any](data []E, a, b, limit int, less func(a, b E) bool) {
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+func pdqsortCmpFunc[E any](data []E, a, b, limit int, cmp func(a, b E) int) {
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const maxInsertion = 12
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var (
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@@ -70,25 +70,25 @@ func pdqsortLessFunc[E any](data []E, a, b, limit int, less func(a, b E) bool) {
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length := b - a
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if length <= maxInsertion {
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- insertionSortLessFunc(data, a, b, less)
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+ insertionSortCmpFunc(data, a, b, cmp)
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return
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}
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// Fall back to heapsort if too many bad choices were made.
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if limit == 0 {
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- heapSortLessFunc(data, a, b, less)
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+ heapSortCmpFunc(data, a, b, cmp)
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return
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}
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// If the last partitioning was imbalanced, we need to breaking patterns.
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if !wasBalanced {
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- breakPatternsLessFunc(data, a, b, less)
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+ breakPatternsCmpFunc(data, a, b, cmp)
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limit--
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}
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- pivot, hint := choosePivotLessFunc(data, a, b, less)
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+ pivot, hint := choosePivotCmpFunc(data, a, b, cmp)
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if hint == decreasingHint {
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- reverseRangeLessFunc(data, a, b, less)
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+ reverseRangeCmpFunc(data, a, b, cmp)
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// The chosen pivot was pivot-a elements after the start of the array.
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// After reversing it is pivot-a elements before the end of the array.
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// The idea came from Rust's implementation.
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@@ -98,48 +98,48 @@ func pdqsortLessFunc[E any](data []E, a, b, limit int, less func(a, b E) bool) {
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// The slice is likely already sorted.
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if wasBalanced && wasPartitioned && hint == increasingHint {
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- if partialInsertionSortLessFunc(data, a, b, less) {
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+ if partialInsertionSortCmpFunc(data, a, b, cmp) {
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return
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}
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}
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// Probably the slice contains many duplicate elements, partition the slice into
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// elements equal to and elements greater than the pivot.
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- if a > 0 && !less(data[a-1], data[pivot]) {
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- mid := partitionEqualLessFunc(data, a, b, pivot, less)
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+ if a > 0 && !(cmp(data[a-1], data[pivot]) < 0) {
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+ mid := partitionEqualCmpFunc(data, a, b, pivot, cmp)
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a = mid
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continue
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}
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- mid, alreadyPartitioned := partitionLessFunc(data, a, b, pivot, less)
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+ mid, alreadyPartitioned := partitionCmpFunc(data, a, b, pivot, cmp)
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wasPartitioned = alreadyPartitioned
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leftLen, rightLen := mid-a, b-mid
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balanceThreshold := length / 8
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if leftLen < rightLen {
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wasBalanced = leftLen >= balanceThreshold
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- pdqsortLessFunc(data, a, mid, limit, less)
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+ pdqsortCmpFunc(data, a, mid, limit, cmp)
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a = mid + 1
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} else {
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wasBalanced = rightLen >= balanceThreshold
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- pdqsortLessFunc(data, mid+1, b, limit, less)
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+ pdqsortCmpFunc(data, mid+1, b, limit, cmp)
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b = mid
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}
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}
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}
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-// partitionLessFunc does one quicksort partition.
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+// partitionCmpFunc does one quicksort partition.
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// Let p = data[pivot]
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// Moves elements in data[a:b] around, so that data[i]<p and data[j]>=p for i<newpivot and j>newpivot.
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// On return, data[newpivot] = p
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-func partitionLessFunc[E any](data []E, a, b, pivot int, less func(a, b E) bool) (newpivot int, alreadyPartitioned bool) {
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+func partitionCmpFunc[E any](data []E, a, b, pivot int, cmp func(a, b E) int) (newpivot int, alreadyPartitioned bool) {
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data[a], data[pivot] = data[pivot], data[a]
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i, j := a+1, b-1 // i and j are inclusive of the elements remaining to be partitioned
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- for i <= j && less(data[i], data[a]) {
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+ for i <= j && (cmp(data[i], data[a]) < 0) {
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i++
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}
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- for i <= j && !less(data[j], data[a]) {
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+ for i <= j && !(cmp(data[j], data[a]) < 0) {
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j--
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}
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if i > j {
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@@ -151,10 +151,10 @@ func partitionLessFunc[E any](data []E, a, b, pivot int, less func(a, b E) bool)
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j--
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for {
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- for i <= j && less(data[i], data[a]) {
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+ for i <= j && (cmp(data[i], data[a]) < 0) {
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i++
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}
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- for i <= j && !less(data[j], data[a]) {
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+ for i <= j && !(cmp(data[j], data[a]) < 0) {
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j--
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}
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if i > j {
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@@ -168,17 +168,17 @@ func partitionLessFunc[E any](data []E, a, b, pivot int, less func(a, b E) bool)
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return j, false
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}
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-// partitionEqualLessFunc partitions data[a:b] into elements equal to data[pivot] followed by elements greater than data[pivot].
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+// partitionEqualCmpFunc partitions data[a:b] into elements equal to data[pivot] followed by elements greater than data[pivot].
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// It assumed that data[a:b] does not contain elements smaller than the data[pivot].
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-func partitionEqualLessFunc[E any](data []E, a, b, pivot int, less func(a, b E) bool) (newpivot int) {
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+func partitionEqualCmpFunc[E any](data []E, a, b, pivot int, cmp func(a, b E) int) (newpivot int) {
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data[a], data[pivot] = data[pivot], data[a]
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i, j := a+1, b-1 // i and j are inclusive of the elements remaining to be partitioned
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for {
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- for i <= j && !less(data[a], data[i]) {
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+ for i <= j && !(cmp(data[a], data[i]) < 0) {
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i++
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}
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- for i <= j && less(data[a], data[j]) {
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+ for i <= j && (cmp(data[a], data[j]) < 0) {
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j--
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}
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if i > j {
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@@ -191,15 +191,15 @@ func partitionEqualLessFunc[E any](data []E, a, b, pivot int, less func(a, b E)
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return i
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}
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-// partialInsertionSortLessFunc partially sorts a slice, returns true if the slice is sorted at the end.
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-func partialInsertionSortLessFunc[E any](data []E, a, b int, less func(a, b E) bool) bool {
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+// partialInsertionSortCmpFunc partially sorts a slice, returns true if the slice is sorted at the end.
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+func partialInsertionSortCmpFunc[E any](data []E, a, b int, cmp func(a, b E) int) bool {
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const (
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maxSteps = 5 // maximum number of adjacent out-of-order pairs that will get shifted
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shortestShifting = 50 // don't shift any elements on short arrays
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)
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i := a + 1
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for j := 0; j < maxSteps; j++ {
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- for i < b && !less(data[i], data[i-1]) {
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+ for i < b && !(cmp(data[i], data[i-1]) < 0) {
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i++
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}
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@@ -216,7 +216,7 @@ func partialInsertionSortLessFunc[E any](data []E, a, b int, less func(a, b E) b
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// Shift the smaller one to the left.
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if i-a >= 2 {
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for j := i - 1; j >= 1; j-- {
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- if !less(data[j], data[j-1]) {
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+ if !(cmp(data[j], data[j-1]) < 0) {
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break
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}
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data[j], data[j-1] = data[j-1], data[j]
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@@ -225,7 +225,7 @@ func partialInsertionSortLessFunc[E any](data []E, a, b int, less func(a, b E) b
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// Shift the greater one to the right.
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if b-i >= 2 {
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for j := i + 1; j < b; j++ {
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- if !less(data[j], data[j-1]) {
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+ if !(cmp(data[j], data[j-1]) < 0) {
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break
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}
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data[j], data[j-1] = data[j-1], data[j]
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@@ -235,9 +235,9 @@ func partialInsertionSortLessFunc[E any](data []E, a, b int, less func(a, b E) b
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return false
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}
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-// breakPatternsLessFunc scatters some elements around in an attempt to break some patterns
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+// breakPatternsCmpFunc scatters some elements around in an attempt to break some patterns
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// that might cause imbalanced partitions in quicksort.
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-func breakPatternsLessFunc[E any](data []E, a, b int, less func(a, b E) bool) {
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+func breakPatternsCmpFunc[E any](data []E, a, b int, cmp func(a, b E) int) {
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length := b - a
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if length >= 8 {
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random := xorshift(length)
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@@ -253,12 +253,12 @@ func breakPatternsLessFunc[E any](data []E, a, b int, less func(a, b E) bool) {
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}
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}
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-// choosePivotLessFunc chooses a pivot in data[a:b].
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+// choosePivotCmpFunc chooses a pivot in data[a:b].
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//
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// [0,8): chooses a static pivot.
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// [8,shortestNinther): uses the simple median-of-three method.
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// [shortestNinther,∞): uses the Tukey ninther method.
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-func choosePivotLessFunc[E any](data []E, a, b int, less func(a, b E) bool) (pivot int, hint sortedHint) {
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+func choosePivotCmpFunc[E any](data []E, a, b int, cmp func(a, b E) int) (pivot int, hint sortedHint) {
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const (
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shortestNinther = 50
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maxSwaps = 4 * 3
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@@ -276,12 +276,12 @@ func choosePivotLessFunc[E any](data []E, a, b int, less func(a, b E) bool) (piv
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if l >= 8 {
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if l >= shortestNinther {
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// Tukey ninther method, the idea came from Rust's implementation.
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- i = medianAdjacentLessFunc(data, i, &swaps, less)
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- j = medianAdjacentLessFunc(data, j, &swaps, less)
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- k = medianAdjacentLessFunc(data, k, &swaps, less)
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+ i = medianAdjacentCmpFunc(data, i, &swaps, cmp)
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+ j = medianAdjacentCmpFunc(data, j, &swaps, cmp)
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+ k = medianAdjacentCmpFunc(data, k, &swaps, cmp)
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}
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// Find the median among i, j, k and stores it into j.
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- j = medianLessFunc(data, i, j, k, &swaps, less)
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+ j = medianCmpFunc(data, i, j, k, &swaps, cmp)
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}
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switch swaps {
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@@ -294,29 +294,29 @@ func choosePivotLessFunc[E any](data []E, a, b int, less func(a, b E) bool) (piv
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}
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}
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-// order2LessFunc returns x,y where data[x] <= data[y], where x,y=a,b or x,y=b,a.
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-func order2LessFunc[E any](data []E, a, b int, swaps *int, less func(a, b E) bool) (int, int) {
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- if less(data[b], data[a]) {
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+// order2CmpFunc returns x,y where data[x] <= data[y], where x,y=a,b or x,y=b,a.
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+func order2CmpFunc[E any](data []E, a, b int, swaps *int, cmp func(a, b E) int) (int, int) {
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+ if cmp(data[b], data[a]) < 0 {
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*swaps++
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return b, a
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}
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return a, b
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}
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-// medianLessFunc returns x where data[x] is the median of data[a],data[b],data[c], where x is a, b, or c.
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-func medianLessFunc[E any](data []E, a, b, c int, swaps *int, less func(a, b E) bool) int {
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- a, b = order2LessFunc(data, a, b, swaps, less)
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- b, c = order2LessFunc(data, b, c, swaps, less)
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- a, b = order2LessFunc(data, a, b, swaps, less)
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+// medianCmpFunc returns x where data[x] is the median of data[a],data[b],data[c], where x is a, b, or c.
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+func medianCmpFunc[E any](data []E, a, b, c int, swaps *int, cmp func(a, b E) int) int {
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+ a, b = order2CmpFunc(data, a, b, swaps, cmp)
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+ b, c = order2CmpFunc(data, b, c, swaps, cmp)
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+ a, b = order2CmpFunc(data, a, b, swaps, cmp)
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return b
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}
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-// medianAdjacentLessFunc finds the median of data[a - 1], data[a], data[a + 1] and stores the index into a.
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-func medianAdjacentLessFunc[E any](data []E, a int, swaps *int, less func(a, b E) bool) int {
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- return medianLessFunc(data, a-1, a, a+1, swaps, less)
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+// medianAdjacentCmpFunc finds the median of data[a - 1], data[a], data[a + 1] and stores the index into a.
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+func medianAdjacentCmpFunc[E any](data []E, a int, swaps *int, cmp func(a, b E) int) int {
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+ return medianCmpFunc(data, a-1, a, a+1, swaps, cmp)
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}
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-func reverseRangeLessFunc[E any](data []E, a, b int, less func(a, b E) bool) {
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+func reverseRangeCmpFunc[E any](data []E, a, b int, cmp func(a, b E) int) {
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i := a
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j := b - 1
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for i < j {
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@@ -326,37 +326,37 @@ func reverseRangeLessFunc[E any](data []E, a, b int, less func(a, b E) bool) {
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}
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}
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-func swapRangeLessFunc[E any](data []E, a, b, n int, less func(a, b E) bool) {
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+func swapRangeCmpFunc[E any](data []E, a, b, n int, cmp func(a, b E) int) {
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for i := 0; i < n; i++ {
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data[a+i], data[b+i] = data[b+i], data[a+i]
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}
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}
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-func stableLessFunc[E any](data []E, n int, less func(a, b E) bool) {
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+func stableCmpFunc[E any](data []E, n int, cmp func(a, b E) int) {
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blockSize := 20 // must be > 0
|
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|
a, b := 0, blockSize
|
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|
for b <= n {
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- insertionSortLessFunc(data, a, b, less)
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|
+ insertionSortCmpFunc(data, a, b, cmp)
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a = b
|
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|
b += blockSize
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|
}
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|
- insertionSortLessFunc(data, a, n, less)
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|
+ insertionSortCmpFunc(data, a, n, cmp)
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|
|
|
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|
for blockSize < n {
|
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|
a, b = 0, 2*blockSize
|
|
|
for b <= n {
|
|
|
- symMergeLessFunc(data, a, a+blockSize, b, less)
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|
+ symMergeCmpFunc(data, a, a+blockSize, b, cmp)
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|
a = b
|
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|
b += 2 * blockSize
|
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|
}
|
|
|
if m := a + blockSize; m < n {
|
|
|
- symMergeLessFunc(data, a, m, n, less)
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|
+ symMergeCmpFunc(data, a, m, n, cmp)
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|
}
|
|
|
blockSize *= 2
|
|
|
}
|
|
|
}
|
|
|
|
|
|
-// symMergeLessFunc merges the two sorted subsequences data[a:m] and data[m:b] using
|
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|
+// symMergeCmpFunc 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
|
|
@@ -375,7 +375,7 @@ func stableLessFunc[E any](data []E, n int, less func(a, b E) bool) {
|
|
|
// symMerge assumes non-degenerate arguments: a < m && m < b.
|
|
|
// Having the caller check this condition eliminates many leaf recursion calls,
|
|
|
// which improves performance.
|
|
|
-func symMergeLessFunc[E any](data []E, a, m, b int, less func(a, b E) bool) {
|
|
|
+func symMergeCmpFunc[E any](data []E, a, m, b int, cmp func(a, b E) int) {
|
|
|
// Avoid unnecessary recursions of symMerge
|
|
|
// by direct insertion of data[a] into data[m:b]
|
|
|
// if data[a:m] only contains one element.
|
|
@@ -387,7 +387,7 @@ func symMergeLessFunc[E any](data []E, a, m, b int, less func(a, b E) bool) {
|
|
|
j := b
|
|
|
for i < j {
|
|
|
h := int(uint(i+j) >> 1)
|
|
|
- if less(data[h], data[a]) {
|
|
|
+ if cmp(data[h], data[a]) < 0 {
|
|
|
i = h + 1
|
|
|
} else {
|
|
|
j = h
|
|
@@ -411,7 +411,7 @@ func symMergeLessFunc[E any](data []E, a, m, b int, less func(a, b E) bool) {
|
|
|
j := m
|
|
|
for i < j {
|
|
|
h := int(uint(i+j) >> 1)
|
|
|
- if !less(data[m], data[h]) {
|
|
|
+ if !(cmp(data[m], data[h]) < 0) {
|
|
|
i = h + 1
|
|
|
} else {
|
|
|
j = h
|
|
@@ -438,7 +438,7 @@ func symMergeLessFunc[E any](data []E, a, m, b int, less func(a, b E) bool) {
|
|
|
|
|
|
for start < r {
|
|
|
c := int(uint(start+r) >> 1)
|
|
|
- if !less(data[p-c], data[c]) {
|
|
|
+ if !(cmp(data[p-c], data[c]) < 0) {
|
|
|
start = c + 1
|
|
|
} else {
|
|
|
r = c
|
|
@@ -447,33 +447,33 @@ func symMergeLessFunc[E any](data []E, a, m, b int, less func(a, b E) bool) {
|
|
|
|
|
|
end := n - start
|
|
|
if start < m && m < end {
|
|
|
- rotateLessFunc(data, start, m, end, less)
|
|
|
+ rotateCmpFunc(data, start, m, end, cmp)
|
|
|
}
|
|
|
if a < start && start < mid {
|
|
|
- symMergeLessFunc(data, a, start, mid, less)
|
|
|
+ symMergeCmpFunc(data, a, start, mid, cmp)
|
|
|
}
|
|
|
if mid < end && end < b {
|
|
|
- symMergeLessFunc(data, mid, end, b, less)
|
|
|
+ symMergeCmpFunc(data, mid, end, b, cmp)
|
|
|
}
|
|
|
}
|
|
|
|
|
|
-// rotateLessFunc rotates two consecutive blocks u = data[a:m] and v = data[m:b] in data:
|
|
|
+// rotateCmpFunc 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 rotateLessFunc[E any](data []E, a, m, b int, less func(a, b E) bool) {
|
|
|
+func rotateCmpFunc[E any](data []E, a, m, b int, cmp func(a, b E) int) {
|
|
|
i := m - a
|
|
|
j := b - m
|
|
|
|
|
|
for i != j {
|
|
|
if i > j {
|
|
|
- swapRangeLessFunc(data, m-i, m, j, less)
|
|
|
+ swapRangeCmpFunc(data, m-i, m, j, cmp)
|
|
|
i -= j
|
|
|
} else {
|
|
|
- swapRangeLessFunc(data, m-i, m+j-i, i, less)
|
|
|
+ swapRangeCmpFunc(data, m-i, m+j-i, i, cmp)
|
|
|
j -= i
|
|
|
}
|
|
|
}
|
|
|
// i == j
|
|
|
- swapRangeLessFunc(data, m-i, m, i, less)
|
|
|
+ swapRangeCmpFunc(data, m-i, m, i, cmp)
|
|
|
}
|