結果

問題 No.1332 Range Nearest Query
ユーザー 草苺奶昔
提出日時 2023-03-13 16:53:56
言語 Go
(1.23.4)
結果
AC  
実行時間 1,002 ms / 2,500 ms
コード長 9,513 bytes
コンパイル時間 10,605 ms
コンパイル使用メモリ 223,200 KB
実行使用メモリ 96,804 KB
最終ジャッジ日時 2024-09-18 07:37:41
合計ジャッジ時間 45,320 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge5
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ファイルパターン 結果
other AC * 48
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ソースコード

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プレゼンテーションモードにする

package main
import (
    "bufio"
    "fmt"
    "math/bits"
    "os"
)
func 区间最短距离和() {
    // 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)
    }
}
func main() {
    // nums := []int{3, 1, 2, 4, 5, 6, 7, 8, 9, 10}
    // wm := NewWaveletMatrixSum(nums, 32)
    // fmt.Println(wm.MaxRightValue(0, 10, 0, func(preSum E) bool { return preSum < 11 })) // 5 即值域在 [0,5) 中的数的和小于 11
    // fmt.Println(wm.MaxRightCount(0, 10, 0, func(preSum E) bool { return preSum < 11 })) // 4 即排序后前 4 个数的和小于 11
    // fmt.Println(wm.Ceil(0, 10, 3, 0))
    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])
    }
    M := NewWaveletMatrixSum(nums, 32)
    var q int
    fmt.Fscan(in, &q)
    for i := 0; i < q; i++ {
        var left, right, x int
        fmt.Fscan(in, &left, &right, &x)
        left--
        res := INF
        lower := M.Floor(left, right, x, 0) // 小于等于x的最大值
        if lower != -INF {
            res = min(res, abs(lower-x))
        }
        higher := M.Ceil(left, right, x, 0) // 大于等于x的最小值
        if higher != INF {
            res = min(res, abs(higher-x))
        }
        fmt.Fprintln(out, res)
    }
}
func min(a, b int) int {
    if a < b {
        return a
    }
    return b
}
const INF int = 1e18
type E = int
func (*WaveletMatrixSum) e() E        { return 0 }
func (*WaveletMatrixSum) op(a, b E) E { return a + b }
func (*WaveletMatrixSum) 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] = res.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] = res.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, wm.op(wm.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 := wm.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 = wm.op(sum, wm.get(d, left+wm.mid[d]-l0, right+wm.mid[d]-r0))
                left, right = l0, r0
            } else {
                sum = wm.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, wm.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 = wm.op(sum, wm.get(d, left+wm.mid[d]-l0, right+wm.mid[d]-r0))
                left, right = l0, r0
            } else {
                sum = wm.op(sum, wm.get(d, l0, r0))
                left, right = left+wm.mid[d]-l0, right+wm.mid[d]-r0
            }
        }
    }
    if k != 0 {
        sum = wm.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 := wm.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(wm.op(sum, loSum)) {
            sum = wm.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 := wm.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(wm.op(sum, loSum)) {
            sum = wm.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(wm.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 wm.op(wm.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) 内の 1 の個数
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
}
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