968 lines
20 KiB
Go
968 lines
20 KiB
Go
// Copyright 2014 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 intsets provides Sparse, a compact and fast representation
|
||
// for sparse sets of int values.
|
||
//
|
||
// The time complexity of the operations Len, Insert, Remove and Has
|
||
// is in O(n) but in practice those methods are faster and more
|
||
// space-efficient than equivalent operations on sets based on the Go
|
||
// map type. The IsEmpty, Min, Max, Clear and TakeMin operations
|
||
// require constant time.
|
||
//
|
||
package intsets // import "golang.org/x/tools/container/intsets"
|
||
|
||
// TODO(adonovan):
|
||
// - Add InsertAll(...int), RemoveAll(...int)
|
||
// - Add 'bool changed' results for {Intersection,Difference}With too.
|
||
//
|
||
// TODO(adonovan): implement Dense, a dense bit vector with a similar API.
|
||
// The space usage would be proportional to Max(), not Len(), and the
|
||
// implementation would be based upon big.Int.
|
||
//
|
||
// TODO(adonovan): experiment with making the root block indirect (nil
|
||
// iff IsEmpty). This would reduce the memory usage when empty and
|
||
// might simplify the aliasing invariants.
|
||
//
|
||
// TODO(adonovan): opt: make UnionWith and Difference faster.
|
||
// These are the hot-spots for go/pointer.
|
||
|
||
import (
|
||
"bytes"
|
||
"fmt"
|
||
)
|
||
|
||
// A Sparse is a set of int values.
|
||
// Sparse operations (even queries) are not concurrency-safe.
|
||
//
|
||
// The zero value for Sparse is a valid empty set.
|
||
//
|
||
// Sparse sets must be copied using the Copy method, not by assigning
|
||
// a Sparse value.
|
||
//
|
||
type Sparse struct {
|
||
// An uninitialized Sparse represents an empty set.
|
||
// An empty set may also be represented by
|
||
// root.next == root.prev == &root.
|
||
// In a non-empty set, root.next points to the first block and
|
||
// root.prev to the last.
|
||
// root.offset and root.bits are unused.
|
||
root block
|
||
}
|
||
|
||
type word uintptr
|
||
|
||
const (
|
||
_m = ^word(0)
|
||
bitsPerWord = 8 << (_m>>8&1 + _m>>16&1 + _m>>32&1)
|
||
bitsPerBlock = 256 // optimal value for go/pointer solver performance
|
||
wordsPerBlock = bitsPerBlock / bitsPerWord
|
||
)
|
||
|
||
// Limit values of implementation-specific int type.
|
||
const (
|
||
MaxInt = int(^uint(0) >> 1)
|
||
MinInt = -MaxInt - 1
|
||
)
|
||
|
||
// -- block ------------------------------------------------------------
|
||
|
||
// A set is represented as a circular doubly-linked list of blocks,
|
||
// each containing an offset and a bit array of fixed size
|
||
// bitsPerBlock; the blocks are ordered by increasing offset.
|
||
//
|
||
// The set contains an element x iff the block whose offset is x - (x
|
||
// mod bitsPerBlock) has the bit (x mod bitsPerBlock) set, where mod
|
||
// is the Euclidean remainder.
|
||
//
|
||
// A block may only be empty transiently.
|
||
//
|
||
type block struct {
|
||
offset int // offset mod bitsPerBlock == 0
|
||
bits [wordsPerBlock]word // contains at least one set bit
|
||
next, prev *block // doubly-linked list of blocks
|
||
}
|
||
|
||
// wordMask returns the word index (in block.bits)
|
||
// and single-bit mask for the block's ith bit.
|
||
func wordMask(i uint) (w uint, mask word) {
|
||
w = i / bitsPerWord
|
||
mask = 1 << (i % bitsPerWord)
|
||
return
|
||
}
|
||
|
||
// insert sets the block b's ith bit and
|
||
// returns true if it was not already set.
|
||
//
|
||
func (b *block) insert(i uint) bool {
|
||
w, mask := wordMask(i)
|
||
if b.bits[w]&mask == 0 {
|
||
b.bits[w] |= mask
|
||
return true
|
||
}
|
||
return false
|
||
}
|
||
|
||
// remove clears the block's ith bit and
|
||
// returns true if the bit was previously set.
|
||
// NB: may leave the block empty.
|
||
//
|
||
func (b *block) remove(i uint) bool {
|
||
w, mask := wordMask(i)
|
||
if b.bits[w]&mask != 0 {
|
||
b.bits[w] &^= mask
|
||
return true
|
||
}
|
||
return false
|
||
}
|
||
|
||
// has reports whether the block's ith bit is set.
|
||
func (b *block) has(i uint) bool {
|
||
w, mask := wordMask(i)
|
||
return b.bits[w]&mask != 0
|
||
}
|
||
|
||
// empty reports whether b.len()==0, but more efficiently.
|
||
func (b *block) empty() bool {
|
||
for _, w := range b.bits {
|
||
if w != 0 {
|
||
return false
|
||
}
|
||
}
|
||
return true
|
||
}
|
||
|
||
// len returns the number of set bits in block b.
|
||
func (b *block) len() int {
|
||
var l int
|
||
for _, w := range b.bits {
|
||
l += popcount(w)
|
||
}
|
||
return l
|
||
}
|
||
|
||
// max returns the maximum element of the block.
|
||
// The block must not be empty.
|
||
//
|
||
func (b *block) max() int {
|
||
bi := b.offset + bitsPerBlock
|
||
// Decrement bi by number of high zeros in last.bits.
|
||
for i := len(b.bits) - 1; i >= 0; i-- {
|
||
if w := b.bits[i]; w != 0 {
|
||
return bi - nlz(w) - 1
|
||
}
|
||
bi -= bitsPerWord
|
||
}
|
||
panic("BUG: empty block")
|
||
}
|
||
|
||
// min returns the minimum element of the block,
|
||
// and also removes it if take is set.
|
||
// The block must not be initially empty.
|
||
// NB: may leave the block empty.
|
||
//
|
||
func (b *block) min(take bool) int {
|
||
for i, w := range b.bits {
|
||
if w != 0 {
|
||
tz := ntz(w)
|
||
if take {
|
||
b.bits[i] = w &^ (1 << uint(tz))
|
||
}
|
||
return b.offset + int(i*bitsPerWord) + tz
|
||
}
|
||
}
|
||
panic("BUG: empty block")
|
||
}
|
||
|
||
// forEach calls f for each element of block b.
|
||
// f must not mutate b's enclosing Sparse.
|
||
func (b *block) forEach(f func(int)) {
|
||
for i, w := range b.bits {
|
||
offset := b.offset + i*bitsPerWord
|
||
for bi := 0; w != 0 && bi < bitsPerWord; bi++ {
|
||
if w&1 != 0 {
|
||
f(offset)
|
||
}
|
||
offset++
|
||
w >>= 1
|
||
}
|
||
}
|
||
}
|
||
|
||
// offsetAndBitIndex returns the offset of the block that would
|
||
// contain x and the bit index of x within that block.
|
||
//
|
||
func offsetAndBitIndex(x int) (int, uint) {
|
||
mod := x % bitsPerBlock
|
||
if mod < 0 {
|
||
// Euclidean (non-negative) remainder
|
||
mod += bitsPerBlock
|
||
}
|
||
return x - mod, uint(mod)
|
||
}
|
||
|
||
// -- Sparse --------------------------------------------------------------
|
||
|
||
// start returns the root's next block, which is the root block
|
||
// (if s.IsEmpty()) or the first true block otherwise.
|
||
// start has the side effect of ensuring that s is properly
|
||
// initialized.
|
||
//
|
||
func (s *Sparse) start() *block {
|
||
root := &s.root
|
||
if root.next == nil {
|
||
root.next = root
|
||
root.prev = root
|
||
} else if root.next.prev != root {
|
||
// Copying a Sparse x leads to pernicious corruption: the
|
||
// new Sparse y shares the old linked list, but iteration
|
||
// on y will never encounter &y.root so it goes into a
|
||
// loop. Fail fast before this occurs.
|
||
panic("A Sparse has been copied without (*Sparse).Copy()")
|
||
}
|
||
|
||
return root.next
|
||
}
|
||
|
||
// IsEmpty reports whether the set s is empty.
|
||
func (s *Sparse) IsEmpty() bool {
|
||
return s.start() == &s.root
|
||
}
|
||
|
||
// Len returns the number of elements in the set s.
|
||
func (s *Sparse) Len() int {
|
||
var l int
|
||
for b := s.start(); b != &s.root; b = b.next {
|
||
l += b.len()
|
||
}
|
||
return l
|
||
}
|
||
|
||
// Max returns the maximum element of the set s, or MinInt if s is empty.
|
||
func (s *Sparse) Max() int {
|
||
if s.IsEmpty() {
|
||
return MinInt
|
||
}
|
||
return s.root.prev.max()
|
||
}
|
||
|
||
// Min returns the minimum element of the set s, or MaxInt if s is empty.
|
||
func (s *Sparse) Min() int {
|
||
if s.IsEmpty() {
|
||
return MaxInt
|
||
}
|
||
return s.root.next.min(false)
|
||
}
|
||
|
||
// block returns the block that would contain offset,
|
||
// or nil if s contains no such block.
|
||
//
|
||
func (s *Sparse) block(offset int) *block {
|
||
b := s.start()
|
||
for b != &s.root && b.offset <= offset {
|
||
if b.offset == offset {
|
||
return b
|
||
}
|
||
b = b.next
|
||
}
|
||
return nil
|
||
}
|
||
|
||
// Insert adds x to the set s, and reports whether the set grew.
|
||
func (s *Sparse) Insert(x int) bool {
|
||
offset, i := offsetAndBitIndex(x)
|
||
b := s.start()
|
||
for b != &s.root && b.offset <= offset {
|
||
if b.offset == offset {
|
||
return b.insert(i)
|
||
}
|
||
b = b.next
|
||
}
|
||
|
||
// Insert new block before b.
|
||
new := &block{offset: offset}
|
||
new.next = b
|
||
new.prev = b.prev
|
||
new.prev.next = new
|
||
new.next.prev = new
|
||
return new.insert(i)
|
||
}
|
||
|
||
func (s *Sparse) removeBlock(b *block) {
|
||
b.prev.next = b.next
|
||
b.next.prev = b.prev
|
||
}
|
||
|
||
// Remove removes x from the set s, and reports whether the set shrank.
|
||
func (s *Sparse) Remove(x int) bool {
|
||
offset, i := offsetAndBitIndex(x)
|
||
if b := s.block(offset); b != nil {
|
||
if !b.remove(i) {
|
||
return false
|
||
}
|
||
if b.empty() {
|
||
s.removeBlock(b)
|
||
}
|
||
return true
|
||
}
|
||
return false
|
||
}
|
||
|
||
// Clear removes all elements from the set s.
|
||
func (s *Sparse) Clear() {
|
||
s.root.next = &s.root
|
||
s.root.prev = &s.root
|
||
}
|
||
|
||
// If set s is non-empty, TakeMin sets *p to the minimum element of
|
||
// the set s, removes that element from the set and returns true.
|
||
// Otherwise, it returns false and *p is undefined.
|
||
//
|
||
// This method may be used for iteration over a worklist like so:
|
||
//
|
||
// var x int
|
||
// for worklist.TakeMin(&x) { use(x) }
|
||
//
|
||
func (s *Sparse) TakeMin(p *int) bool {
|
||
head := s.start()
|
||
if head == &s.root {
|
||
return false
|
||
}
|
||
*p = head.min(true)
|
||
if head.empty() {
|
||
s.removeBlock(head)
|
||
}
|
||
return true
|
||
}
|
||
|
||
// Has reports whether x is an element of the set s.
|
||
func (s *Sparse) Has(x int) bool {
|
||
offset, i := offsetAndBitIndex(x)
|
||
if b := s.block(offset); b != nil {
|
||
return b.has(i)
|
||
}
|
||
return false
|
||
}
|
||
|
||
// forEach applies function f to each element of the set s in order.
|
||
//
|
||
// f must not mutate s. Consequently, forEach is not safe to expose
|
||
// to clients. In any case, using "range s.AppendTo()" allows more
|
||
// natural control flow with continue/break/return.
|
||
//
|
||
func (s *Sparse) forEach(f func(int)) {
|
||
for b := s.start(); b != &s.root; b = b.next {
|
||
b.forEach(f)
|
||
}
|
||
}
|
||
|
||
// Copy sets s to the value of x.
|
||
func (s *Sparse) Copy(x *Sparse) {
|
||
if s == x {
|
||
return
|
||
}
|
||
|
||
xb := x.start()
|
||
sb := s.start()
|
||
for xb != &x.root {
|
||
if sb == &s.root {
|
||
sb = s.insertBlockBefore(sb)
|
||
}
|
||
sb.offset = xb.offset
|
||
sb.bits = xb.bits
|
||
xb = xb.next
|
||
sb = sb.next
|
||
}
|
||
s.discardTail(sb)
|
||
}
|
||
|
||
// insertBlockBefore returns a new block, inserting it before next.
|
||
func (s *Sparse) insertBlockBefore(next *block) *block {
|
||
b := new(block)
|
||
b.next = next
|
||
b.prev = next.prev
|
||
b.prev.next = b
|
||
next.prev = b
|
||
return b
|
||
}
|
||
|
||
// discardTail removes block b and all its successors from s.
|
||
func (s *Sparse) discardTail(b *block) {
|
||
if b != &s.root {
|
||
b.prev.next = &s.root
|
||
s.root.prev = b.prev
|
||
}
|
||
}
|
||
|
||
// IntersectionWith sets s to the intersection s ∩ x.
|
||
func (s *Sparse) IntersectionWith(x *Sparse) {
|
||
if s == x {
|
||
return
|
||
}
|
||
|
||
xb := x.start()
|
||
sb := s.start()
|
||
for xb != &x.root && sb != &s.root {
|
||
switch {
|
||
case xb.offset < sb.offset:
|
||
xb = xb.next
|
||
|
||
case xb.offset > sb.offset:
|
||
sb = sb.next
|
||
s.removeBlock(sb.prev)
|
||
|
||
default:
|
||
var sum word
|
||
for i := range sb.bits {
|
||
r := xb.bits[i] & sb.bits[i]
|
||
sb.bits[i] = r
|
||
sum |= r
|
||
}
|
||
if sum != 0 {
|
||
sb = sb.next
|
||
} else {
|
||
// sb will be overwritten or removed
|
||
}
|
||
|
||
xb = xb.next
|
||
}
|
||
}
|
||
|
||
s.discardTail(sb)
|
||
}
|
||
|
||
// Intersection sets s to the intersection x ∩ y.
|
||
func (s *Sparse) Intersection(x, y *Sparse) {
|
||
switch {
|
||
case s == x:
|
||
s.IntersectionWith(y)
|
||
return
|
||
case s == y:
|
||
s.IntersectionWith(x)
|
||
return
|
||
case x == y:
|
||
s.Copy(x)
|
||
return
|
||
}
|
||
|
||
xb := x.start()
|
||
yb := y.start()
|
||
sb := s.start()
|
||
for xb != &x.root && yb != &y.root {
|
||
switch {
|
||
case xb.offset < yb.offset:
|
||
xb = xb.next
|
||
continue
|
||
case xb.offset > yb.offset:
|
||
yb = yb.next
|
||
continue
|
||
}
|
||
|
||
if sb == &s.root {
|
||
sb = s.insertBlockBefore(sb)
|
||
}
|
||
sb.offset = xb.offset
|
||
|
||
var sum word
|
||
for i := range sb.bits {
|
||
r := xb.bits[i] & yb.bits[i]
|
||
sb.bits[i] = r
|
||
sum |= r
|
||
}
|
||
if sum != 0 {
|
||
sb = sb.next
|
||
} else {
|
||
// sb will be overwritten or removed
|
||
}
|
||
|
||
xb = xb.next
|
||
yb = yb.next
|
||
}
|
||
|
||
s.discardTail(sb)
|
||
}
|
||
|
||
// Intersects reports whether s ∩ x ≠ ∅.
|
||
func (s *Sparse) Intersects(x *Sparse) bool {
|
||
sb := s.start()
|
||
xb := x.start()
|
||
for sb != &s.root && xb != &x.root {
|
||
switch {
|
||
case xb.offset < sb.offset:
|
||
xb = xb.next
|
||
case xb.offset > sb.offset:
|
||
sb = sb.next
|
||
default:
|
||
for i := range sb.bits {
|
||
if sb.bits[i]&xb.bits[i] != 0 {
|
||
return true
|
||
}
|
||
}
|
||
sb = sb.next
|
||
xb = xb.next
|
||
}
|
||
}
|
||
return false
|
||
}
|
||
|
||
// UnionWith sets s to the union s ∪ x, and reports whether s grew.
|
||
func (s *Sparse) UnionWith(x *Sparse) bool {
|
||
if s == x {
|
||
return false
|
||
}
|
||
|
||
var changed bool
|
||
xb := x.start()
|
||
sb := s.start()
|
||
for xb != &x.root {
|
||
if sb != &s.root && sb.offset == xb.offset {
|
||
for i := range xb.bits {
|
||
if sb.bits[i] != xb.bits[i] {
|
||
sb.bits[i] |= xb.bits[i]
|
||
changed = true
|
||
}
|
||
}
|
||
xb = xb.next
|
||
} else if sb == &s.root || sb.offset > xb.offset {
|
||
sb = s.insertBlockBefore(sb)
|
||
sb.offset = xb.offset
|
||
sb.bits = xb.bits
|
||
changed = true
|
||
|
||
xb = xb.next
|
||
}
|
||
sb = sb.next
|
||
}
|
||
return changed
|
||
}
|
||
|
||
// Union sets s to the union x ∪ y.
|
||
func (s *Sparse) Union(x, y *Sparse) {
|
||
switch {
|
||
case x == y:
|
||
s.Copy(x)
|
||
return
|
||
case s == x:
|
||
s.UnionWith(y)
|
||
return
|
||
case s == y:
|
||
s.UnionWith(x)
|
||
return
|
||
}
|
||
|
||
xb := x.start()
|
||
yb := y.start()
|
||
sb := s.start()
|
||
for xb != &x.root || yb != &y.root {
|
||
if sb == &s.root {
|
||
sb = s.insertBlockBefore(sb)
|
||
}
|
||
switch {
|
||
case yb == &y.root || (xb != &x.root && xb.offset < yb.offset):
|
||
sb.offset = xb.offset
|
||
sb.bits = xb.bits
|
||
xb = xb.next
|
||
|
||
case xb == &x.root || (yb != &y.root && yb.offset < xb.offset):
|
||
sb.offset = yb.offset
|
||
sb.bits = yb.bits
|
||
yb = yb.next
|
||
|
||
default:
|
||
sb.offset = xb.offset
|
||
for i := range xb.bits {
|
||
sb.bits[i] = xb.bits[i] | yb.bits[i]
|
||
}
|
||
xb = xb.next
|
||
yb = yb.next
|
||
}
|
||
sb = sb.next
|
||
}
|
||
|
||
s.discardTail(sb)
|
||
}
|
||
|
||
// DifferenceWith sets s to the difference s ∖ x.
|
||
func (s *Sparse) DifferenceWith(x *Sparse) {
|
||
if s == x {
|
||
s.Clear()
|
||
return
|
||
}
|
||
|
||
xb := x.start()
|
||
sb := s.start()
|
||
for xb != &x.root && sb != &s.root {
|
||
switch {
|
||
case xb.offset > sb.offset:
|
||
sb = sb.next
|
||
|
||
case xb.offset < sb.offset:
|
||
xb = xb.next
|
||
|
||
default:
|
||
var sum word
|
||
for i := range sb.bits {
|
||
r := sb.bits[i] & ^xb.bits[i]
|
||
sb.bits[i] = r
|
||
sum |= r
|
||
}
|
||
sb = sb.next
|
||
xb = xb.next
|
||
|
||
if sum == 0 {
|
||
s.removeBlock(sb.prev)
|
||
}
|
||
}
|
||
}
|
||
}
|
||
|
||
// Difference sets s to the difference x ∖ y.
|
||
func (s *Sparse) Difference(x, y *Sparse) {
|
||
switch {
|
||
case x == y:
|
||
s.Clear()
|
||
return
|
||
case s == x:
|
||
s.DifferenceWith(y)
|
||
return
|
||
case s == y:
|
||
var y2 Sparse
|
||
y2.Copy(y)
|
||
s.Difference(x, &y2)
|
||
return
|
||
}
|
||
|
||
xb := x.start()
|
||
yb := y.start()
|
||
sb := s.start()
|
||
for xb != &x.root && yb != &y.root {
|
||
if xb.offset > yb.offset {
|
||
// y has block, x has none
|
||
yb = yb.next
|
||
continue
|
||
}
|
||
|
||
if sb == &s.root {
|
||
sb = s.insertBlockBefore(sb)
|
||
}
|
||
sb.offset = xb.offset
|
||
|
||
switch {
|
||
case xb.offset < yb.offset:
|
||
// x has block, y has none
|
||
sb.bits = xb.bits
|
||
|
||
sb = sb.next
|
||
|
||
default:
|
||
// x and y have corresponding blocks
|
||
var sum word
|
||
for i := range sb.bits {
|
||
r := xb.bits[i] & ^yb.bits[i]
|
||
sb.bits[i] = r
|
||
sum |= r
|
||
}
|
||
if sum != 0 {
|
||
sb = sb.next
|
||
} else {
|
||
// sb will be overwritten or removed
|
||
}
|
||
|
||
yb = yb.next
|
||
}
|
||
xb = xb.next
|
||
}
|
||
|
||
for xb != &x.root {
|
||
if sb == &s.root {
|
||
sb = s.insertBlockBefore(sb)
|
||
}
|
||
sb.offset = xb.offset
|
||
sb.bits = xb.bits
|
||
sb = sb.next
|
||
|
||
xb = xb.next
|
||
}
|
||
|
||
s.discardTail(sb)
|
||
}
|
||
|
||
// SymmetricDifferenceWith sets s to the symmetric difference s ∆ x.
|
||
func (s *Sparse) SymmetricDifferenceWith(x *Sparse) {
|
||
if s == x {
|
||
s.Clear()
|
||
return
|
||
}
|
||
|
||
sb := s.start()
|
||
xb := x.start()
|
||
for xb != &x.root && sb != &s.root {
|
||
switch {
|
||
case sb.offset < xb.offset:
|
||
sb = sb.next
|
||
case xb.offset < sb.offset:
|
||
nb := s.insertBlockBefore(sb)
|
||
nb.offset = xb.offset
|
||
nb.bits = xb.bits
|
||
xb = xb.next
|
||
default:
|
||
var sum word
|
||
for i := range sb.bits {
|
||
r := sb.bits[i] ^ xb.bits[i]
|
||
sb.bits[i] = r
|
||
sum |= r
|
||
}
|
||
sb = sb.next
|
||
xb = xb.next
|
||
if sum == 0 {
|
||
s.removeBlock(sb.prev)
|
||
}
|
||
}
|
||
}
|
||
|
||
for xb != &x.root { // append the tail of x to s
|
||
sb = s.insertBlockBefore(sb)
|
||
sb.offset = xb.offset
|
||
sb.bits = xb.bits
|
||
sb = sb.next
|
||
xb = xb.next
|
||
}
|
||
}
|
||
|
||
// SymmetricDifference sets s to the symmetric difference x ∆ y.
|
||
func (s *Sparse) SymmetricDifference(x, y *Sparse) {
|
||
switch {
|
||
case x == y:
|
||
s.Clear()
|
||
return
|
||
case s == x:
|
||
s.SymmetricDifferenceWith(y)
|
||
return
|
||
case s == y:
|
||
s.SymmetricDifferenceWith(x)
|
||
return
|
||
}
|
||
|
||
sb := s.start()
|
||
xb := x.start()
|
||
yb := y.start()
|
||
for xb != &x.root && yb != &y.root {
|
||
if sb == &s.root {
|
||
sb = s.insertBlockBefore(sb)
|
||
}
|
||
switch {
|
||
case yb.offset < xb.offset:
|
||
sb.offset = yb.offset
|
||
sb.bits = yb.bits
|
||
sb = sb.next
|
||
yb = yb.next
|
||
case xb.offset < yb.offset:
|
||
sb.offset = xb.offset
|
||
sb.bits = xb.bits
|
||
sb = sb.next
|
||
xb = xb.next
|
||
default:
|
||
var sum word
|
||
for i := range sb.bits {
|
||
r := xb.bits[i] ^ yb.bits[i]
|
||
sb.bits[i] = r
|
||
sum |= r
|
||
}
|
||
if sum != 0 {
|
||
sb.offset = xb.offset
|
||
sb = sb.next
|
||
}
|
||
xb = xb.next
|
||
yb = yb.next
|
||
}
|
||
}
|
||
|
||
for xb != &x.root { // append the tail of x to s
|
||
if sb == &s.root {
|
||
sb = s.insertBlockBefore(sb)
|
||
}
|
||
sb.offset = xb.offset
|
||
sb.bits = xb.bits
|
||
sb = sb.next
|
||
xb = xb.next
|
||
}
|
||
|
||
for yb != &y.root { // append the tail of y to s
|
||
if sb == &s.root {
|
||
sb = s.insertBlockBefore(sb)
|
||
}
|
||
sb.offset = yb.offset
|
||
sb.bits = yb.bits
|
||
sb = sb.next
|
||
yb = yb.next
|
||
}
|
||
|
||
s.discardTail(sb)
|
||
}
|
||
|
||
// SubsetOf reports whether s ∖ x = ∅.
|
||
func (s *Sparse) SubsetOf(x *Sparse) bool {
|
||
if s == x {
|
||
return true
|
||
}
|
||
|
||
sb := s.start()
|
||
xb := x.start()
|
||
for sb != &s.root {
|
||
switch {
|
||
case xb == &x.root || xb.offset > sb.offset:
|
||
return false
|
||
case xb.offset < sb.offset:
|
||
xb = xb.next
|
||
default:
|
||
for i := range sb.bits {
|
||
if sb.bits[i]&^xb.bits[i] != 0 {
|
||
return false
|
||
}
|
||
}
|
||
sb = sb.next
|
||
xb = xb.next
|
||
}
|
||
}
|
||
return true
|
||
}
|
||
|
||
// Equals reports whether the sets s and t have the same elements.
|
||
func (s *Sparse) Equals(t *Sparse) bool {
|
||
if s == t {
|
||
return true
|
||
}
|
||
sb := s.start()
|
||
tb := t.start()
|
||
for {
|
||
switch {
|
||
case sb == &s.root && tb == &t.root:
|
||
return true
|
||
case sb == &s.root || tb == &t.root:
|
||
return false
|
||
case sb.offset != tb.offset:
|
||
return false
|
||
case sb.bits != tb.bits:
|
||
return false
|
||
}
|
||
|
||
sb = sb.next
|
||
tb = tb.next
|
||
}
|
||
}
|
||
|
||
// String returns a human-readable description of the set s.
|
||
func (s *Sparse) String() string {
|
||
var buf bytes.Buffer
|
||
buf.WriteByte('{')
|
||
s.forEach(func(x int) {
|
||
if buf.Len() > 1 {
|
||
buf.WriteByte(' ')
|
||
}
|
||
fmt.Fprintf(&buf, "%d", x)
|
||
})
|
||
buf.WriteByte('}')
|
||
return buf.String()
|
||
}
|
||
|
||
// BitString returns the set as a string of 1s and 0s denoting the sum
|
||
// of the i'th powers of 2, for each i in s. A radix point, always
|
||
// preceded by a digit, appears if the sum is non-integral.
|
||
//
|
||
// Examples:
|
||
// {}.BitString() = "0"
|
||
// {4,5}.BitString() = "110000"
|
||
// {-3}.BitString() = "0.001"
|
||
// {-3,0,4,5}.BitString() = "110001.001"
|
||
//
|
||
func (s *Sparse) BitString() string {
|
||
if s.IsEmpty() {
|
||
return "0"
|
||
}
|
||
|
||
min, max := s.Min(), s.Max()
|
||
var nbytes int
|
||
if max > 0 {
|
||
nbytes = max
|
||
}
|
||
nbytes++ // zero bit
|
||
radix := nbytes
|
||
if min < 0 {
|
||
nbytes += len(".") - min
|
||
}
|
||
|
||
b := make([]byte, nbytes)
|
||
for i := range b {
|
||
b[i] = '0'
|
||
}
|
||
if radix < nbytes {
|
||
b[radix] = '.'
|
||
}
|
||
s.forEach(func(x int) {
|
||
if x >= 0 {
|
||
x += len(".")
|
||
}
|
||
b[radix-x] = '1'
|
||
})
|
||
return string(b)
|
||
}
|
||
|
||
// GoString returns a string showing the internal representation of
|
||
// the set s.
|
||
//
|
||
func (s *Sparse) GoString() string {
|
||
var buf bytes.Buffer
|
||
for b := s.start(); b != &s.root; b = b.next {
|
||
fmt.Fprintf(&buf, "block %p {offset=%d next=%p prev=%p",
|
||
b, b.offset, b.next, b.prev)
|
||
for _, w := range b.bits {
|
||
fmt.Fprintf(&buf, " 0%016x", w)
|
||
}
|
||
fmt.Fprintf(&buf, "}\n")
|
||
}
|
||
return buf.String()
|
||
}
|
||
|
||
// AppendTo returns the result of appending the elements of s to slice
|
||
// in order.
|
||
func (s *Sparse) AppendTo(slice []int) []int {
|
||
s.forEach(func(x int) {
|
||
slice = append(slice, x)
|
||
})
|
||
return slice
|
||
}
|
||
|
||
// -- Testing/debugging ------------------------------------------------
|
||
|
||
// check returns an error if the representation invariants of s are violated.
|
||
func (s *Sparse) check() error {
|
||
if !s.root.empty() {
|
||
return fmt.Errorf("non-empty root block")
|
||
}
|
||
if s.root.offset != 0 {
|
||
return fmt.Errorf("root block has non-zero offset %d", s.root.offset)
|
||
}
|
||
for b := s.start(); b != &s.root; b = b.next {
|
||
if b.offset%bitsPerBlock != 0 {
|
||
return fmt.Errorf("bad offset modulo: %d", b.offset)
|
||
}
|
||
if b.empty() {
|
||
return fmt.Errorf("empty block")
|
||
}
|
||
if b.prev.next != b {
|
||
return fmt.Errorf("bad prev.next link")
|
||
}
|
||
if b.next.prev != b {
|
||
return fmt.Errorf("bad next.prev link")
|
||
}
|
||
if b.prev != &s.root {
|
||
if b.offset <= b.prev.offset {
|
||
return fmt.Errorf("bad offset order: b.offset=%d, prev.offset=%d",
|
||
b.offset, b.prev.offset)
|
||
}
|
||
}
|
||
}
|
||
return nil
|
||
}
|