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BfsNumbering.go
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BfsNumbering.go
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// bfs序编号.
// https://maspypy.github.io/library/graph/ds/bfs_numbering.hpp
// !求每个root的子树中,绝对深度为dep的顶点的bfs序的范围.
// !ID[v]:每个顶点的bfs序 (0-indexed)
// !GetRange(v, dep):以v为顶点的子树中, `绝对深度`为depth的顶点的bfs序的范围(左闭右开)
// !DiskRange(v, r):到v的距离不超过r的顶点的bfs序的范围.
package main
import (
"bufio"
"fmt"
"os"
)
// 顶点(bfs序)
//
// 0(0)
// / \
// / \
// / \
// 1(1) 2(2)
// / | \
// / | \
// 3(3) 4(4) 6(5)
// |
// 5(6)
func main() {
edges := [][2]int{{0, 1}, {0, 2}, {1, 3}, {1, 4}, {1, 6}, {3, 5}}
tree := make([][][2]int, 7)
for _, e := range edges {
tree[e[0]] = append(tree[e[0]], [2]int{e[1], 1})
tree[e[1]] = append(tree[e[1]], [2]int{e[0], 1})
}
B := NewBFSNumbering(tree, 0)
fmt.Println(B.GetRange(0, 1)) // 1 3
fmt.Println(B.GetRange(0, 2)) // 1 6
fmt.Println(B.DiskRange(1, 1)) // 3 6
}
func abc202e() {
// https://atcoder.jp/contests/abc202/tasks/abc202_e
// !子树中特定深度的结点个数
in := bufio.NewReader(os.Stdin)
out := bufio.NewWriter(os.Stdout)
defer out.Flush()
var n int
fmt.Fscan(in, &n)
parents := make([]int, n-1)
for i := 0; i < n-1; i++ {
fmt.Fscan(in, &parents[i])
parents[i]--
}
g := make([][][2]int, n)
for i := 0; i < n-1; i++ {
p := parents[i]
g[p] = append(g[p], [2]int{i + 1, 1})
}
B := NewBFSNumbering(g, 0)
var q int
fmt.Fscan(in, &q)
for i := 0; i < q; i++ {
var root, dep int
fmt.Fscan(in, &root, &dep)
root--
left, right := B.GetRange(root, dep)
fmt.Fprintln(out, right-left)
}
}
// BFS序编号.
type BFSNumbering struct {
Id []int32 // 每个点的bfs序编号(0-based)
Depth []int32 // 每个点的绝对深度(0-based)
Parent []int32 // 不存在时为-1
Lid, Rid []int32 // 每个点欧拉序的左右区间
graph [][][2]int
root int32
dfn int32
bfsOrder []int32 // 按照bfs序遍历的顶点
depthPreSum []int32
lidSeq []int32
}
func NewBFSNumbering(graph [][][2]int, root int) *BFSNumbering {
res := &BFSNumbering{graph: graph, root: int32(root)}
res.build()
return res
}
// 查询root的子树中,`绝对深度`为depth的顶点的欧拉序/括号序的左闭右开区间[start, end).
//
// 0 <= start < end <= n.
func (b *BFSNumbering) GetRange(root, depth int) (start, end int) {
if depth < int(b.Depth[root]) || depth >= len(b.depthPreSum)-1 {
return 0, 0
}
left1, right1 := b.Lid[root], b.Rid[root]
left2, right2 := b.depthPreSum[depth], b.depthPreSum[depth+1]
start = int(b.bs(left2-1, right2, left1))
end = int(b.bs(left2-1, right2, right1))
return
}
// dist(p,v)<=r
// 到v的距离不超过r的顶点的bfs序的范围.
func (b *BFSNumbering) DiskRange(v, r int) [][2]int {
if r < 0 {
return nil
}
var res [][2]int
d := int(b.Depth[v])
for k := 0; k <= r; k++ {
if v == -1 {
break
}
hi := d + r - k
lo := hi - 1
if lo < d {
lo = d
}
if b.Parent[v] == -1 {
lo = 0
}
for i := lo; i <= hi; i++ {
start, end := b.GetRange(v, i)
res = append(res, [2]int{start, end})
}
v = int(b.Parent[v])
d--
}
return res
}
func (b *BFSNumbering) build() {
n := len(b.graph)
b.Id = make([]int32, n)
b.Depth = make([]int32, n)
b.Lid = make([]int32, n)
b.Rid = make([]int32, n)
b.Parent = make([]int32, n)
for i := range b.Parent {
b.Parent[i] = -1
}
b.bfsOrder = make([]int32, 0, n)
b.bfs()
b.dfs(b.root)
d := int32(-1)
for _, v := range b.Depth {
if v > d {
d = v
}
}
b.depthPreSum = make([]int32, d+2)
for i := 0; i < n; i++ {
b.depthPreSum[b.Depth[i]+1]++
}
for i := int32(0); i < d+1; i++ {
b.depthPreSum[i+1] += b.depthPreSum[i]
}
b.lidSeq = make([]int32, 0, n)
for i := 0; i < n; i++ {
b.lidSeq = append(b.lidSeq, b.Lid[b.bfsOrder[i]])
}
}
func (b *BFSNumbering) bfs() {
queue := make([]int32, len(b.graph))
head, tail := 0, 0
queue[tail] = b.root
tail++
for head < tail {
v := queue[head]
head++
b.Id[v] = int32(len(b.bfsOrder))
b.bfsOrder = append(b.bfsOrder, v)
for _, e := range b.graph[v] {
next := int32(e[0])
if next == b.Parent[v] {
continue
}
queue[tail] = next
tail++
b.Parent[next] = v
b.Depth[next] = b.Depth[v] + 1
}
}
}
func (b *BFSNumbering) dfs(v int32) {
b.Lid[v] = b.dfn
b.dfn++
for _, e := range b.graph[v] {
next := int32(e[0])
if next != b.Parent[v] {
b.dfs(next)
}
}
b.Rid[v] = b.dfn
}
func (b *BFSNumbering) bs(left, right, x int32) int32 {
for left+1 < right {
mid := (left + right) / 2
if b.lidSeq[mid] >= x {
right = mid
} else {
left = mid
}
}
return right
}
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
}