#851672 (Go) No.924 紲星

提出ソース

結果

問題	No.924 紲星
ユーザー	草苺奶昔
提出日時	2023-03-22 21:15:21
言語	Go (1.22.1)
結果	AC
実行時間	765 ms / 4,000 ms
コード長	8,242 bytes
コンパイル時間	11,505 ms
コンパイル使用メモリ	222,800 KB
実行使用メモリ	74,996 KB
最終ジャッジ日時	2023-10-18 19:06:34
合計ジャッジ時間	19,419 ms
ジャッジサーバーID （参考情報）	judge14 / judge15

このコードへのチャレンジ
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テストケース

テストケース表示

入力	結果	実行時間実行使用メモリ
testcase_00	AC	1 ms 4,348 KB
testcase_01	AC	1 ms 4,348 KB
testcase_02	AC	1 ms 4,348 KB
testcase_03	AC	3 ms 4,348 KB
testcase_04	AC	2 ms 4,348 KB
testcase_05	AC	3 ms 4,348 KB
testcase_06	AC	3 ms 4,348 KB
testcase_07	AC	2 ms 4,348 KB
testcase_08	AC	765 ms 74,988 KB
testcase_09	AC	732 ms 74,996 KB
testcase_10	AC	748 ms 74,988 KB
testcase_11	AC	752 ms 74,996 KB
testcase_12	AC	758 ms 74,996 KB
testcase_13	AC	346 ms 31,104 KB
testcase_14	AC	337 ms 22,808 KB
testcase_15	AC	314 ms 26,940 KB
testcase_16	AC	309 ms 60,264 KB
testcase_17	AC	502 ms 35,324 KB
testcase_18	AC	1 ms 4,348 KB

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ソースコード

raw source code

package main

import (
	"bufio"
	"fmt"
	"math/bits"
	"os"
)

func main() {
	// https://yukicoder.me/problems/no/924
	// n,q<=2e5
	// -1e9 <= nums[i] <= 1e9
	// 给定n个查询[l,r]
	// !求区间[l,r]中位数到区间[l,r]中每个数的距离之和
	// !也就求函数 f(x)= ∑|nums[i]-x| (l<=i<=right) 的最小值
	// !区间中位数
	in := bufio.NewReader(os.Stdin)
	out := bufio.NewWriter(os.Stdout)
	defer out.Flush()

	var n, q int
	fmt.Fscan(in, &n, &q)
	OFFSET := int(1e9 + 10)
	nums := make([]int, n)
	for i := range nums {
		fmt.Fscan(in, &nums[i])
		nums[i] += OFFSET
	}
	preSum := make([]int, n+1)
	for i := range nums {
		preSum[i+1] = preSum[i] + nums[i]
	}

	wm := NewWaveletMatrixSum(nums, 32+2)
	for i := 0; i < q; i++ {
		var left, right int
		fmt.Fscan(in, &left, &right)
		left--

		n := right - left
		lowerCount := n / 2
		ceilCount := n - lowerCount
		mid, lowerSum := wm.Kth(left, right, lowerCount, 0)
		_, allSum := wm.Kth(left, right, n, 0)
		ceilSum := allSum - lowerSum

		res := 0
		res += mid*lowerCount - lowerSum
		res += ceilSum - mid*ceilCount
		fmt.Fprintln(out, res)
	}
}


const INF int = 1e18

type E = int

func e() E        { return 0 }
func op(a, b E) E { return a + b }
func inv(a E) E   { return -a }

type WaveletMatrixSum struct {
	n, log int
	mid    []int
	bv     []*BitVector
	preSum [][]int
}

func NewWaveletMatrixSum(nums []int, log int) *WaveletMatrixSum {
	nums = append(nums[:0:0], nums...)
	res := &WaveletMatrixSum{}
	n := len(nums)
	mid := make([]int, log)
	bv := make([]*BitVector, log)
	for i := 0; i < log; i++ {
		bv[i] = NewBitVector(n)
	}
	preSum := make([][]int, log+1)
	for i := range preSum {
		preSum[i] = make([]int, n+1)
		for j := range preSum[i] {
			preSum[i][j] = e()
		}
	}

	a0, a1 := make([]int, n), make([]int, n)
	for d := log - 1; d >= -1; d-- {
		p0, p1 := 0, 0
		for i := 0; i < n; i++ {
			preSum[d+1][i+1] = op(preSum[d+1][i], nums[i])
		}
		if d == -1 {
			break
		}
		for i := 0; i < n; i++ {
			f := (nums[i] >> d) & 1
			if f == 0 {
				a0[p0] = nums[i]
				p0++
			} else {
				bv[d].Set(i)
				a1[p1] = nums[i]
				p1++
			}
		}
		mid[d] = p0
		bv[d].Build()
		nums, a0 = a0, nums
		for i := 0; i < p1; i++ {
			nums[p0+i] = a1[i]
		}
	}

	res.n, res.log = n, log
	res.mid, res.bv, res.preSum = mid, bv, preSum
	return res
}

// 返回区间 [left, right) 中 范围在 [a, b) 中的 (元素的个数, op 的结果)
func (wm *WaveletMatrixSum) Count(left, right, a, b, xor int) (int, E) {
	c1, s1 := wm.CountPrefix(left, right, a, xor)
	c2, s2 := wm.CountPrefix(left, right, b, xor)
	return c2 - c1, op(inv(s1), s2)
}

// 返回区间 [left, right) 中 范围在 [0, x) 中的 (元素的个数, op 的结果)
func (wm *WaveletMatrixSum) CountPrefix(left, right, x, xor int) (int, E) {
	if x >= 1<<wm.log {
		return right - left, wm.get(wm.log, left, right)
	}
	count := 0
	sum := e()
	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)
		var kf int
		if f == 0 {
			kf = r0 - l0
		} else {
			kf = (right - left) - (r0 - l0)
		}
		if add == 1 {
			count += kf
			if f == 1 {
				sum = op(sum, wm.get(d, left+wm.mid[d]-l0, right+wm.mid[d]-r0))
				left, right = l0, r0
			} else {
				sum = op(sum, wm.get(d, l0, r0))
				left, right = left+wm.mid[d]-l0, right+wm.mid[d]-r0
			}
		} else {
			if f == 0 {
				left, right = l0, r0
			} else {
				left, right = left+wm.mid[d]-l0, right+wm.mid[d]-r0
			}
		}
	}

	return count, sum
}

// 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 *WaveletMatrixSum) Kth(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, e()
	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)
		var kf int
		if f == 0 {
			kf = r0 - l0
		} else {
			kf = (right - left) - (r0 - l0)
		}
		if k < kf {
			if f == 0 {
				left, right = l0, r0
			} else {
				left, right = left+wm.mid[d]-l0, right+wm.mid[d]-r0
			}
		} else {
			k -= kf
			res |= 1 << d
			if f == 1 {
				sum = op(sum, wm.get(d, left+wm.mid[d]-l0, right+wm.mid[d]-r0))
				left, right = l0, r0
			} else {
				sum = op(sum, wm.get(d, l0, r0))
				left, right = left+wm.mid[d]-l0, right+wm.mid[d]-r0
			}
		}
	}

	if k != 0 {
		sum = op(sum, wm.get(0, left, left+k))
	}
	return res, sum
}

// 返回使得 check(prefixSum) 为 true 的最大值 val.
//  !(即区间内小于 val 的数的和 prefixSum 满足 check函数, 找到这样的最大的 val)
//  如果整个区间都满足, 返回 INF.
//  eg: val = 5 => 即区间内值域在 [0,5) 中的数的和满足 check 函数.
func (wm *WaveletMatrixSum) MaxRightValue(left, right, xor int, check func(preSum E) bool) E {
	if check(wm.get(wm.log, left, right)) {
		return INF
	}
	res := 0
	sum := e()
	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)
		var loSum E
		if f == 0 {
			loSum = wm.get(d, l0, r0)
		} else {
			loSum = wm.get(d, left+wm.mid[d]-l0, right+wm.mid[d]-r0)
		}
		if check(op(sum, loSum)) {
			sum = op(sum, loSum)
			res |= 1 << d
			if f == 1 {
				left, right = l0, r0
			} else {
				left, right = left+wm.mid[d]-l0, right+wm.mid[d]-r0
			}
		} else {
			if f == 0 {
				left, right = l0, r0
			} else {
				left, right = left+wm.mid[d]-l0, right+wm.mid[d]-r0
			}
		}
	}

	return res
}

// 返回使得 check(prefixSum) 为 true 的区间前缀个数的最大值.
//  eg: count = 4 => 即区间内的数排序后, 前4个数的和满足 check 函数.
func (wm *WaveletMatrixSum) MaxRightCount(left, right, xor int, check func(preSum E) bool) int {
	if check(wm.get(wm.log, left, right)) {
		return right - left
	}
	res := 0
	sum := e()
	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)
		var kf int
		var loSum E
		if f == 0 {
			kf = r0 - l0
			loSum = wm.get(d, l0, r0)
		} else {
			kf = (right - left) - (r0 - l0)
			loSum = wm.get(d, left+wm.mid[d]-l0, right+wm.mid[d]-r0)
		}

		if check(op(sum, loSum)) {
			sum = op(sum, loSum)
			res += kf
			if f == 1 {
				left, right = l0, r0
			} else {
				left, right = left+wm.mid[d]-l0, right+wm.mid[d]-r0
			}
		} else {
			if f == 0 {
				left, right = l0, r0
			} else {
				left, right = left+wm.mid[d]-l0, right+wm.mid[d]-r0
			}
		}
	}

	res += wm.binarySearch(func(k int) bool {
		return check(op(sum, wm.get(0, left, left+k)))
	}, 0, right-left)

	return res
}

// [left, right) 中小于等于 x 的数中最大的数
//  如果不存在则返回-INF
func (w *WaveletMatrixSum) Floor(start, end, value, xor int) int {
	less, _ := w.CountPrefix(start, end, value, xor)
	if less == 0 {
		return -INF
	}
	res, _ := w.Kth(start, end, less-1, xor)
	return res
}

// [left, right) 中大于等于 x 的数中最小的数
//  如果不存在则返回INF
func (w *WaveletMatrixSum) Ceil(start, end, value, xor int) int {
	less, _ := w.CountPrefix(start, end, value, xor)
	if less == end-start {
		return INF
	}
	res, _ := w.Kth(start, end, less, xor)
	return res
}

func (wm *WaveletMatrixSum) 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
}

func (wm *WaveletMatrixSum) get(d, l, r int) E {
	return op(inv(wm.preSum[d][l]), wm.preSum[d][r])
}

func abs(a int) int {
	if a < 0 {
		return -a
	}
	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]))
	}
}

// [0, k) 内1的個数
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
}