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set_1_10.go
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// +build go1.10
// Package bit provides a bit array implementation.
//
// Bit set
//
// A bit set, or bit array, is an efficient set data structure
// that consists of an array of 64-bit words. Because it uses
// bit-level parallelism, limits memory access, and efficiently uses
// the data cache, a bit set often outperforms other data structures.
//
// Tutorial
//
// The Basics example shows how to create, combine, compare and
// print bit sets.
//
// Primes contains a short and simple, but still efficient,
// implementation of a prime number sieve.
//
// Union is a more advanced example demonstrating how to build
// an efficient variadic Union function using the SetOr method.
//
package bit
import (
"fmt"
"math/bits"
"strings"
)
const (
bpw = 64 // bits per word
maxw = 1<<bpw - 1 // maximum value of a word
shift = 6
mask = 0x3f
)
// Set represents a mutable set of non-negative integers.
// The zero value is an empty set ready to use.
// A set occupies approximately n bits, where n is the maximum value
// that has been stored in the set.
type Set struct {
// Invariants:
// • data[n>>shift] & (1<<(n&mask)) == 1 iff n belongs to set,
// • data[len(data)-1] != 0 if set is nonempty,
// • data[i] == 0 for all i such that len(data) ≤ i < cap(data).
data []uint64
}
// New creates a new set with the given elements.
// Negative numbers are not included in the set.
func New(n ...int) *Set {
if len(n) == 0 {
return new(Set)
}
max := n[0]
for _, e := range n {
if e > max {
max = e
}
}
if max < 0 {
return new(Set)
}
s := &Set{
data: make([]uint64, max>>shift+1),
}
for _, e := range n {
if e >= 0 {
s.data[e>>shift] |= 1 << uint(e&mask)
}
}
return s
}
// Contains tells if n is an element of the set.
func (s *Set) Contains(n int) bool {
if n < 0 {
return false
}
d := s.data
i := n >> shift
if i >= len(d) {
return false
}
return d[i]&(1<<uint(n&mask)) != 0
}
// Equal tells if s1 and s2 contain the same elements.
func (s1 *Set) Equal(s2 *Set) bool {
if s1 == s2 {
return true
}
a, b := s1.data, s2.data
la := len(a)
if la != len(b) {
return false
}
for i := 0; i < la; i++ {
if a[i] != b[i] {
return false
}
}
return true
}
// Subset tells if s1 is a subset of s2.
func (s1 *Set) Subset(s2 *Set) bool {
if s1 == s2 {
return true
}
a, b := s1.data, s2.data
la := len(a)
if la > len(b) {
return false
}
for i := 0; i < la; i++ {
if a[i]&^b[i] != 0 {
return false
}
}
return true
}
// Max returns the maximum element of the set;
// it panics if the set is empty.
func (s *Set) Max() int {
if len(s.data) == 0 {
panic("max not defined for empty set")
}
d := s.data
i := len(d) - 1
return i<<shift + bits.Len64(d[i]) - 1
}
// Size returns the number of elements in the set.
// This method scans the set; to check if a set is empty,
// consider using the more efficient Empty method.
func (s *Set) Size() int {
d := s.data
n := 0
for i, len := 0, len(d); i < len; i++ {
if w := d[i]; w != 0 {
n += bits.OnesCount64(w)
}
}
return n
}
// Empty tells if the set is empty.
func (s *Set) Empty() bool {
return len(s.data) == 0
}
// Next returns the next element n, n > m, in the set,
// or -1 if there is no such element.
func (s *Set) Next(m int) int {
d := s.data
len := len(d)
if len == 0 {
return -1
}
if m < 0 {
if d[0]&1 != 0 {
return 0
}
m = 0
}
i := m >> shift
if i >= len {
return -1
}
t := 1 + uint(m&mask)
w := d[i] >> t << t // Zero out bits for numbers ≤ m.
for i < len-1 && w == 0 {
i++
w = d[i]
}
if w == 0 {
return -1
}
return i<<shift + bits.TrailingZeros64(w)
}
// Prev returns the previous element n, n < m, in the set,
// or -1 if there is no such element.
func (s *Set) Prev(m int) int {
d := s.data
len := len(d)
if len == 0 || m <= 0 {
return -1
}
i := len - 1
if max := i<<shift + bits.Len64(d[i]) - 1; m > max {
return max
}
i = m >> shift
t := bpw - uint(m&mask)
w := d[i] << t >> t // Zero out bits for numbers ≥ m.
for i > 0 && w == 0 {
i--
w = d[i]
}
if w == 0 {
return -1
}
return i<<shift + bits.Len64(w) - 1
}
// Visit calls the do function for each element of s in numerical order.
// If do returns true, Visit returns immediately, skipping any remaining
// elements, and returns true. It is safe for do to add or delete
// elements e, e ≤ n. The behavior of Visit is undefined if do changes
// the set in any other way.
func (s *Set) Visit(do func(n int) (skip bool)) (aborted bool) {
d := s.data
for i, len := 0, len(d); i < len; i++ {
w := d[i]
if w == 0 {
continue
}
n := i << shift // element represented by w&1
for w != 0 {
b := bits.TrailingZeros64(w)
n += b
if do(n) {
return true
}
n++
w >>= uint(b + 1)
for w&1 != 0 { // common case
if do(n) {
return true
}
n++
w >>= 1
}
}
}
return false
}
// String returns a string representation of the set. The elements
// are listed in ascending order. Runs of at least three consecutive
// elements from a to b are given as a..b.
func (s *Set) String() string {
buf := new(strings.Builder)
buf.WriteByte('{')
a, b := -1, -2 // Keep track of a range a..b of elements.
first := true
s.Visit(func(n int) (skip bool) {
if n == b+1 {
b++ // Increase current range from a..b to a..b+1.
return
}
if first && a <= b {
first = false
} else if a <= b {
buf.WriteByte(' ')
}
writeRange(buf, a, b)
a, b = n, n // Start new range.
return
})
if !first && a <= b {
buf.WriteByte(' ')
}
writeRange(buf, a, b)
buf.WriteByte('}')
return buf.String()
}
// writeRange appends either "", "a", "a b" or "a..b" to buf.
func writeRange(buf *strings.Builder, a, b int) {
switch {
case a > b:
return // Append nothing.
case a == b:
fmt.Fprintf(buf, "%d", a)
case a+1 == b:
fmt.Fprintf(buf, "%d %d", a, b)
default:
fmt.Fprintf(buf, "%d..%d", a, b)
}
}
// Add adds n to s and returns a pointer to the updated set.
// A negative n will not be added.
func (s *Set) Add(n int) *Set {
if n < 0 {
return s
}
i := n >> shift
if i >= len(s.data) {
s.resize(i + 1)
}
s.data[i] |= 1 << uint(n&mask)
return s
}
// Delete removes n from s and returns a pointer to the updated set.
func (s *Set) Delete(n int) *Set {
if n < 0 {
return s
}
i := n >> shift
if i >= len(s.data) {
return s
}
s.data[i] &^= 1 << uint(n&mask)
s.trim()
return s
}
// AddRange adds all integers from m to n-1 to s
// and returns a pointer to the updated set.
// Negative numbers will not be added.
func (s *Set) AddRange(m, n int) *Set {
if n < 1 || m >= n {
return s
}
m = max(0, m)
n--
low, high := m>>shift, n>>shift
if high >= len(s.data) {
s.resize(high + 1)
}
d := s.data
// Range fits in one word.
if low == high {
d[low] |= bitMask(m&mask, n&mask)
return s
}
// Range spans at least two words.
d[low] |= bitMask(m&mask, bpw-1)
for i := low + 1; i < high; i++ {
d[i] = maxw
}
d[high] |= bitMask(0, n&mask)
return s
}
// DeleteRange removes all integers from m to n-1 from s
// and returns a pointer to the updated set.
func (s *Set) DeleteRange(m, n int) *Set {
if n < 1 || m >= n {
return s
}
m = max(0, m)
n--
d := s.data
low, high := m>>shift, n>>shift
// Range does not intersect set.
if low >= len(d) {
return s
}
// Top of range overshoots set.
if len(d) <= high {
high = len(d) - 1 // low ≤ high still holds, since low < len(d).
n = bpw - 1 // To assure that n&mask == bpw-1 below.
}
// Range fits in one word.
if low == high {
d[low] &^= bitMask(m&mask, n&mask)
s.trim()
return s
}
// Range spans at least two words.
d[low] &^= bitMask(m&mask, bpw-1)
for i := low + 1; i < high; i++ {
d[i] = 0
}
d[high] &^= bitMask(0, n&mask)
s.trim()
return s
}
// And creates a new set that consists of all elements that belong
// to both s1 and s2.
func (s1 *Set) And(s2 *Set) *Set {
return new(Set).SetAnd(s1, s2)
}
// Or creates a new set that contains all elements that belong
// to either s1 or s2.
func (s1 *Set) Or(s2 *Set) *Set {
return new(Set).SetOr(s1, s2)
}
// Xor creates a new set that contains all elements that belong
// to either s1 or s2, but not to both.
func (s1 *Set) Xor(s2 *Set) *Set {
return new(Set).SetXor(s1, s2)
}
// AndNot creates a new set that consists of all elements that belong
// to s1, but not to s2.
func (s1 *Set) AndNot(s2 *Set) *Set {
return new(Set).SetAndNot(s1, s2)
}
// Set sets s to s1 and then returns a pointer to the updated set s.
func (s *Set) Set(s1 *Set) *Set {
s.realloc(len(s1.data))
copy(s.data, s1.data)
return s
}
// SetAnd sets s to the intersection s1 ∩ s2 and then returns a pointer to s.
func (s *Set) SetAnd(s1, s2 *Set) *Set {
a, b := s1.data, s2.data
// Find last nonzero word in result.
n := min(len(a), len(b)) - 1
for n >= 0 && a[n]&b[n] == 0 {
n--
}
if s == s1 || s == s2 {
s.resize(n + 1)
} else {
s.realloc(n + 1)
}
for i := 0; i <= n; i++ {
s.data[i] = a[i] & b[i]
}
return s
}
// SetAndNot sets s to the set difference s1 ∖ s2 and then returns a pointer to s.
func (s *Set) SetAndNot(s1, s2 *Set) *Set {
a, b := s1.data, s2.data
la, lb := len(a), len(b)
// Result requires len(a) words if len(a) > len(b),
// otherwise find last nonzero word in result.
n := la - 1
if la <= lb {
for n >= 0 && a[n]&^b[n] == 0 {
n--
}
}
if s == s1 || s == s2 {
s.resize(n + 1)
} else {
s.realloc(n + 1)
}
d := s.data
if m := lb; m <= n {
copy(d[m:n+1], a[m:n+1])
n = m - 1
}
for i := 0; i <= n; i++ {
d[i] = a[i] &^ b[i]
}
return s
}
// SetOr sets s to the union s1 ∪ s2 and then returns a pointer to s.
func (s *Set) SetOr(s1, s2 *Set) *Set {
// Swap, if necessary, to make s1 shorter than s2.
if len(s1.data) > len(s2.data) {
s1, s2 = s2, s1
}
a, b := s1.data, s2.data
la := len(a)
n := len(b) - 1
if s == s1 || s == s2 {
s.resize(n + 1)
} else {
s.realloc(n + 1)
}
d := s.data
copy(d[la:n+1], b[la:n+1])
for i := 0; i < la; i++ {
d[i] = a[i] | b[i]
}
return s
}
// SetXor sets s to the symmetric difference A ∆ B = (A ∪ B) ∖ (A ∩ B)
// and then returns a pointer to s.
func (s *Set) SetXor(s1, s2 *Set) *Set {
// Swap, if necessary, to make s1 shorter than s2.
if len(s1.data) > len(s2.data) {
s1, s2 = s2, s1
}
a, b := s1.data, s2.data
la, lb := len(a), len(b)
n := lb - 1
if la == lb { // The only case where result may be shorter than len(b).
for n >= 0 && a[n]^b[n] == 0 {
n--
}
if n == -1 { // No elements left.
s.realloc(0)
return s
}
}
if s == s1 || s == s2 {
s.resize(n + 1)
} else {
s.realloc(n + 1)
}
d := s.data
if la <= n {
copy(d[la:n+1], b[la:n+1])
n = la - 1
}
for i := 0; i <= n; i++ {
d[i] = a[i] ^ b[i]
}
return s
}
// resize changes the length of s.data to n, keeping old values.
// It preserves the invariant s.data[i] = 0, n ≤ i < cap(data).
func (s *Set) resize(n int) {
d := s.data
if s.realloc(n) {
copy(s.data, d)
}
}
// realloc creates a slice s.data of length n, possibly zeroing out old values.
// It preserves the invariant s.data[i] = 0, n ≤ i < cap(data).
// It returns true if new memory has been allocated.
func (s *Set) realloc(n int) (didAlloc bool) {
if c := cap(s.data); c < n {
s.data = make([]uint64, n, newCap(n, c))
return true
}
// Add zeroes if shrinking.
d := s.data
for i := len(d) - 1; i >= n; i-- {
d[i] = 0
}
s.data = d[:n]
return false
}
// newCap suggests a new increased capacity, favoring powers of two,
// when growing a slice to length n. The suggested capacities guarantee
// linear amortized cost for repeated memory allocations.
func newCap(n, prevCap int) int {
return max(n, nextPow2(prevCap))
}
// nextPow2 returns the smallest p = 1, 2, 4, ..., 2^k such that p > n,
// or MaxInt if p > MaxInt.
func nextPow2(n int) (p int) {
if n <= 0 {
return 1
}
if k := bits.Len64(uint64(n)); k < bitsPerWord-1 {
return 1 << uint(k)
}
return MaxInt
}
// trim slices s.data by removing all trailing words equal to zero.
func (s *Set) trim() {
d := s.data
n := len(d) - 1
for n >= 0 && d[n] == 0 {
n--
}
s.data = d[:n+1]
}
// bitMask returns a bit mask with nonzero bits from m to n, 0 ≤ m ≤ n < bpw.
func bitMask(m, n int) uint64 {
return maxw >> uint(bpw-1-(n-m)) << uint(m)
}
func min(a, b int) int {
if a < b {
return a
}
return b
}
func max(a, b int) int {
if a > b {
return a
}
return b
}