結果

問題 No.1418 Sum of Sum of Subtree Size
ユーザー 草苺奶昔草苺奶昔
提出日時 2023-03-15 23:34:26
言語 Go
(1.22.1)
結果
AC  
実行時間 243 ms / 2,000 ms
コード長 6,632 bytes
コンパイル時間 14,764 ms
コンパイル使用メモリ 210,028 KB
実行使用メモリ 49,624 KB
最終ジャッジ日時 2023-10-18 12:38:00
合計ジャッジ時間 20,566 ms
ジャッジサーバーID
（参考情報） 		judge15 / judge11
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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 2 ms
4,348 KB
testcase_02 AC 1 ms
4,348 KB
testcase_03 AC 229 ms
29,228 KB
testcase_04 AC 238 ms
29,232 KB
testcase_05 AC 236 ms
29,236 KB
testcase_06 AC 230 ms
29,236 KB
testcase_07 AC 243 ms
29,232 KB
testcase_08 AC 158 ms
20,844 KB
testcase_09 AC 64 ms
10,156 KB
testcase_10 AC 72 ms
12,248 KB
testcase_11 AC 34 ms
7,968 KB
testcase_12 AC 111 ms
16,636 KB
testcase_13 AC 128 ms
18,720 KB
testcase_14 AC 136 ms
18,700 KB
testcase_15 AC 100 ms
16,516 KB
testcase_16 AC 11 ms
5,640 KB
testcase_17 AC 11 ms
5,640 KB
testcase_18 AC 208 ms
25,032 KB
testcase_19 AC 30 ms
7,972 KB
testcase_20 AC 5 ms
4,348 KB
testcase_21 AC 102 ms
16,512 KB
testcase_22 AC 80 ms
14,324 KB
testcase_23 AC 7 ms
4,348 KB
testcase_24 AC 6 ms
4,348 KB
testcase_25 AC 5 ms
4,348 KB
testcase_26 AC 6 ms
4,348 KB
testcase_27 AC 2 ms
4,348 KB
testcase_28 AC 3 ms
4,348 KB
testcase_29 AC 8 ms
4,348 KB
testcase_30 AC 7 ms
4,348 KB
testcase_31 AC 4 ms
4,348 KB
testcase_32 AC 5 ms
4,348 KB
testcase_33 AC 41 ms
14,068 KB
testcase_34 AC 206 ms
49,624 KB
testcase_35 AC 82 ms
24,468 KB
testcase_36 AC 17 ms
7,832 KB
testcase_37 AC 151 ms
29,060 KB
testcase_38 AC 136 ms
26,928 KB
testcase_39 AC 1 ms
4,348 KB
testcase_40 AC 1 ms
4,348 KB
testcase_41 AC 1 ms
4,348 KB
testcase_42 AC 2 ms
4,348 KB
testcase_43 AC 1 ms
4,348 KB
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ソースコード

diff # 

package main

import (
	"bufio"
	"fmt"
	"os"
)

func main() {

	in := bufio.NewReader(os.Stdin)
	out := bufio.NewWriter(os.Stdout)
	defer out.Flush()

	var n int
	fmt.Fscan(in, &n)

	R := NewRerootingEdge(n)
	for i := 0; i < n-1; i++ {
		var a, b int
		fmt.Fscan(in, &a, &b)
		a, b = a-1, b-1
		R.AddEdge(a, b, 1)
	}

	dp := R.ReRooting(
		func() E { return E{0, 0} },
		func(a, b E) E { return E{a[0] + b[0], a[1] + b[1]} },
		func(a E, v int) E { return E{a[0] + 1, a[1] + a[0] + 1} },
		func(a E, edge [2]int) E { return a },
	)

	res := 0
	for _, v := range dp {
		res += v[1]
	}
	fmt.Fprintln(out, res)
}

type E = [2]int
type ReRootingEdge struct {
	tree *_T
	dp1  []E // 边 pv 的子树v的dp值
	dp2  []E // 边 pv 的子树p的dp值
	dp   []E // 所有顶点v的子树dp值
}

func NewRerootingEdge(n int) *ReRootingEdge {
	return &ReRootingEdge{tree: _NT(n)}
}

func (rr *ReRootingEdge) AddEdge(from, to, weight int) {
	rr.tree.AddEdge(from, to, weight)
}

// !root 作为根节点时, 子树 v 的 dp 值
func (rr *ReRootingEdge) Get(root, v int) E {
	if root == v {
		return rr.dp[v]
	}
	if !rr.tree.IsInSubtree(root, v) {
		return rr.dp1[v]
	}
	w := rr.tree.Jump(v, root, 1)
	return rr.dp2[w]
}

func (rr *ReRootingEdge) ReRooting(
	e func() E,
	op func(a, b E) E,
	fev func(dp E, v int) E,
	fve func(dp E, edge [2]int /*next, weight*/) E,
) []E {
	rr.tree.Build(0)
	unit := e()
	N := len(rr.tree.Tree)
	dp1, dp2, dp := make([]E, N), make([]E, N), make([]E, N)
	for i := 0; i < N; i++ {
		dp1[i] = unit
		dp2[i] = unit
		dp[i] = unit
	}

	V := rr.tree.idToNode
	par := rr.tree.Parent
	for i := N - 1; i >= 0; i-- {
		v := V[i]
		ch := rr.tree.CollectChild(v)
		n := len(ch)
		x1, x2 := make([]E, n+1), make([]E, n+1)
		for i := range x1 {
			x1[i] = unit
			x2[i] = unit
		}
		for i := 0; i < n; i++ {
			x1[i+1] = op(x1[i], dp2[ch[i]])
		}
		for i := n - 1; i >= 0; i-- {
			x2[i] = op(dp2[ch[i]], x2[i+1])
		}
		for i := 0; i < n; i++ {
			dp2[ch[i]] = op(x1[i], x2[i+1])
		}
		dp[v] = x2[0]
		dp1[v] = fev(dp[v], v)
		for _, e := range rr.tree.Tree[v] {
			to := e[0]
			if to == par[v] {
				dp2[v] = fve(dp1[v], e)
			}
		}
	}

	v := V[0]
	dp[v] = fev(dp[v], v)
	for _, e := range rr.tree.Tree[v] {
		to := e[0]
		dp2[to] = fev(dp2[to], v)
	}

	for i := 0; i < N; i++ {
		v := V[i]
		for _, e := range rr.tree.Tree[v] {
			to := e[0]
			if to == par[v] {
				continue
			}
			x := fve(dp2[to], e)
			for _, f := range rr.tree.Tree[to] {
				to := f[0]
				if to == par[to] {
					continue
				}
				dp2[to] = op(dp2[to], x)
				dp2[to] = fev(dp2[to], to)
			}
			x = op(dp[to], x)
			dp[to] = fev(x, to)
		}
	}

	rr.dp1, rr.dp2, rr.dp = dp1, dp2, dp
	return dp
}

type _T struct {
	Tree          [][][2]int // (next, weight)
	Depth         []int
	Parent        []int
	LID, RID      []int // 欧拉序[in,out)
	idToNode      []int
	top, heavySon []int
	timer         int
}

func _NT(n int) *_T {
	tree := make([][][2]int, n)
	lid := make([]int, n)
	rid := make([]int, n)
	idToNode := make([]int, n)
	top := make([]int, n)      // 所处轻/重链的顶点（深度最小），轻链的顶点为自身
	depth := make([]int, n)    // 深度
	parent := make([]int, n)   // 父结点
	heavySon := make([]int, n) // 重儿子
	for i := range parent {
		parent[i] = -1
	}

	return &_T{
		Tree:     tree,
		Depth:    depth,
		Parent:   parent,
		LID:      lid,
		RID:      rid,
		idToNode: idToNode,
		top:      top,
		heavySon: heavySon,
	}
}

// 添加无向边 u-v, 边权为w.
func (tree *_T) AddEdge(u, v, w int) {
	tree.Tree[u] = append(tree.Tree[u], [2]int{v, w})
	tree.Tree[v] = append(tree.Tree[v], [2]int{u, w})
}

// 添加有向边 u->v, 边权为w.
func (tree *_T) AddDirectedEdge(u, v, w int) {
	tree.Tree[u] = append(tree.Tree[u], [2]int{v, w})
}

// root:0-based
//  当root设为-1时，会从0开始遍历未访问过的连通分量
func (tree *_T) Build(root int) {
	if root != -1 {
		tree.build(root, -1, 0)
		tree.markTop(root, root)
	} else {
		for i := 0; i < len(tree.Tree); i++ {
			if tree.Parent[i] == -1 {
				tree.build(i, -1, 0)
				tree.markTop(i, i)
			}
		}
	}
}

func (tree *_T) LCA(u, v int) int {
	for {
		if tree.LID[u] > tree.LID[v] {
			u, v = v, u
		}
		if tree.top[u] == tree.top[v] {
			return u
		}
		v = tree.Parent[tree.top[v]]
	}
}

// k: 0-based
//  如果不存在第k个祖先，返回-1
func (tree *_T) KthAncestor(root, k int) int {
	if k > tree.Depth[root] {
		return -1
	}
	for {
		u := tree.top[root]
		if tree.LID[root]-k >= tree.LID[u] {
			return tree.idToNode[tree.LID[root]-k]
		}
		k -= tree.LID[root] - tree.LID[u] + 1
		root = tree.Parent[u]
	}
}

// 从 from 节点跳向 to 节点,跳过 step 个节点(0-indexed)
//  返回跳到的节点,如果不存在这样的节点,返回-1
func (tree *_T) Jump(from, to, step int) int {
	if step == 1 {
		if from == to {
			return -1
		}
		if tree.IsInSubtree(to, from) {
			return tree.KthAncestor(to, tree.Depth[to]-tree.Depth[from]-1)
		}
		return tree.Parent[from]
	}
	c := tree.LCA(from, to)
	dac := tree.Depth[from] - tree.Depth[c]
	dbc := tree.Depth[to] - tree.Depth[c]
	if step > dac+dbc {
		return -1
	}
	if step <= dac {
		return tree.KthAncestor(from, step)
	}
	return tree.KthAncestor(to, dac+dbc-step)
}

func (tree *_T) CollectChild(root int) []int {
	res := []int{}
	for _, e := range tree.Tree[root] {
		next := e[0]
		if next != tree.Parent[root] {
			res = append(res, next)
		}
	}
	return res
}

func (tree *_T) SubtreeSize(u int) int {
	return tree.RID[u] - tree.LID[u]
}

// child 是否在 root 的子树中 (child和root不能相等)
func (tree *_T) IsInSubtree(child, root int) bool {
	return tree.LID[root] <= tree.LID[child] && tree.LID[child] < tree.RID[root]
}

func (tree *_T) build(cur, pre, dep int) int {
	subSize, heavySize, heavySon := 1, 0, -1
	for _, e := range tree.Tree[cur] {
		next := e[0]
		if next != pre {
			nextSize := tree.build(next, cur, dep+1)
			subSize += nextSize
			if nextSize > heavySize {
				heavySize, heavySon = nextSize, next
			}
		}
	}
	tree.Depth[cur] = dep
	tree.heavySon[cur] = heavySon
	tree.Parent[cur] = pre
	return subSize
}

func (tree *_T) markTop(cur, top int) {
	tree.top[cur] = top
	tree.LID[cur] = tree.timer
	tree.idToNode[tree.timer] = cur
	tree.timer++
	if tree.heavySon[cur] != -1 {
		tree.markTop(tree.heavySon[cur], top)
		for _, e := range tree.Tree[cur] {
			next := e[0]
			if next != tree.heavySon[cur] && next != tree.Parent[cur] {
				tree.markTop(next, next)
			}
		}
	}
	tree.RID[cur] = tree.timer
}

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
}
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