結果

問題 No.738 平らな農地
ユーザー 草苺奶昔
提出日時 2024-04-24 20:44:48
言語 Go
(1.23.4)
結果
AC  
実行時間 164 ms / 2,000 ms
コード長 15,542 bytes
コンパイル時間 13,209 ms
コンパイル使用メモリ 220,272 KB
実行使用メモリ 22,528 KB
最終ジャッジ日時 2024-11-07 05:43:49
合計ジャッジ時間 22,938 ms
ジャッジサーバーID
(参考情報)
judge4 / judge1
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 5
other AC * 87
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ソースコード

diff #
プレゼンテーションモードにする

package main
import (
"bufio"
"fmt"
"math/bits"
"math/rand"
"os"
"sort"
)
func main() {
// test()
yuki738()
}
// No.738
// https://yukicoder.me/problems/no/738
// !
func yuki738() {
in := bufio.NewReader(os.Stdin)
out := bufio.NewWriter(os.Stdout)
defer out.Flush()
var n, k int32
fmt.Fscan(in, &n, &k)
nums := make([]int, n)
for i := int32(0); i < n; i++ {
fmt.Fscan(in, &nums[i])
}
wm := NewWaveletMatrixWithSum(nums, nums, -1, true)
res := INF
mf := NewMedianFinderWaveletMatrix(wm)
for i := int32(0); i < n-k+1; i++ {
start, end := i, i+k
res = min(res, mf.DistSumToMedianRange(start, end))
}
fmt.Fprintln(out, res)
}
// waveletMatrix.
type MedianFinderWaveletMatrix struct {
Wm *WaveletMatrixWithSum
}
// WaveletMatrix .
// `Proxy WaveletMatrix `.
func NewMedianFinderWaveletMatrix(wm *WaveletMatrixWithSum) *MedianFinderWaveletMatrix {
return &MedianFinderWaveletMatrix{Wm: wm}
}
func (mf *MedianFinderWaveletMatrix) Median() int {
return mf.MedianRange(0, mf.Wm.n)
}
// [start, end) ().
func (mf *MedianFinderWaveletMatrix) MedianRange(start, end int32) int {
if start < 0 {
start = 0
}
if end > mf.Wm.n {
end = mf.Wm.n
}
if start >= end {
return 0
}
return mf.Wm.Median(start, end, false, 0)
}
func (mf *MedianFinderWaveletMatrix) DistSum(to int) int {
return mf.DistSumRange(to, 0, mf.Wm.n)
}
func (mf *MedianFinderWaveletMatrix) DistSumRange(to int, start, end int32) int {
if start < 0 {
start = 0
}
if end > mf.Wm.n {
end = mf.Wm.n
}
if start >= end {
return 0
}
m := end - start
less := mf.Wm.CountPrefix(start, end, WmValue(to), 0) // bisect_left
allSum := mf.Wm.SumAll(start, end)
if less == 0 {
return allSum - int(m)*to
}
if less == m {
return int(m)*to - allSum
}
sum1 := mf.Wm.SumPrefix(start, end, less, 0)
sum2 := allSum - sum1
leftSum := to*int(less) - sum1
rightSum := sum2 - to*int(m-less)
return leftSum + rightSum
}
func (mf *MedianFinderWaveletMatrix) DistSumToMedian() int {
return mf.DistSumToMedianRange(0, mf.Wm.n)
}
func (mf *MedianFinderWaveletMatrix) DistSumToMedianRange(start, end int32) int {
if start < 0 {
start = 0
}
if end > mf.Wm.n {
end = mf.Wm.n
}
if start >= end {
return 0
}
m := end - start
count1 := m / 2
count2 := m - count1
mid, sum1 := mf.Wm.KthValueAndSum(start, end, count1, 0)
allSum := mf.Wm.SumAll(start, end)
sum2 := allSum - sum1
res := 0
res += mid*int(count1) - sum1
res += sum2 - mid*int(count2)
return res
}
const INF WmValue = 1e18
type WmValue = int
type WmSum = int
func (*WaveletMatrixWithSum) e() WmSum { return 0 }
func (*WaveletMatrixWithSum) op(a, b WmSum) WmSum { return a + b }
func (*WaveletMatrixWithSum) inv(a WmSum) WmSum { return -a }
type WaveletMatrixWithSum struct {
n, log int32
mid []int32
bv []*BitVector
key []WmValue
setLog bool
presum [][]WmSum
compress bool
}
// nums: .
// sumData: nil.
// log: log-1.
// compress: nums((1e9)).
func NewWaveletMatrixWithSum(nums []WmValue, sumData []WmSum, log int32, compress bool) *WaveletMatrixWithSum {
wm := &WaveletMatrixWithSum{}
wm.build(nums, sumData, log, compress)
return wm
}
func (wm *WaveletMatrixWithSum) build(nums []WmValue, sumData []WmSum, log int32, compress bool) {
numsCopy := append(nums[:0:0], nums...)
sumDataCopy := append(sumData[:0:0], sumData...)
wm.n = int32(len(numsCopy))
wm.log = log
wm.compress = compress
wm.setLog = log != -1
if wm.n == 0 {
wm.log = 0
return
}
makeSum := len(sumData) > 0
if compress {
if wm.setLog {
panic("compress and log should not be set at the same time")
}
wm.key = make([]WmValue, 0, wm.n)
order := wm._argSort(numsCopy)
for _, i := range order {
if len(wm.key) == 0 || wm.key[len(wm.key)-1] != numsCopy[i] {
wm.key = append(wm.key, numsCopy[i])
}
numsCopy[i] = WmValue(len(wm.key) - 1)
}
}
if wm.log == -1 {
tmp := wm._maxs(numsCopy)
if tmp < 1 {
tmp = 1
}
wm.log = int32(bits.Len(uint(tmp)))
}
wm.mid = make([]int32, wm.log)
wm.bv = make([]*BitVector, wm.log)
for i := range wm.bv {
wm.bv[i] = NewBitVector(wm.n)
}
if makeSum {
wm.presum = make([][]WmSum, 1+wm.log)
for i := range wm.presum {
sums := make([]WmSum, wm.n+1)
for j := range sums {
sums[j] = wm.e()
}
wm.presum[i] = sums
}
}
if len(sumDataCopy) == 0 {
sumDataCopy = make([]WmSum, len(numsCopy))
}
A, S := numsCopy, sumDataCopy
A0, A1 := make([]WmValue, wm.n), make([]WmValue, wm.n)
S0, S1 := make([]WmSum, wm.n), make([]WmSum, wm.n)
for d := wm.log - 1; d >= -1; d-- {
p0, p1 := int32(0), int32(0)
if makeSum {
tmp := wm.presum[d+1]
for i := int32(0); i < wm.n; i++ {
tmp[i+1] = wm.op(tmp[i], S[i])
}
}
if d == -1 {
break
}
for i := int32(0); i < wm.n; i++ {
f := (A[i] >> d & 1) == 1
if !f {
if makeSum {
S0[p0] = S[i]
}
A0[p0] = A[i]
p0++
} else {
if makeSum {
S1[p1] = S[i]
}
wm.bv[d].Set(i)
A1[p1] = A[i]
p1++
}
}
wm.mid[d] = p0
wm.bv[d].Build()
A, A0 = A0, A
S, S0 = S0, S
for i := int32(0); i < p1; i++ {
A[p0+i] = A1[i]
S[p0+i] = S1[i]
}
}
}
// [start, end) [a, b) .
func (wm *WaveletMatrixWithSum) CountRange(start, end int32, a, b WmValue, xorVal WmValue) int32 {
return wm.CountPrefix(start, end, b, xorVal) - wm.CountPrefix(start, end, a, xorVal)
}
func (wm *WaveletMatrixWithSum) SumRange(start, end, k1, k2 int32, xorVal WmValue) WmSum {
if k1 < 0 {
k1 = 0
}
if k2 > end-start {
k2 = end - start
}
if k1 >= k2 {
return wm.e()
}
add := wm.SumPrefix(start, end, k2, xorVal)
sub := wm.SumPrefix(start, end, k1, xorVal)
return wm.op(add, wm.inv(sub))
}
// [start, end) [0, x) .
func (wm *WaveletMatrixWithSum) CountPrefix(start, end int32, x WmValue, xor WmValue) int32 {
if xor != 0 {
if !wm.setLog {
panic("log should be set when xor is used")
}
}
if wm.compress {
x = wm._lowerBound(wm.key, x)
}
if x <= 0 {
return 0
}
if x >= 1<<wm.log {
return end - start
}
count := int32(0)
for d := wm.log - 1; d >= 0; d-- {
add := (x>>d)&1 == 1
f := (xor>>d)&1 == 1
l0, r0 := wm.bv[d].Rank(start, false), wm.bv[d].Rank(end, false)
kf := int32(0)
if f {
kf = (end - start - r0 + l0)
} else {
kf = (r0 - l0)
}
if add {
count += kf
if f {
start, end = l0, r0
} else {
start += wm.mid[d] - l0
end += wm.mid[d] - r0
}
} else {
if !f {
start, end = l0, r0
} else {
start += wm.mid[d] - l0
end += wm.mid[d] - r0
}
}
}
return count
}
// [start, end) [0, k) .
func (wm *WaveletMatrixWithSum) SumPrefix(start, end, k int32, xor WmValue) WmSum {
_, sum := wm.KthValueAndSum(start, end, k, xor)
return sum
}
// [start, end)k(k>=0).
func (wm *WaveletMatrixWithSum) Kth(start, end, k int32, xorVal WmValue) WmValue {
if xorVal != 0 {
if !wm.setLog {
panic("log should be set")
}
}
count := int32(0)
res := WmValue(0)
for d := wm.log - 1; d >= 0; d-- {
f := (xorVal>>d)&1 == 1
l0, r0 := wm.bv[d].Rank(start, false), wm.bv[d].Rank(end, false)
var c int32
if f {
c = (end - start) - (r0 - l0)
} else {
c = r0 - l0
}
if count+c > k {
if !f {
start, end = l0, r0
} else {
start += wm.mid[d] - l0
end += wm.mid[d] - r0
}
} else {
count += c
res |= 1 << d
if !f {
start += wm.mid[d] - l0
end += wm.mid[d] - r0
} else {
start, end = l0, r0
}
}
}
if wm.compress {
res = wm.key[res]
}
return res
}
// [start, end) (k, k(k) op ).
// k >= end-start, (-1, op ).
func (wm *WaveletMatrixWithSum) KthValueAndSum(start, end, k int32, xorVal WmValue) (WmValue, WmSum) {
if start >= end {
return -1, wm.e()
}
if k >= end-start {
return -1, wm.SumAll(start, end)
}
if xorVal != 0 {
if !wm.setLog {
panic("log should be set when xor is used")
}
}
if len(wm.presum) == 0 {
panic("sumData is not provided")
}
count := int32(0)
sum := wm.e()
res := WmValue(0)
for d := wm.log - 1; d >= 0; d-- {
f := (xorVal>>d)&1 == 1
l0, r0 := wm.bv[d].Rank(start, false), wm.bv[d].Rank(end, false)
c := int32(0)
if f {
c = (end - start) - (r0 - l0)
} else {
c = r0 - l0
}
if count+c > k {
if !f {
start, end = l0, r0
} else {
start += wm.mid[d] - l0
end += wm.mid[d] - r0
}
} else {
var s WmSum
if f {
s = wm._get(d, start+wm.mid[d]-l0, end+wm.mid[d]-r0)
} else {
s = wm._get(d, l0, r0)
}
count += c
sum = wm.op(sum, s)
res |= 1 << d
if !f {
start += wm.mid[d] - l0
end += wm.mid[d] - r0
} else {
start, end = l0, r0
}
}
}
sum = wm.op(sum, wm._get(0, start, start+k-count))
if wm.compress {
res = wm.key[res]
}
return res, sum
}
// upper: .
func (wm *WaveletMatrixWithSum) Median(start, end int32, upper bool, xorVal WmValue) WmValue {
n := end - start
var k int32
if upper {
k = n / 2
} else {
k = (n - 1) / 2
}
return wm.Kth(start, end, k, xorVal)
}
func (wm *WaveletMatrixWithSum) SumAll(start, end int32) WmSum {
return wm._get(wm.log, start, end)
}
// 使predicate(count, sum)true(count, sum).
func (wm *WaveletMatrixWithSum) MaxRight(predicate func(int32, WmSum) bool, start, end int32, xorVal WmValue) (int32, WmSum) {
if xorVal != 0 {
if !wm.setLog {
panic("log should be set when xor is used")
}
}
if start == end {
return end - start, wm.e()
}
if s := wm._get(wm.log, start, end); predicate(end-start, s) {
return end - start, s
}
count := int32(0)
sum := wm.e()
for d := wm.log - 1; d >= 0; d-- {
f := (xorVal>>d)&1 == 1
l0, r0 := wm.bv[d].Rank(start, false), wm.bv[d].Rank(end, false)
c := int32(0)
if f {
c = (end - start) - (r0 - l0)
} else {
c = (r0 - l0)
}
var s WmSum
if f {
s = wm._get(d, start+wm.mid[d]-l0, end+wm.mid[d]-r0)
} else {
s = wm._get(d, l0, r0)
}
if tmp := wm.op(sum, s); predicate(count+c, tmp) {
count += c
sum = tmp
if f {
start, end = l0, r0
} else {
start += wm.mid[d] - l0
end += wm.mid[d] - r0
}
} else {
if !f {
start, end = l0, r0
} else {
start += wm.mid[d] - l0
end += wm.mid[d] - r0
}
}
}
k := wm._binarySearch(func(k int32) bool {
return predicate(count+k, wm.op(sum, wm._get(0, start, start+k)))
}, 0, end-start)
count += k
sum = wm.op(sum, wm._get(0, start, start+k))
return count, sum
}
// [start, end) x
//
// -INF
func (wm *WaveletMatrixWithSum) Floor(start, end int32, x WmValue, xor WmValue) WmValue {
less := wm.CountPrefix(start, end, x, xor)
if less == 0 {
return -INF
}
res := wm.Kth(start, end, less-1, xor)
return res
}
// [start, end) x
//
// INF
func (wm *WaveletMatrixWithSum) Ceil(start, end int32, x WmValue, xor WmValue) int {
less := wm.CountPrefix(start, end, x, xor)
if less == end-start {
return INF
}
res := wm.Kth(start, end, less, xor)
return res
}
func (wm *WaveletMatrixWithSum) _get(d, l, r int32) WmSum {
return wm.op(wm.inv(wm.presum[d][l]), wm.presum[d][r])
}
func (wm *WaveletMatrixWithSum) _argSort(nums []WmValue) []int32 {
order := make([]int32, len(nums))
for i := range order {
order[i] = int32(i)
}
sort.Slice(order, func(i, j int) bool { return nums[order[i]] < nums[order[j]] })
return order
}
func (wm *WaveletMatrixWithSum) _maxs(nums []WmValue) WmValue {
res := nums[0]
for _, v := range nums {
if v > res {
res = v
}
}
return res
}
func (wm *WaveletMatrixWithSum) _lowerBound(nums []WmValue, target WmValue) WmValue {
left, right := int32(0), int32(len(nums)-1)
for left <= right {
mid := (left + right) >> 1
if nums[mid] < target {
left = mid + 1
} else {
right = mid - 1
}
}
return WmValue(left)
}
func (wm *WaveletMatrixWithSum) _binarySearch(f func(int32) bool, ok, ng int32) int32 {
for abs32(ok-ng) > 1 {
x := (ok + ng) >> 1
if f(x) {
ok = x
} else {
ng = x
}
}
return ok
}
type BitVector struct {
bits []uint64
preSum []int32
}
func NewBitVector(n int32) *BitVector {
return &BitVector{bits: make([]uint64, n>>6+1), preSum: make([]int32, n>>6+1)}
}
func (bv *BitVector) Set(i int32) {
bv.bits[i>>6] |= 1 << (i & 63)
}
func (bv *BitVector) Build() {
for i := 0; i < len(bv.bits)-1; i++ {
bv.preSum[i+1] = bv.preSum[i] + int32(bits.OnesCount64(bv.bits[i]))
}
}
func (bv *BitVector) Rank(k int32, f bool) int32 {
m, s := bv.bits[k>>6], bv.preSum[k>>6]
res := s + int32(bits.OnesCount64(m&((1<<(k&63))-1)))
if f {
return res
}
return k - res
}
func abs(x int) int {
if x < 0 {
return -x
}
return x
}
func abs32(x int32) int32 {
if x < 0 {
return -x
}
return x
}
func min32(a, b int32) int32 {
if a < b {
return a
}
return b
}
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
}
func test() {
medianBruteForce := func(nums []int) int {
if len(nums) == 0 {
return 0
}
sortedNums := append([]int(nil), nums...)
sort.Ints(sortedNums)
mid := (len(sortedNums) - 1) / 2
return sortedNums[mid]
}
distSumBruteForce := func(nums []int, to int) int {
res := 0
for _, num := range nums {
res += abs(num - to)
}
return res
}
distSumRangeBruteForce := func(nums []int, to, start, end int) int {
res := 0
for i := start; i < end; i++ {
res += abs(nums[i] - to)
}
return res
}
distSumToMedianBruteForce := func(nums []int) int {
median := medianBruteForce(nums)
return distSumBruteForce(nums, median)
}
distSumToMedianRangeBruteForce := func(nums []int, start, end int) int {
median := medianBruteForce(nums[start:end])
return distSumRangeBruteForce(nums, median, start, end)
}
for tc := 0; tc < 1000; tc++ {
n := rand.Intn(1000) + 1
nums := make([]int, n)
for i := 0; i < n; i++ {
nums[i] = rand.Intn(1e6) - 5e5
}
mf := NewMedianFinderWaveletMatrix(NewWaveletMatrixWithSum(nums, nums, -1, true))
for i := 0; i < 100; i++ {
start, end := rand.Intn(n), rand.Intn(n)+1
if start > end {
start, end = end, start
}
to := rand.Intn(1e5) - 5e4
if mf.MedianRange(int32(start), int32(end)) != medianBruteForce(nums[start:end]) {
panic("err0")
}
if mf.DistSum(int(to)) != distSumBruteForce(nums, to) {
panic("err1")
}
if mf.DistSumRange(int(to), int32(start), int32(end)) != distSumRangeBruteForce(nums, to, start, end) {
panic("err2")
}
if mf.DistSumToMedian() != distSumToMedianBruteForce(nums) {
panic("err3")
}
if mf.DistSumToMedianRange(int32(start), int32(end)) != distSumToMedianRangeBruteForce(nums, start, end) {
fmt.Println(mf.DistSumToMedianRange(int32(start), int32(end)), distSumToMedianRangeBruteForce(nums, start, end))
panic("err4")
}
}
}
fmt.Println("pass")
}
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