結果
| 問題 | No.1332 Range Nearest Query |
| ユーザー |
 草苺奶昔
|
| 提出日時 | 2023-03-30 19:28:12 |
| 言語 | Go (1.23.4) |
| 結果 |
AC
|
| 実行時間 | 755 ms / 2,500 ms |
| コード長 | 12,759 bytes |
| コンパイル時間 | 12,891 ms |
| コンパイル使用メモリ | 223,084 KB |
| 実行使用メモリ | 24,544 KB |
| 最終ジャッジ日時 | 2024-09-22 05:36:06 |
| 合計ジャッジ時間 | 41,314 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / judge3 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| other | AC * 48 |
ソースコード
package main
import (
"bufio"
"fmt"
"math/bits"
"os"
)
func main() {
// https://yukicoder.me/problems/no/1332
// 区间前驱后继
in := bufio.NewReader(os.Stdin)
out := bufio.NewWriter(os.Stdout)
defer out.Flush()
var n int
fmt.Fscan(in, &n)
nums := make([]int, n)
for i := 0; i < n; i++ {
fmt.Fscan(in, &nums[i])
}
wm := NewWaveletMatrixSegments(nums, -1, nil)
var q int
fmt.Fscan(in, &q)
for i := 0; i < q; i++ {
var l, r, x int
fmt.Fscan(in, &l, &r, &x)
l--
res := INF
n := wm.CountRange(l, r, 0, x, 0)
if n > 0 {
res = min(res, abs(x-wm.Kth(l, r, n-1, 0)))
}
if n < r-l {
res = min(res, abs(x-wm.Kth(l, r, n, 0)))
}
fmt.Fprintln(out, res)
}
}
func demo() {
nums := []int{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
wm := NewWaveletMatrixSegments(nums, -1, nums)
fmt.Println(wm.CountRange(0, 10, 3, 7, 0))
fmt.Println(wm.Kth(0, 10, 9, 0))
fmt.Println(wm.KthValueAndSum(0, 10, 10, 0))
fmt.Println(wm.Sum(0, 10, 1, 3, 0))
fmt.Println(wm.SumAll(0, 10))
fmt.Println(wm.Median(false, 0, 5, 0))
fmt.Println(wm.CountRangeSegments([][2]int{{0, 1}, {5, 10}}, 3, 90, 0))
fmt.Println(wm.KthSegments([][2]int{{0, 1}, {5, 10}}, 3, 0))
fmt.Println(wm.KthValueAndSumSegments([][2]int{{0, 1}, {5, 10}}, 30, 0))
fmt.Println(wm.SumAllSegments([][2]int{{0, 1}, {5, 10}}))
fmt.Println(wm.MedianSegments(true, [][2]int{{0, 5}}, 0))
count, sum := wm.MaxRight(0, 10, 0, func(count int, sum int) bool {
return count <= 3
})
fmt.Println(count, sum)
}
const INF int = 1e18
type E = int
func (*WaveletMatrixSegments) e() E { return 0 }
func (*WaveletMatrixSegments) op(a, b E) E { return a + b }
func (*WaveletMatrixSegments) inv(a E) E { return -a }
type WaveletMatrixSegments struct {
n, log int
mid []int
bv []*BitVector
preSum [][]int
unit E
}
//
// log:如果要支持异或,则需要按照异或的值来决定值域
// 设为-1时表示不使用异或
// sumData:如果要支持区间和,则需要传入前缀和数组
// 设为nil时表示不使用区间和
func NewWaveletMatrixSegments(nums []E, log int, sumData []E) *WaveletMatrixSegments {
res := &WaveletMatrixSegments{}
res.build(nums, log, sumData)
return res
}
// 返回区间 [left, right) 中 范围在 [a, b) 中的 元素的个数.
func (wm *WaveletMatrixSegments) CountRange(left, right, a, b, xor int) int {
return wm.prefixCount(left, right, b, xor) - wm.prefixCount(left, right, a, xor)
}
func (wm *WaveletMatrixSegments) CountRangeSegments(segments [][2]int, a, b, xor int) int {
res := 0
for _, seg := range segments {
res += wm.CountRange(seg[0], seg[1], a, b, xor)
}
return res
}
// 返回区间 [left, right) 中的 (第k小的元素, 前k个元素(不包括第k小的元素) 的 op 的结果)
// 如果k < 0, 返回 (-1, 0); 如果k >= right-left, 返回 (-1, 区间 op 的结果)
func (wm *WaveletMatrixSegments) KthValueAndSum(left, right, k, xor int) (int, E) {
if k < 0 {
return -1, 0
}
if right-left <= k {
return -1, wm.get(wm.log, left, right)
}
res, sum := 0, wm.unit
count := 0
for d := wm.log - 1; d >= 0; d-- {
f := (xor >> d) & 1
l0, r0 := wm.bv[d].Rank(left, 0), wm.bv[d].Rank(right, 0)
kf := f*(right-left-r0+l0) + (f^1)*(r0-l0)
if count+kf > k {
if f == 0 {
left, right = l0, r0
} else {
left += wm.mid[d] - l0
right += wm.mid[d] - r0
}
} else {
var s E
if f == 0 {
s = wm.get(d, l0, r0)
} else {
s = wm.get(d, wm.mid[d]-l0+left, wm.mid[d]-r0+right)
}
count += kf
res |= 1 << d
sum = wm.op(sum, s)
if f == 0 {
left += wm.mid[d] - l0
right += wm.mid[d] - r0
} else {
left, right = l0, r0
}
}
}
sum = wm.op(sum, wm.get(0, left, left+k-count))
return res, sum
}
// 如果k < 0, 返回 (-1, 0); 如果k >= segments总长, 返回 (-1, 区间 op 的结果)
func (wm *WaveletMatrixSegments) KthValueAndSumSegments(segments [][2]int, k, xor int) (int, E) {
if k < 0 {
return -1, 0
}
totalLen := 0
for _, seg := range segments {
totalLen += seg[1] - seg[0]
}
if k >= totalLen {
return -1, wm.SumAllSegments(segments)
}
count := 0
sum := wm.unit
res := 0
for d := wm.log - 1; d >= 0; d-- {
f := (xor >> d) & 1
c := 0
for _, seg := range segments {
L, R := seg[0], seg[1]
l0, r0 := wm.bv[d].Rank(L, 0), wm.bv[d].Rank(R, 0)
c += f*(R-L-r0+l0) + (f^1)*(r0-l0)
}
if count+c > k {
for i := range segments {
seg := &segments[i]
L, R := seg[0], seg[1]
l0, r0 := wm.bv[d].Rank(L, 0), wm.bv[d].Rank(R, 0)
if f == 0 {
seg[0], seg[1] = l0, r0
} else {
seg[0] += wm.mid[d] - l0
seg[1] += wm.mid[d] - r0
}
}
} else {
count += c
res |= 1 << d
for i := range segments {
seg := &segments[i]
L, R := seg[0], seg[1]
l0, r0 := wm.bv[d].Rank(L, 0), wm.bv[d].Rank(R, 0)
var s E
if f == 0 {
s = wm.get(d, l0, r0)
} else {
s = wm.get(d, wm.mid[d]-l0+L, wm.mid[d]-r0+R)
}
sum = wm.op(sum, s)
if f == 0 {
seg[0] += wm.mid[d] - l0
seg[1] += wm.mid[d] - r0
} else {
seg[0], seg[1] = l0, r0
}
}
}
}
for _, seg := range segments {
L, R := seg[0], seg[1]
t := min(R-L, k-count)
sum = wm.op(sum, wm.get(0, L, L+t))
count += t
}
return res, sum
}
// 如果不存在,返回-1.
func (wm *WaveletMatrixSegments) Kth(left, right, k, xor int) E {
if k < 0 || k >= right-left {
return -1
}
count := 0
res := 0
for d := wm.log - 1; d >= 0; d-- {
f := (xor >> d) & 1
l0, r0 := wm.bv[d].Rank(left, 0), wm.bv[d].Rank(right, 0)
c := f*(right-left-r0+l0) + (f^1)*(r0-l0)
if count+c > k {
if f == 0 {
left, right = l0, r0
} else {
left += wm.mid[d] - l0
right += wm.mid[d] - r0
}
} else {
count += c
res |= 1 << d
if f == 0 {
left += wm.mid[d] - l0
right += wm.mid[d] - r0
} else {
left, right = l0, r0
}
}
}
return res
}
// 如果不存在,返回-1.
func (wm *WaveletMatrixSegments) KthSegments(segments [][2]int, k, xor int) E {
if k < 0 {
return -1
}
totalLen := 0
for _, seg := range segments {
totalLen += seg[1] - seg[0]
}
if k >= totalLen {
return -1
}
count := 0
res := 0
for d := wm.log - 1; d >= 0; d-- {
f := (xor >> d) & 1
c := 0
for i := range segments {
seg := &segments[i]
L, R := seg[0], seg[1]
l0, r0 := wm.bv[d].Rank(L, 0), wm.bv[d].Rank(R, 0)
c += f*(R-L-r0+l0) + (f^1)*(r0-l0)
}
if count+c > k {
for i := range segments {
seg := &segments[i]
L, R := seg[0], seg[1]
l0, r0 := wm.bv[d].Rank(L, 0), wm.bv[d].Rank(R, 0)
if f == 0 {
seg[0], seg[1] = l0, r0
} else {
seg[0] += wm.mid[d] - l0
seg[1] += wm.mid[d] - r0
}
}
} else {
count += c
res |= 1 << d
for i := range segments {
seg := &segments[i]
L, R := seg[0], seg[1]
l0, r0 := wm.bv[d].Rank(L, 0), wm.bv[d].Rank(R, 0)
if f == 0 {
seg[0] += wm.mid[d] - l0
seg[1] += wm.mid[d] - r0
} else {
seg[0], seg[1] = l0, r0
}
}
}
}
return res
}
// 区间中位数.
// upper: true表示上中位数, false表示下中位数.
func (wm *WaveletMatrixSegments) Median(upper bool, left, right, xor int) E {
n := right - left
var k int
if upper {
k = n / 2
} else {
k = (n - 1) / 2
}
return wm.Kth(left, right, k, xor)
}
func (wm *WaveletMatrixSegments) MedianSegments(upper bool, segments [][2]int, xor int) E {
n := 0
for _, seg := range segments {
n += seg[1] - seg[0]
}
var k int
if upper {
k = n / 2
} else {
k = (n - 1) / 2
}
return wm.KthSegments(segments, k, xor)
}
func (wm *WaveletMatrixSegments) Sum(left, right, k1, k2, xor int) E {
return wm.prefixSum(left, right, k2, xor) - wm.prefixSum(left, right, k1, xor)
}
func (wm *WaveletMatrixSegments) SumAll(left, right int) E {
return wm.get(wm.log, left, right)
}
func (wm *WaveletMatrixSegments) SumAllSegments(segments [][2]int) E {
res := wm.unit
for _, seg := range segments {
res = wm.op(res, wm.get(wm.log, seg[0], seg[1]))
}
return res
}
// 返回使得 check(count,prefixSum) 为 true 的最大 (count, prefixSum) 对.
// !(即区间内小于 val 的数的个数count和 和 prefixSum 满足 check函数, 找到这样的最大的 (count, prefixSum).
// eg: val = 5 => 即区间内值域在 [0,5) 中的数的和满足 check 函数.
func (wm *WaveletMatrixSegments) MaxRight(left, right, xor int, check func(count int, preSum E) bool) (int, E) {
if tmp := wm.get(wm.log, left, right); check(right-left, tmp) {
return right - left, tmp
}
count := 0
res := wm.unit
for d := wm.log - 1; d >= 0; d-- {
f := (xor >> d) & 1
l0, r0 := wm.bv[d].Rank(left, 0), wm.bv[d].Rank(right, 0)
c := f*(right-left-r0+l0) + (f^1)*(r0-l0)
var s E
if f == 0 {
s = wm.get(d, l0, r0)
} else {
s = wm.get(d, left+wm.mid[d]-l0, right+wm.mid[d]-r0)
}
if tmp := wm.op(res, s); check(count+c, tmp) {
count += c
res = tmp
if f == 0 {
left += wm.mid[d] - l0
right += wm.mid[d] - r0
} else {
left, right = l0, r0
}
} else {
if f == 0 {
left, right = l0, r0
} else {
left += wm.mid[d] - l0
right += wm.mid[d] - r0
}
}
}
k := wm.binarySearch(func(k int) bool {
return check(count+k, wm.op(res, wm.get(0, left, left+k)))
}, 0, right-left)
count += k
res = wm.op(res, wm.get(0, left, left+k))
return count, res
}
func (w *WaveletMatrixSegments) build(nums []E, log int, sumData []E) {
numsCopy := make([]E, len(nums))
max_ := 1
for i, v := range nums {
numsCopy[i] = v
if v > max_ {
max_ = v
}
}
if log == -1 {
log = bits.Len(uint(max_))
}
makeSum := sumData != nil
sumData = append(sumData[:0:0], sumData...)
w.unit = w.e()
n := len(numsCopy)
mid := make([]int, log)
bv := make([]*BitVector, log)
for i := 0; i < log; i++ {
bv[i] = NewBitVector(n)
}
var preSum [][]E
if makeSum {
preSum = make([][]E, log+1)
for i := range preSum {
preSum[i] = make([]E, n+1)
for j := range preSum[i] {
preSum[i][j] = w.unit
}
}
}
a0, a1 := make([]E, n), make([]E, n)
s0, s1 := make([]E, n), make([]E, n)
for d := log - 1; d >= -1; d-- {
p0, p1 := 0, 0
if makeSum {
for i := 0; i < n; i++ {
preSum[d+1][i+1] = w.op(preSum[d+1][i], sumData[i])
}
}
if d == -1 {
break
}
for i := 0; i < n; i++ {
f := (numsCopy[i] >> d) & 1
if f == 0 {
if makeSum {
s0[p0] = sumData[i]
}
a0[p0] = numsCopy[i]
p0++
} else {
if makeSum {
s1[p1] = sumData[i]
}
bv[d].Set(i)
a1[p1] = numsCopy[i]
p1++
}
}
mid[d] = p0
bv[d].Build()
numsCopy, a0 = a0, numsCopy
sumData, s0 = s0, sumData
for i := 0; i < p1; i++ {
numsCopy[p0+i] = a1[i]
if makeSum {
sumData[p0+i] = s1[i]
}
}
}
w.n, w.log = n, log
w.mid, w.bv, w.preSum = mid, bv, preSum
}
func (wm *WaveletMatrixSegments) binarySearch(f func(E) bool, ok, ng int) int {
for abs(ok-ng) > 1 {
x := (ok + ng) >> 1
if f(x) {
ok = x
} else {
ng = x
}
}
return ok
}
// 返回区间 [left, right) 中 范围在 [0, x) 中的 元素的个数.
func (wm *WaveletMatrixSegments) prefixCount(left, right, x, xor int) int {
if x == 0 {
return 0
}
if x >= 1<<wm.log {
return right - left
}
count := 0
for d := wm.log - 1; d >= 0; d-- {
add := (x >> d) & 1
f := (xor >> d) & 1
l0, r0 := wm.bv[d].Rank(left, 0), wm.bv[d].Rank(right, 0)
kf := f*(right-left-r0+l0) + (f^1)*(r0-l0)
if add == 1 {
count += kf
if f == 1 {
left, right = l0, r0
} else {
left += wm.mid[d] - l0
right += wm.mid[d] - r0
}
} else if f == 0 {
left, right = l0, r0
} else {
left += wm.mid[d] - l0
right += wm.mid[d] - r0
}
}
return count
}
func (wm *WaveletMatrixSegments) prefixSum(left, right, k, xor int) E {
_, res := wm.KthValueAndSum(left, right, k, xor)
return res
}
func (wm *WaveletMatrixSegments) prefixSumSegments(segments [][2]int, k, xor int) E {
_, res := wm.KthValueAndSumSegments(segments, k, xor)
return res
}
func (wm *WaveletMatrixSegments) get(d, l, r int) E {
return wm.op(wm.inv(wm.preSum[d][l]), wm.preSum[d][r])
}
func abs(a int) int {
if a < 0 {
return -a
}
return a
}
func min(a, b int) int {
if a > b {
return b
}
return a
}
type BitVector struct {
data [][2]int
}
func NewBitVector(n int) *BitVector {
return &BitVector{data: make([][2]int, (n+63)>>5)}
}
func (bv *BitVector) Set(i int) {
bv.data[i>>5][0] |= 1 << (i & 31)
}
func (bv *BitVector) Build() {
for i := 0; i < len(bv.data)-1; i++ {
bv.data[i+1][1] = bv.data[i][1] + bits.OnesCount(uint(bv.data[i][0]))
}
}
func (bv *BitVector) Rank(k int, f int) int {
a, b := bv.data[k>>5][0], bv.data[k>>5][1]
ret := b + bits.OnesCount(uint(a&((1<<(k&31))-1)))
if f == 1 {
return ret
}
return k - ret
}