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@@ -1,1091 +0,0 @@
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-// Copyright 2014 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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-
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-// Package intsets provides Sparse, a compact and fast representation
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-// for sparse sets of int values.
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-//
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-// The time complexity of the operations Len, Insert, Remove and Has
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-// is in O(n) but in practice those methods are faster and more
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-// space-efficient than equivalent operations on sets based on the Go
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-// map type. The IsEmpty, Min, Max, Clear and TakeMin operations
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-// require constant time.
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-//
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-package intsets // import "golang.org/x/tools/container/intsets"
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-
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-// TODO(adonovan):
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-// - Add InsertAll(...int), RemoveAll(...int)
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-// - Add 'bool changed' results for {Intersection,Difference}With too.
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-//
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-// TODO(adonovan): implement Dense, a dense bit vector with a similar API.
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-// The space usage would be proportional to Max(), not Len(), and the
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-// implementation would be based upon big.Int.
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-//
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-// TODO(adonovan): opt: make UnionWith and Difference faster.
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-// These are the hot-spots for go/pointer.
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-
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-import (
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- "bytes"
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- "fmt"
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-)
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-
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-// A Sparse is a set of int values.
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-// Sparse operations (even queries) are not concurrency-safe.
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-//
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-// The zero value for Sparse is a valid empty set.
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-//
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-// Sparse sets must be copied using the Copy method, not by assigning
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-// a Sparse value.
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-//
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-type Sparse struct {
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- // An uninitialized Sparse represents an empty set.
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- // An empty set may also be represented by
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- // root.next == root.prev == &root.
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- //
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- // The root is always the block with the smallest offset.
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- // It can be empty, but only if it is the only block; in that case, offset is
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- // MaxInt (which is not a valid offset).
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- root block
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-}
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-
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-type word uintptr
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-
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-const (
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- _m = ^word(0)
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- bitsPerWord = 8 << (_m>>8&1 + _m>>16&1 + _m>>32&1)
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- bitsPerBlock = 256 // optimal value for go/pointer solver performance
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- wordsPerBlock = bitsPerBlock / bitsPerWord
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-)
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-
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-// Limit values of implementation-specific int type.
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-const (
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- MaxInt = int(^uint(0) >> 1)
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- MinInt = -MaxInt - 1
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-)
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-
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-// -- block ------------------------------------------------------------
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-
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-// A set is represented as a circular doubly-linked list of blocks,
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-// each containing an offset and a bit array of fixed size
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-// bitsPerBlock; the blocks are ordered by increasing offset.
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-//
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-// The set contains an element x iff the block whose offset is x - (x
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-// mod bitsPerBlock) has the bit (x mod bitsPerBlock) set, where mod
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-// is the Euclidean remainder.
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-//
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-// A block may only be empty transiently.
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-//
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-type block struct {
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- offset int // offset mod bitsPerBlock == 0
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- bits [wordsPerBlock]word // contains at least one set bit
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- next, prev *block // doubly-linked list of blocks
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-}
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-
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-// wordMask returns the word index (in block.bits)
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-// and single-bit mask for the block's ith bit.
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-func wordMask(i uint) (w uint, mask word) {
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- w = i / bitsPerWord
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- mask = 1 << (i % bitsPerWord)
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- return
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-}
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-
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-// insert sets the block b's ith bit and
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-// returns true if it was not already set.
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-//
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-func (b *block) insert(i uint) bool {
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- w, mask := wordMask(i)
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- if b.bits[w]&mask == 0 {
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- b.bits[w] |= mask
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- return true
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- }
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- return false
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-}
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-
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-// remove clears the block's ith bit and
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-// returns true if the bit was previously set.
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-// NB: may leave the block empty.
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-//
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-func (b *block) remove(i uint) bool {
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- w, mask := wordMask(i)
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- if b.bits[w]&mask != 0 {
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- b.bits[w] &^= mask
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- return true
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- }
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- return false
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-}
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-
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-// has reports whether the block's ith bit is set.
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-func (b *block) has(i uint) bool {
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- w, mask := wordMask(i)
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- return b.bits[w]&mask != 0
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-}
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-
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-// empty reports whether b.len()==0, but more efficiently.
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-func (b *block) empty() bool {
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- for _, w := range b.bits {
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- if w != 0 {
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- return false
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- }
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- }
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- return true
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-}
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-
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-// len returns the number of set bits in block b.
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-func (b *block) len() int {
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- var l int
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- for _, w := range b.bits {
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- l += popcount(w)
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- }
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- return l
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-}
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-
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-// max returns the maximum element of the block.
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-// The block must not be empty.
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-func (b *block) max() int {
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- bi := b.offset + bitsPerBlock
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- // Decrement bi by number of high zeros in last.bits.
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- for i := len(b.bits) - 1; i >= 0; i-- {
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- if w := b.bits[i]; w != 0 {
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- return bi - nlz(w) - 1
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- }
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- bi -= bitsPerWord
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- }
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- panic("BUG: empty block")
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-}
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-
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-// min returns the minimum element of the block,
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-// and also removes it if take is set.
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-// The block must not be initially empty.
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-// NB: may leave the block empty.
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-func (b *block) min(take bool) int {
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- for i, w := range b.bits {
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- if w != 0 {
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- tz := ntz(w)
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- if take {
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- b.bits[i] = w &^ (1 << uint(tz))
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- }
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- return b.offset + int(i*bitsPerWord) + tz
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- }
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- }
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- panic("BUG: empty block")
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-}
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-
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-// lowerBound returns the smallest element of the block that is greater than or
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-// equal to the element corresponding to the ith bit. If there is no such
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-// element, the second return value is false.
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-func (b *block) lowerBound(i uint) (int, bool) {
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- w := i / bitsPerWord
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- bit := i % bitsPerWord
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-
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- if val := b.bits[w] >> bit; val != 0 {
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- return b.offset + int(i) + ntz(val), true
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- }
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-
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- for w++; w < wordsPerBlock; w++ {
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- if val := b.bits[w]; val != 0 {
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- return b.offset + int(w*bitsPerWord) + ntz(val), true
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- }
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- }
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-
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- return 0, false
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-}
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-
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-// forEach calls f for each element of block b.
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-// f must not mutate b's enclosing Sparse.
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-func (b *block) forEach(f func(int)) {
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- for i, w := range b.bits {
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- offset := b.offset + i*bitsPerWord
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- for bi := 0; w != 0 && bi < bitsPerWord; bi++ {
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- if w&1 != 0 {
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- f(offset)
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- }
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- offset++
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- w >>= 1
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- }
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- }
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-}
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-
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-// offsetAndBitIndex returns the offset of the block that would
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-// contain x and the bit index of x within that block.
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-//
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-func offsetAndBitIndex(x int) (int, uint) {
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- mod := x % bitsPerBlock
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- if mod < 0 {
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- // Euclidean (non-negative) remainder
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- mod += bitsPerBlock
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- }
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- return x - mod, uint(mod)
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-}
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-
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-// -- Sparse --------------------------------------------------------------
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-
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-// none is a shared, empty, sentinel block that indicates the end of a block
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-// list.
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-var none block
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-
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-// Dummy type used to generate an implicit panic. This must be defined at the
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-// package level; if it is defined inside a function, it prevents the inlining
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-// of that function.
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-type to_copy_a_sparse_you_must_call_its_Copy_method struct{}
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-
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-// init ensures s is properly initialized.
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-func (s *Sparse) init() {
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- root := &s.root
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- if root.next == nil {
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- root.offset = MaxInt
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- root.next = root
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- root.prev = root
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- } else if root.next.prev != root {
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- // Copying a Sparse x leads to pernicious corruption: the
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- // new Sparse y shares the old linked list, but iteration
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- // on y will never encounter &y.root so it goes into a
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- // loop. Fail fast before this occurs.
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- // We don't want to call panic here because it prevents the
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- // inlining of this function.
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- _ = (interface{}(nil)).(to_copy_a_sparse_you_must_call_its_Copy_method)
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- }
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-}
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-
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-func (s *Sparse) first() *block {
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- s.init()
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- if s.root.offset == MaxInt {
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- return &none
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- }
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- return &s.root
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-}
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-
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-// next returns the next block in the list, or end if b is the last block.
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-func (s *Sparse) next(b *block) *block {
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- if b.next == &s.root {
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- return &none
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- }
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- return b.next
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-}
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-
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-// prev returns the previous block in the list, or end if b is the first block.
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-func (s *Sparse) prev(b *block) *block {
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- if b.prev == &s.root {
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- return &none
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- }
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- return b.prev
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-}
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-
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-// IsEmpty reports whether the set s is empty.
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-func (s *Sparse) IsEmpty() bool {
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- return s.root.next == nil || s.root.offset == MaxInt
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-}
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-
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-// Len returns the number of elements in the set s.
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-func (s *Sparse) Len() int {
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- var l int
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- for b := s.first(); b != &none; b = s.next(b) {
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- l += b.len()
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- }
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- return l
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-}
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-
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-// Max returns the maximum element of the set s, or MinInt if s is empty.
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-func (s *Sparse) Max() int {
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- if s.IsEmpty() {
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- return MinInt
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- }
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- return s.root.prev.max()
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-}
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-
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-// Min returns the minimum element of the set s, or MaxInt if s is empty.
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-func (s *Sparse) Min() int {
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- if s.IsEmpty() {
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- return MaxInt
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- }
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- return s.root.min(false)
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-}
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-
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-// LowerBound returns the smallest element >= x, or MaxInt if there is no such
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-// element.
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-func (s *Sparse) LowerBound(x int) int {
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- offset, i := offsetAndBitIndex(x)
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- for b := s.first(); b != &none; b = s.next(b) {
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- if b.offset > offset {
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- return b.min(false)
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- }
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- if b.offset == offset {
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- if y, ok := b.lowerBound(i); ok {
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- return y
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- }
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- }
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- }
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- return MaxInt
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-}
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-
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-// block returns the block that would contain offset,
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-// or nil if s contains no such block.
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-// Precondition: offset is a multiple of bitsPerBlock.
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-func (s *Sparse) block(offset int) *block {
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- for b := s.first(); b != &none && b.offset <= offset; b = s.next(b) {
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- if b.offset == offset {
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- return b
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- }
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- }
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- return nil
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-}
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-
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-// Insert adds x to the set s, and reports whether the set grew.
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-func (s *Sparse) Insert(x int) bool {
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- offset, i := offsetAndBitIndex(x)
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-
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- b := s.first()
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- for ; b != &none && b.offset <= offset; b = s.next(b) {
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- if b.offset == offset {
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- return b.insert(i)
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- }
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- }
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-
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- // Insert new block before b.
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- new := s.insertBlockBefore(b)
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- new.offset = offset
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- return new.insert(i)
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-}
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-
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-// removeBlock removes a block and returns the block that followed it (or end if
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-// it was the last block).
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-func (s *Sparse) removeBlock(b *block) *block {
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- if b != &s.root {
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- b.prev.next = b.next
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- b.next.prev = b.prev
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- if b.next == &s.root {
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- return &none
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- }
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- return b.next
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- }
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-
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- first := s.root.next
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- if first == &s.root {
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- // This was the only block.
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- s.Clear()
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- return &none
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- }
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- s.root.offset = first.offset
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- s.root.bits = first.bits
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- if first.next == &s.root {
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- // Single block remaining.
|
|
|
|
- s.root.next = &s.root
|
|
|
|
- s.root.prev = &s.root
|
|
|
|
- } else {
|
|
|
|
- s.root.next = first.next
|
|
|
|
- first.next.prev = &s.root
|
|
|
|
- }
|
|
|
|
- return &s.root
|
|
|
|
-}
|
|
|
|
-
|
|
|
|
-// 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 = block{
|
|
|
|
- offset: MaxInt,
|
|
|
|
- next: &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 {
|
|
|
|
- if s.IsEmpty() {
|
|
|
|
- return false
|
|
|
|
- }
|
|
|
|
- *p = s.root.min(true)
|
|
|
|
- if s.root.empty() {
|
|
|
|
- s.removeBlock(&s.root)
|
|
|
|
- }
|
|
|
|
- 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.first(); b != &none; b = s.next(b) {
|
|
|
|
- b.forEach(f)
|
|
|
|
- }
|
|
|
|
-}
|
|
|
|
-
|
|
|
|
-// Copy sets s to the value of x.
|
|
|
|
-func (s *Sparse) Copy(x *Sparse) {
|
|
|
|
- if s == x {
|
|
|
|
- return
|
|
|
|
- }
|
|
|
|
-
|
|
|
|
- xb := x.first()
|
|
|
|
- sb := s.first()
|
|
|
|
- for xb != &none {
|
|
|
|
- if sb == &none {
|
|
|
|
- sb = s.insertBlockBefore(sb)
|
|
|
|
- }
|
|
|
|
- sb.offset = xb.offset
|
|
|
|
- sb.bits = xb.bits
|
|
|
|
- xb = x.next(xb)
|
|
|
|
- sb = s.next(sb)
|
|
|
|
- }
|
|
|
|
- s.discardTail(sb)
|
|
|
|
-}
|
|
|
|
-
|
|
|
|
-// insertBlockBefore returns a new block, inserting it before next.
|
|
|
|
-// If next is the root, the root is replaced. If next is end, the block is
|
|
|
|
-// inserted at the end.
|
|
|
|
-func (s *Sparse) insertBlockBefore(next *block) *block {
|
|
|
|
- if s.IsEmpty() {
|
|
|
|
- if next != &none {
|
|
|
|
- panic("BUG: passed block with empty set")
|
|
|
|
- }
|
|
|
|
- return &s.root
|
|
|
|
- }
|
|
|
|
-
|
|
|
|
- if next == &s.root {
|
|
|
|
- // Special case: we need to create a new block that will become the root
|
|
|
|
- // block.The old root block becomes the second block.
|
|
|
|
- second := s.root
|
|
|
|
- s.root = block{
|
|
|
|
- next: &second,
|
|
|
|
- }
|
|
|
|
- if second.next == &s.root {
|
|
|
|
- s.root.prev = &second
|
|
|
|
- } else {
|
|
|
|
- s.root.prev = second.prev
|
|
|
|
- second.next.prev = &second
|
|
|
|
- second.prev = &s.root
|
|
|
|
- }
|
|
|
|
- return &s.root
|
|
|
|
- }
|
|
|
|
- if next == &none {
|
|
|
|
- // Insert before root.
|
|
|
|
- next = &s.root
|
|
|
|
- }
|
|
|
|
- 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 != &none {
|
|
|
|
- if b == &s.root {
|
|
|
|
- s.Clear()
|
|
|
|
- } else {
|
|
|
|
- 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.first()
|
|
|
|
- sb := s.first()
|
|
|
|
- for xb != &none && sb != &none {
|
|
|
|
- switch {
|
|
|
|
- case xb.offset < sb.offset:
|
|
|
|
- xb = x.next(xb)
|
|
|
|
-
|
|
|
|
- case xb.offset > sb.offset:
|
|
|
|
- sb = s.removeBlock(sb)
|
|
|
|
-
|
|
|
|
- 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 = s.next(sb)
|
|
|
|
- } else {
|
|
|
|
- // sb will be overwritten or removed
|
|
|
|
- }
|
|
|
|
-
|
|
|
|
- xb = x.next(xb)
|
|
|
|
- }
|
|
|
|
- }
|
|
|
|
-
|
|
|
|
- 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.first()
|
|
|
|
- yb := y.first()
|
|
|
|
- sb := s.first()
|
|
|
|
- for xb != &none && yb != &none {
|
|
|
|
- switch {
|
|
|
|
- case xb.offset < yb.offset:
|
|
|
|
- xb = x.next(xb)
|
|
|
|
- continue
|
|
|
|
- case xb.offset > yb.offset:
|
|
|
|
- yb = y.next(yb)
|
|
|
|
- continue
|
|
|
|
- }
|
|
|
|
-
|
|
|
|
- if sb == &none {
|
|
|
|
- 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 = s.next(sb)
|
|
|
|
- } else {
|
|
|
|
- // sb will be overwritten or removed
|
|
|
|
- }
|
|
|
|
-
|
|
|
|
- xb = x.next(xb)
|
|
|
|
- yb = y.next(yb)
|
|
|
|
- }
|
|
|
|
-
|
|
|
|
- s.discardTail(sb)
|
|
|
|
-}
|
|
|
|
-
|
|
|
|
-// Intersects reports whether s ∩ x ≠ ∅.
|
|
|
|
-func (s *Sparse) Intersects(x *Sparse) bool {
|
|
|
|
- sb := s.first()
|
|
|
|
- xb := x.first()
|
|
|
|
- for sb != &none && xb != &none {
|
|
|
|
- switch {
|
|
|
|
- case xb.offset < sb.offset:
|
|
|
|
- xb = x.next(xb)
|
|
|
|
- case xb.offset > sb.offset:
|
|
|
|
- sb = s.next(sb)
|
|
|
|
- default:
|
|
|
|
- for i := range sb.bits {
|
|
|
|
- if sb.bits[i]&xb.bits[i] != 0 {
|
|
|
|
- return true
|
|
|
|
- }
|
|
|
|
- }
|
|
|
|
- sb = s.next(sb)
|
|
|
|
- xb = x.next(xb)
|
|
|
|
- }
|
|
|
|
- }
|
|
|
|
- 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.first()
|
|
|
|
- sb := s.first()
|
|
|
|
- for xb != &none {
|
|
|
|
- if sb != &none && 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 = x.next(xb)
|
|
|
|
- } else if sb == &none || sb.offset > xb.offset {
|
|
|
|
- sb = s.insertBlockBefore(sb)
|
|
|
|
- sb.offset = xb.offset
|
|
|
|
- sb.bits = xb.bits
|
|
|
|
- changed = true
|
|
|
|
-
|
|
|
|
- xb = x.next(xb)
|
|
|
|
- }
|
|
|
|
- sb = s.next(sb)
|
|
|
|
- }
|
|
|
|
- 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.first()
|
|
|
|
- yb := y.first()
|
|
|
|
- sb := s.first()
|
|
|
|
- for xb != &none || yb != &none {
|
|
|
|
- if sb == &none {
|
|
|
|
- sb = s.insertBlockBefore(sb)
|
|
|
|
- }
|
|
|
|
- switch {
|
|
|
|
- case yb == &none || (xb != &none && xb.offset < yb.offset):
|
|
|
|
- sb.offset = xb.offset
|
|
|
|
- sb.bits = xb.bits
|
|
|
|
- xb = x.next(xb)
|
|
|
|
-
|
|
|
|
- case xb == &none || (yb != &none && yb.offset < xb.offset):
|
|
|
|
- sb.offset = yb.offset
|
|
|
|
- sb.bits = yb.bits
|
|
|
|
- yb = y.next(yb)
|
|
|
|
-
|
|
|
|
- default:
|
|
|
|
- sb.offset = xb.offset
|
|
|
|
- for i := range xb.bits {
|
|
|
|
- sb.bits[i] = xb.bits[i] | yb.bits[i]
|
|
|
|
- }
|
|
|
|
- xb = x.next(xb)
|
|
|
|
- yb = y.next(yb)
|
|
|
|
- }
|
|
|
|
- sb = s.next(sb)
|
|
|
|
- }
|
|
|
|
-
|
|
|
|
- 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.first()
|
|
|
|
- sb := s.first()
|
|
|
|
- for xb != &none && sb != &none {
|
|
|
|
- switch {
|
|
|
|
- case xb.offset > sb.offset:
|
|
|
|
- sb = s.next(sb)
|
|
|
|
-
|
|
|
|
- case xb.offset < sb.offset:
|
|
|
|
- xb = x.next(xb)
|
|
|
|
-
|
|
|
|
- default:
|
|
|
|
- var sum word
|
|
|
|
- for i := range sb.bits {
|
|
|
|
- r := sb.bits[i] & ^xb.bits[i]
|
|
|
|
- sb.bits[i] = r
|
|
|
|
- sum |= r
|
|
|
|
- }
|
|
|
|
- if sum == 0 {
|
|
|
|
- sb = s.removeBlock(sb)
|
|
|
|
- } else {
|
|
|
|
- sb = s.next(sb)
|
|
|
|
- }
|
|
|
|
- xb = x.next(xb)
|
|
|
|
- }
|
|
|
|
- }
|
|
|
|
-}
|
|
|
|
-
|
|
|
|
-// 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.first()
|
|
|
|
- yb := y.first()
|
|
|
|
- sb := s.first()
|
|
|
|
- for xb != &none && yb != &none {
|
|
|
|
- if xb.offset > yb.offset {
|
|
|
|
- // y has block, x has &none
|
|
|
|
- yb = y.next(yb)
|
|
|
|
- continue
|
|
|
|
- }
|
|
|
|
-
|
|
|
|
- if sb == &none {
|
|
|
|
- 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 = s.next(sb)
|
|
|
|
-
|
|
|
|
- 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 = s.next(sb)
|
|
|
|
- } else {
|
|
|
|
- // sb will be overwritten or removed
|
|
|
|
- }
|
|
|
|
-
|
|
|
|
- yb = y.next(yb)
|
|
|
|
- }
|
|
|
|
- xb = x.next(xb)
|
|
|
|
- }
|
|
|
|
-
|
|
|
|
- for xb != &none {
|
|
|
|
- if sb == &none {
|
|
|
|
- sb = s.insertBlockBefore(sb)
|
|
|
|
- }
|
|
|
|
- sb.offset = xb.offset
|
|
|
|
- sb.bits = xb.bits
|
|
|
|
- sb = s.next(sb)
|
|
|
|
-
|
|
|
|
- xb = x.next(xb)
|
|
|
|
- }
|
|
|
|
-
|
|
|
|
- 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.first()
|
|
|
|
- xb := x.first()
|
|
|
|
- for xb != &none && sb != &none {
|
|
|
|
- switch {
|
|
|
|
- case sb.offset < xb.offset:
|
|
|
|
- sb = s.next(sb)
|
|
|
|
- case xb.offset < sb.offset:
|
|
|
|
- nb := s.insertBlockBefore(sb)
|
|
|
|
- nb.offset = xb.offset
|
|
|
|
- nb.bits = xb.bits
|
|
|
|
- xb = x.next(xb)
|
|
|
|
- default:
|
|
|
|
- var sum word
|
|
|
|
- for i := range sb.bits {
|
|
|
|
- r := sb.bits[i] ^ xb.bits[i]
|
|
|
|
- sb.bits[i] = r
|
|
|
|
- sum |= r
|
|
|
|
- }
|
|
|
|
- if sum == 0 {
|
|
|
|
- sb = s.removeBlock(sb)
|
|
|
|
- } else {
|
|
|
|
- sb = s.next(sb)
|
|
|
|
- }
|
|
|
|
- xb = x.next(xb)
|
|
|
|
- }
|
|
|
|
- }
|
|
|
|
-
|
|
|
|
- for xb != &none { // append the tail of x to s
|
|
|
|
- sb = s.insertBlockBefore(sb)
|
|
|
|
- sb.offset = xb.offset
|
|
|
|
- sb.bits = xb.bits
|
|
|
|
- sb = s.next(sb)
|
|
|
|
- xb = x.next(xb)
|
|
|
|
- }
|
|
|
|
-}
|
|
|
|
-
|
|
|
|
-// 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.first()
|
|
|
|
- xb := x.first()
|
|
|
|
- yb := y.first()
|
|
|
|
- for xb != &none && yb != &none {
|
|
|
|
- if sb == &none {
|
|
|
|
- sb = s.insertBlockBefore(sb)
|
|
|
|
- }
|
|
|
|
- switch {
|
|
|
|
- case yb.offset < xb.offset:
|
|
|
|
- sb.offset = yb.offset
|
|
|
|
- sb.bits = yb.bits
|
|
|
|
- sb = s.next(sb)
|
|
|
|
- yb = y.next(yb)
|
|
|
|
- case xb.offset < yb.offset:
|
|
|
|
- sb.offset = xb.offset
|
|
|
|
- sb.bits = xb.bits
|
|
|
|
- sb = s.next(sb)
|
|
|
|
- xb = x.next(xb)
|
|
|
|
- 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 = s.next(sb)
|
|
|
|
- }
|
|
|
|
- xb = x.next(xb)
|
|
|
|
- yb = y.next(yb)
|
|
|
|
- }
|
|
|
|
- }
|
|
|
|
-
|
|
|
|
- for xb != &none { // append the tail of x to s
|
|
|
|
- if sb == &none {
|
|
|
|
- sb = s.insertBlockBefore(sb)
|
|
|
|
- }
|
|
|
|
- sb.offset = xb.offset
|
|
|
|
- sb.bits = xb.bits
|
|
|
|
- sb = s.next(sb)
|
|
|
|
- xb = x.next(xb)
|
|
|
|
- }
|
|
|
|
-
|
|
|
|
- for yb != &none { // append the tail of y to s
|
|
|
|
- if sb == &none {
|
|
|
|
- sb = s.insertBlockBefore(sb)
|
|
|
|
- }
|
|
|
|
- sb.offset = yb.offset
|
|
|
|
- sb.bits = yb.bits
|
|
|
|
- sb = s.next(sb)
|
|
|
|
- yb = y.next(yb)
|
|
|
|
- }
|
|
|
|
-
|
|
|
|
- s.discardTail(sb)
|
|
|
|
-}
|
|
|
|
-
|
|
|
|
-// SubsetOf reports whether s ∖ x = ∅.
|
|
|
|
-func (s *Sparse) SubsetOf(x *Sparse) bool {
|
|
|
|
- if s == x {
|
|
|
|
- return true
|
|
|
|
- }
|
|
|
|
-
|
|
|
|
- sb := s.first()
|
|
|
|
- xb := x.first()
|
|
|
|
- for sb != &none {
|
|
|
|
- switch {
|
|
|
|
- case xb == &none || xb.offset > sb.offset:
|
|
|
|
- return false
|
|
|
|
- case xb.offset < sb.offset:
|
|
|
|
- xb = x.next(xb)
|
|
|
|
- default:
|
|
|
|
- for i := range sb.bits {
|
|
|
|
- if sb.bits[i]&^xb.bits[i] != 0 {
|
|
|
|
- return false
|
|
|
|
- }
|
|
|
|
- }
|
|
|
|
- sb = s.next(sb)
|
|
|
|
- xb = x.next(xb)
|
|
|
|
- }
|
|
|
|
- }
|
|
|
|
- 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.first()
|
|
|
|
- tb := t.first()
|
|
|
|
- for {
|
|
|
|
- switch {
|
|
|
|
- case sb == &none && tb == &none:
|
|
|
|
- return true
|
|
|
|
- case sb == &none || tb == &none:
|
|
|
|
- return false
|
|
|
|
- case sb.offset != tb.offset:
|
|
|
|
- return false
|
|
|
|
- case sb.bits != tb.bits:
|
|
|
|
- return false
|
|
|
|
- }
|
|
|
|
-
|
|
|
|
- sb = s.next(sb)
|
|
|
|
- tb = t.next(tb)
|
|
|
|
- }
|
|
|
|
-}
|
|
|
|
-
|
|
|
|
-// 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.first(); b != &none; b = s.next(b) {
|
|
|
|
- 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 {
|
|
|
|
- s.init()
|
|
|
|
- if s.root.empty() {
|
|
|
|
- // An empty set must have only the root block with offset MaxInt.
|
|
|
|
- if s.root.next != &s.root {
|
|
|
|
- return fmt.Errorf("multiple blocks with empty root block")
|
|
|
|
- }
|
|
|
|
- if s.root.offset != MaxInt {
|
|
|
|
- return fmt.Errorf("empty set has offset %d, should be MaxInt", s.root.offset)
|
|
|
|
- }
|
|
|
|
- return nil
|
|
|
|
- }
|
|
|
|
- for b := s.first(); ; b = s.next(b) {
|
|
|
|
- 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.next == &s.root {
|
|
|
|
- break
|
|
|
|
- }
|
|
|
|
- if b.offset >= b.next.offset {
|
|
|
|
- return fmt.Errorf("bad offset order: b.offset=%d, b.next.offset=%d",
|
|
|
|
- b.offset, b.next.offset)
|
|
|
|
- }
|
|
|
|
- }
|
|
|
|
- return nil
|
|
|
|
-}
|
|
|