#853332 (Go) No.1254 補強への架け橋

提出ソース

結果

問題	No.1254 補強への架け橋
ユーザー	草苺奶昔
提出日時	2023-03-27 02:13:20
言語	Go (1.22.1)
結果	AC
実行時間	234 ms / 2,000 ms
コード長	12,443 bytes
コンパイル時間	13,452 ms
コンパイル使用メモリ	227,288 KB
実行使用メモリ	45,252 KB
最終ジャッジ日時	2024-09-19 10:06:18
合計ジャッジ時間	27,394 ms
ジャッジサーバーID （参考情報）	judge3 / judge5

このコードへのチャレンジ
（要ログイン）

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	2 ms 5,248 KB
testcase_01	AC	1 ms 5,376 KB
testcase_02	AC	1 ms 5,376 KB
testcase_03	AC	1 ms 5,376 KB
testcase_04	AC	1 ms 5,376 KB
testcase_05	AC	1 ms 5,376 KB
testcase_06	AC	1 ms 5,376 KB
testcase_07	AC	1 ms 5,376 KB
testcase_08	AC	1 ms 5,376 KB
testcase_09	AC	1 ms 5,376 KB
testcase_10	AC	1 ms 5,376 KB
testcase_11	AC	1 ms 5,376 KB
testcase_12	AC	1 ms 5,376 KB
testcase_13	AC	1 ms 5,376 KB
testcase_14	AC	1 ms 5,376 KB
testcase_15	AC	1 ms 5,376 KB
testcase_16	AC	1 ms 5,376 KB
testcase_17	AC	1 ms 5,376 KB
testcase_18	AC	1 ms 5,376 KB
testcase_19	AC	1 ms 5,376 KB
testcase_20	AC	2 ms 5,376 KB
testcase_21	AC	2 ms 5,376 KB
testcase_22	AC	1 ms 5,376 KB
testcase_23	AC	1 ms 5,376 KB
testcase_24	AC	2 ms 5,376 KB
testcase_25	AC	1 ms 5,376 KB
testcase_26	AC	1 ms 5,376 KB
testcase_27	AC	1 ms 5,376 KB
testcase_28	AC	1 ms 5,376 KB
testcase_29	AC	1 ms 5,376 KB
testcase_30	AC	1 ms 5,376 KB
testcase_31	AC	1 ms 5,376 KB
testcase_32	AC	1 ms 5,376 KB
testcase_33	AC	1 ms 5,376 KB
testcase_34	AC	1 ms 5,376 KB
testcase_35	AC	1 ms 5,376 KB
testcase_36	AC	1 ms 5,376 KB
testcase_37	AC	2 ms 5,376 KB
testcase_38	AC	2 ms 5,376 KB
testcase_39	AC	1 ms 5,376 KB
testcase_40	AC	1 ms 5,376 KB
testcase_41	AC	1 ms 5,376 KB
testcase_42	AC	1 ms 5,376 KB
testcase_43	AC	2 ms 5,376 KB
testcase_44	AC	1 ms 5,376 KB
testcase_45	AC	2 ms 5,376 KB
testcase_46	AC	2 ms 5,376 KB
testcase_47	AC	2 ms 5,376 KB
testcase_48	AC	2 ms 5,376 KB
testcase_49	AC	1 ms 5,376 KB
testcase_50	AC	3 ms 5,376 KB
testcase_51	AC	3 ms 5,376 KB
testcase_52	AC	3 ms 5,376 KB
testcase_53	AC	3 ms 5,376 KB
testcase_54	AC	3 ms 5,376 KB
testcase_55	AC	2 ms 5,376 KB
testcase_56	AC	2 ms 5,376 KB
testcase_57	AC	2 ms 5,376 KB
testcase_58	AC	2 ms 5,376 KB
testcase_59	AC	2 ms 5,376 KB
testcase_60	AC	2 ms 5,376 KB
testcase_61	AC	2 ms 5,376 KB
testcase_62	AC	2 ms 5,376 KB
testcase_63	AC	15 ms 5,632 KB
testcase_64	AC	4 ms 5,376 KB
testcase_65	AC	10 ms 5,376 KB
testcase_66	AC	8 ms 5,376 KB
testcase_67	AC	4 ms 5,376 KB
testcase_68	AC	9 ms 5,376 KB
testcase_69	AC	11 ms 5,376 KB
testcase_70	AC	5 ms 5,376 KB
testcase_71	AC	4 ms 5,376 KB
testcase_72	AC	11 ms 5,376 KB
testcase_73	AC	5 ms 5,376 KB
testcase_74	AC	11 ms 5,376 KB
testcase_75	AC	8 ms 5,376 KB
testcase_76	AC	3 ms 5,376 KB
testcase_77	AC	7 ms 5,376 KB
testcase_78	AC	14 ms 5,376 KB
testcase_79	AC	14 ms 5,376 KB
testcase_80	AC	11 ms 5,376 KB
testcase_81	AC	13 ms 5,376 KB
testcase_82	AC	12 ms 5,376 KB
testcase_83	AC	167 ms 29,440 KB
testcase_84	AC	168 ms 27,776 KB
testcase_85	AC	97 ms 18,432 KB
testcase_86	AC	137 ms 23,552 KB
testcase_87	AC	148 ms 25,856 KB
testcase_88	AC	20 ms 5,888 KB
testcase_89	AC	165 ms 28,032 KB
testcase_90	AC	103 ms 18,688 KB
testcase_91	AC	78 ms 16,000 KB
testcase_92	AC	40 ms 9,344 KB
testcase_93	AC	126 ms 21,888 KB
testcase_94	AC	120 ms 22,756 KB
testcase_95	AC	121 ms 23,936 KB
testcase_96	AC	162 ms 24,884 KB
testcase_97	AC	65 ms 12,928 KB
testcase_98	AC	166 ms 26,496 KB
testcase_99	AC	92 ms 18,176 KB
testcase_100	AC	164 ms 29,108 KB
testcase_101	AC	36 ms 9,600 KB
testcase_102	AC	19 ms 6,272 KB
testcase_103	AC	40 ms 9,344 KB
testcase_104	AC	57 ms 11,824 KB
testcase_105	AC	126 ms 22,016 KB
testcase_106	AC	73 ms 16,560 KB
testcase_107	AC	172 ms 28,672 KB
testcase_108	AC	177 ms 26,976 KB
testcase_109	AC	125 ms 22,400 KB
testcase_110	AC	117 ms 20,736 KB
testcase_111	AC	130 ms 21,760 KB
testcase_112	AC	53 ms 12,160 KB
testcase_113	AC	110 ms 19,456 KB
testcase_114	AC	71 ms 14,480 KB
testcase_115	AC	23 ms 6,528 KB
testcase_116	AC	83 ms 15,616 KB
testcase_117	AC	53 ms 12,288 KB
testcase_118	AC	155 ms 26,752 KB
testcase_119	AC	87 ms 17,920 KB
testcase_120	AC	151 ms 26,980 KB
testcase_121	AC	43 ms 10,112 KB
testcase_122	AC	82 ms 16,256 KB
testcase_123	AC	2 ms 5,376 KB
testcase_124	AC	226 ms 44,160 KB
testcase_125	AC	234 ms 45,252 KB

権限があれば一括ダウンロードができます

ソースコード

raw source code

package main

import (
	"bufio"
	"fmt"
	"os"
	"sort"
	"strings"
)

func main() {
	// a, b, c := BuildNamoriForest(5, []Edge{{0, 1, 1, 0}, {1, 2, 1, 1}, {2, 3, 1, 2}, {3, 4, 1, 3}, {4, 0, 1, 4}}, false)

	// fmt.Println(a[0].CycleEdges, b, c)
	yuki1254()
}

func yuki1254() {
	in := bufio.NewReader(os.Stdin)
	out := bufio.NewWriter(os.Stdout)
	defer out.Flush()

	var n int
	fmt.Fscan(in, &n)
	g := make([][]Edge, n)
	for i := 0; i < n; i++ {
		var a, b int
		fmt.Fscan(in, &a, &b)
		a--
		b--
		g[a] = append(g[a], Edge{a, b, 1, i})
		g[b] = append(g[b], Edge{b, a, 1, i})
	}

	G := NewNamoriGraph(g)
	G.Build(false)
	res := []int{}
	for _, e := range G.CycleEdges {
		res = append(res, e.id+1)
	}
	sort.Ints(res)
	fmt.Fprintln(out, len(res))
	for _, v := range res {
		fmt.Fprint(out, v, " ")
	}
}

func abc266_f() {
	// https://atcoder.jp/contests/abc266/tasks/abc266_f
	// 给定一个基环树,问从x到y的路径是否唯一
	// 等价于不能走环上=>在同一个子树中
	in := bufio.NewReader(os.Stdin)
	out := bufio.NewWriter(os.Stdout)
	defer out.Flush()

	var n int
	fmt.Fscan(in, &n)
	graph := make([][]Edge, n)
	for i := 0; i < n; i++ {
		var a, b int
		fmt.Fscan(in, &a, &b)
		a--
		b--
		graph[a] = append(graph[a], Edge{a, b, 1, i})
		graph[b] = append(graph[b], Edge{b, a, 1, i})
	}

	G := NewNamoriGraph(graph)
	G.Build(false) // !without HLD

	var q int
	fmt.Fscan(in, &q)
	for i := 0; i < q; i++ {
		var x, y int
		fmt.Fscan(in, &x, &y)
		x--
		y--
		root1, _ := G.GetId(x)
		root2, _ := G.GetId(y)
		if root1 == root2 {
			fmt.Fprintln(out, "Yes")
		} else {
			fmt.Fprintln(out, "No")
		}
	}
}

func namoriCut() {
	// https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2891
	// 给定一个基环树 q个询问(x,y)
	// 求使得x和y不连通最少需要切掉多少条边
	// 如果两个点都在环上,则答案为2
	// 否则答案为1(两点之间只有唯一的一条路径)

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

	var n int
	fmt.Fscan(in, &n)
	graph := make([][]Edge, n)
	for i := 0; i < n; i++ {
		var a, b int
		fmt.Fscan(in, &a, &b)
		a, b = a-1, b-1
		graph[a] = append(graph[a], Edge{a, b, 1, i})
		graph[b] = append(graph[b], Edge{b, a, 1, i})
	}
	G := NewNamoriGraph(graph)
	G.Build(false)

	var q int
	fmt.Fscan(in, &q)
	for i := 0; i < q; i++ {
		var x, y int
		fmt.Fscan(in, &x, &y)
		x, y = x-1, y-1
		_, treeId1 := G.GetId(x)
		_, treeId2 := G.GetId(y)
		if treeId1 != 0 || treeId2 != 0 {
			fmt.Fprintln(out, 1)
		} else {
			fmt.Fprintln(out, 2)
		}
	}
}

func BuildNamoriForest(n int, edges []Edge, needHLD bool) (forest []*NamoriGraph, groupId, idInGroup []int) {
	uf := NewUnionFindArray(n)
	for _, e := range edges {
		uf.Union(e.from, e.to)
	}
	groups := uf.GetGroups()
	idInGroup = make([]int, n)          // 每个点在连通块中的编号
	groupId = make([]int, n)            // 每个点所在的连通块编号
	gs := make([]Graph, 0, len(groups)) // !每个连通块的图
	gid := 0
	for _, g := range groups {
		id := 0
		for _, v := range g {
			groupId[v] = gid
			idInGroup[v] = id
			id++
		}
		gs = append(gs, make(Graph, len(g)))
		gid++
	}
	for _, e := range edges {
		u, v := e.from, e.to
		gid := groupId[u]
		id1, id2 := idInGroup[u], idInGroup[v]
		gs[gid][id1] = append(gs[gid][id1], Edge{from: id1, to: id2, cost: e.cost, id: e.id})
	}

	forest = make([]*NamoriGraph, len(gs))
	for i, g := range gs {
		forest[i] = NewNamoriGraph(g)
		forest[i].Build(needHLD)
	}
	return
}

type NamoriGraph struct {
	// !以环上各个顶点i为根的无向树
	Trees []Graph
	// !基环树中在环上的边,边i连接着树的 root i和i+1 (i>=0)
	CycleEdges []Edge

	// 每个树的重链剖分(需要在Build(needHLD=true)后才能使用)
	HLDs []*_HLD

	g          Graph
	iv         [][]int
	markId, id []int
}

type Edge = struct{ from, to, cost, id int }
type Graph = [][]Edge

func NewNamoriGraph(g Graph) *NamoriGraph {
	return &NamoriGraph{g: g}
}

// needHLD :是否需要对各个子树进行重链剖分.
func (ng *NamoriGraph) Build(needHLD bool) {
	n := len(ng.g)
	deg := make([]int, n)
	used := make([]bool, n)
	que := []int{}
	for i := 0; i < n; i++ {
		deg[i] = len(ng.g[i])
		if deg[i] == 1 {
			que = append(que, i)
			used[i] = true
		}
	}

	for len(que) > 0 {
		idx := que[0]
		que = que[1:]
		for _, e := range ng.g[idx] {
			if used[e.to] {
				continue
			}
			deg[e.to]--
			if deg[e.to] == 1 {
				que = append(que, e.to)
				used[e.to] = true
			}
		}
	}

	mx := 0
	for _, edges := range ng.g {
		for _, e := range edges {
			mx = max(mx, e.id)
		}
	}

	edgeUsed := make([]bool, mx+1)
	loop := []int{}
	for i := 0; i < n; i++ {
		if used[i] {
			continue
		}
		for update := true; update; {
			update = false
			loop = append(loop, i)
			for _, e := range ng.g[i] {
				if used[e.to] || edgeUsed[e.id] {
					continue
				}
				edgeUsed[e.id] = true
				ng.CycleEdges = append(ng.CycleEdges, Edge{i, e.to, e.cost, e.id})
				i = e.to
				update = true
				break
			}
		}
		break
	}

	if len(loop) > 0 {
		loop = loop[:len(loop)-1]
	}
	ng.markId = make([]int, n)
	ng.id = make([]int, n)
	for i := 0; i < len(loop); i++ {
		pre := loop[(i+len(loop)-1)%len(loop)]
		nxt := loop[(i+1)%len(loop)]
		sz := 0
		ng.markId[loop[i]] = i
		ng.iv = append(ng.iv, []int{})
		ng.id[loop[i]] = sz
		sz++
		ng.iv[len(ng.iv)-1] = append(ng.iv[len(ng.iv)-1], loop[i])
		for _, e := range ng.g[loop[i]] {
			if e.to != pre && e.to != nxt {
				ng.markDfs(e.to, loop[i], i, &sz)
			}
		}
		tree := make(Graph, sz)
		for _, e := range ng.g[loop[i]] {
			if e.to != pre && e.to != nxt {
				tree[ng.id[loop[i]]] = append(tree[ng.id[loop[i]]], Edge{ng.id[loop[i]], ng.id[e.to], e.cost, e.id})
				tree[ng.id[e.to]] = append(tree[ng.id[e.to]], Edge{ng.id[e.to], ng.id[loop[i]], e.cost, e.id})
				ng.buildDfs(e.to, loop[i], tree)
			}
		}
		ng.Trees = append(ng.Trees, tree)
	}

	// HLD
	if !needHLD {
		return
	}

	t := len(ng.Trees)
	ng.HLDs = make([]*_HLD, 0, t)
	for _, tree := range ng.Trees {
		hld := _NewHLD(tree)
		hld.Build(0)
		ng.HLDs = append(ng.HLDs, hld)
	}
}

// 给定原图的顶点rawV,返回rawV所在的树的根节点和rawV在树中的编号.
func (ng *NamoriGraph) GetId(rawV int) (rootId, idInTree int) {
	return ng.markId[rawV], ng.id[rawV]
}

// 给定树的顶点编号root和某个点在树中的顶点编号idInTree,返回这个点在原图中的顶点编号.
//  GetInvId(root,0) 表示在环上的顶点root在原图中对应的顶点.
func (ng *NamoriGraph) GetInvId(rootId, idInTree int) (rawV int) {
	return ng.iv[rootId][idInTree]
}

func (ng *NamoriGraph) markDfs(idx, par, k int, l *int) {
	ng.markId[idx] = k
	ng.id[idx] = *l
	*l++
	ng.iv[len(ng.iv)-1] = append(ng.iv[len(ng.iv)-1], idx)
	for _, e := range ng.g[idx] {
		if e.to != par {
			ng.markDfs(e.to, idx, k, l)
		}
	}
}

func (ng *NamoriGraph) buildDfs(idx, par int, tree Graph) {
	for _, e := range ng.g[idx] {
		if e.to != par {
			tree[ng.id[idx]] = append(tree[ng.id[idx]], Edge{ng.id[idx], ng.id[e.to], e.cost, e.id})
			tree[ng.id[e.to]] = append(tree[ng.id[e.to]], Edge{ng.id[e.to], ng.id[idx], e.cost, e.id})
			ng.buildDfs(e.to, idx, tree)
		}
	}
}

func max(a, b int) int {
	if a > b {
		return a
	}
	return b
}

type _HLD struct {
	Tree                          Graph
	SubSize, Depth, Parent        []int
	dfn, dfnToNode, top, heavySon []int
	dfnId                         int
}

func (hld *_HLD) Build(root int) {
	hld.build(root, -1, 0)
	hld.markTop(root, root)
}

func _NewHLD(tree Graph) *_HLD {
	n := len(tree)
	dfn := make([]int, n)       // vertex => dfn
	dfnToNode := make([]int, n) // dfn => vertex
	top := make([]int, n)       // 所处轻/重链的顶点（深度最小），轻链的顶点为自身
	subSize := make([]int, n)   // 子树大小
	depth := make([]int, n)     // 深度
	parent := make([]int, n)    // 父结点
	heavySon := make([]int, n)  // 重儿子
	return &_HLD{
		Tree:      tree,
		dfn:       dfn,
		dfnToNode: dfnToNode,
		top:       top,
		SubSize:   subSize,
		Depth:     depth,
		Parent:    parent,
		heavySon:  heavySon,
	}
}

// 返回树节点 u 对应的 欧拉序区间 [down, up).
//  0 <= down < up <= n.
func (hld *_HLD) Id(u int) (down, up int) {
	down, up = hld.dfn[u], hld.dfn[u]+hld.SubSize[u]
	return
}

// 返回边 u-v 对应的 欧拉序起点编号.
func (hld *_HLD) Eid(u, v int) int {
	id1, _ := hld.Id(u)
	id2, _ := hld.Id(v)
	if id1 < id2 {
		return id2
	}
	return id1
}

// 处理路径上的可换操作.
//   0 <= start <= end <= n, [start,end).
func (hld *_HLD) QueryPath(u, v int, vertex bool, f func(start, end int)) {
	if vertex {
		hld.forEach(u, v, f)
	} else {
		hld.forEachEdge(u, v, f)
	}
}

// 处理以 root 为根的子树上的查询.
//   0 <= start <= end <= n, [start,end).
func (hld *_HLD) QuerySubTree(u int, vertex bool, f func(start, end int)) {
	if vertex {
		f(hld.dfn[u], hld.dfn[u]+hld.SubSize[u])
	} else {
		f(hld.dfn[u]+1, hld.dfn[u]+hld.SubSize[u])
	}
}

func (hld *_HLD) forEach(u, v int, cb func(start, end int)) {
	for {
		if hld.dfn[u] > hld.dfn[v] {
			u, v = v, u
		}
		cb(max(hld.dfn[hld.top[v]], hld.dfn[u]), hld.dfn[v]+1)
		if hld.top[u] != hld.top[v] {
			v = hld.Parent[hld.top[v]]
		} else {
			break
		}
	}
}

func (hld *_HLD) LCA(u, v int) int {
	for {
		if hld.dfn[u] > hld.dfn[v] {
			u, v = v, u
		}
		if hld.top[u] == hld.top[v] {
			return u
		}
		v = hld.Parent[hld.top[v]]
	}
}

func (hld *_HLD) Dist(u, v int) int {
	return hld.Depth[u] + hld.Depth[v] - 2*hld.Depth[hld.LCA(u, v)]
}

// 寻找以 start 为 top 的重链 ,heavyPath[-1] 即为重链末端节点.
func (hld *_HLD) GetHeavyPath(start int) []int {
	heavyPath := []int{start}
	cur := start
	for hld.heavySon[cur] != -1 {
		cur = hld.heavySon[cur]
		heavyPath = append(heavyPath, cur)
	}
	return heavyPath
}

func (hld *_HLD) forEachEdge(u, v int, cb func(start, end int)) {
	for {
		if hld.dfn[u] > hld.dfn[v] {
			u, v = v, u
		}
		if hld.top[u] != hld.top[v] {
			cb(hld.dfn[hld.top[v]], hld.dfn[v]+1)
			v = hld.Parent[hld.top[v]]
		} else {
			if u != v {
				cb(hld.dfn[u]+1, hld.dfn[v]+1)
			}
			break
		}
	}
}

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

func (hld *_HLD) markTop(cur, top int) {
	hld.top[cur] = top
	hld.dfn[cur] = hld.dfnId
	hld.dfnId++
	hld.dfnToNode[hld.dfn[cur]] = cur
	if hld.heavySon[cur] != -1 {
		hld.markTop(hld.heavySon[cur], top)
		for _, e := range hld.Tree[cur] {
			next := e.to
			if next != hld.heavySon[cur] && next != hld.Parent[cur] {
				hld.markTop(next, next)
			}
		}
	}
}

// NewUnionFindWithCallback ...
func NewUnionFindArray(n int) *UnionFindArray {
	parent, rank := make([]int, n), make([]int, n)
	for i := 0; i < n; i++ {
		parent[i] = i
		rank[i] = 1
	}

	return &UnionFindArray{
		Part:   n,
		rank:   rank,
		n:      n,
		parent: parent,
	}
}

type UnionFindArray struct {
	// 连通分量的个数
	Part int

	rank   []int
	n      int
	parent []int
}

func (ufa *UnionFindArray) Union(key1, key2 int) bool {
	root1, root2 := ufa.Find(key1), ufa.Find(key2)
	if root1 == root2 {
		return false
	}

	if ufa.rank[root1] > ufa.rank[root2] {
		root1, root2 = root2, root1
	}
	ufa.parent[root1] = root2
	ufa.rank[root2] += ufa.rank[root1]
	ufa.Part--
	return true
}

func (ufa *UnionFindArray) Find(key int) int {
	for ufa.parent[key] != key {
		ufa.parent[key] = ufa.parent[ufa.parent[key]]
		key = ufa.parent[key]
	}
	return key
}

func (ufa *UnionFindArray) IsConnected(key1, key2 int) bool {
	return ufa.Find(key1) == ufa.Find(key2)
}

func (ufa *UnionFindArray) GetGroups() map[int][]int {
	groups := make(map[int][]int)
	for i := 0; i < ufa.n; i++ {
		root := ufa.Find(i)
		groups[root] = append(groups[root], i)
	}
	return groups
}

func (ufa *UnionFindArray) Size(key int) int {
	return ufa.rank[ufa.Find(key)]
}

func (ufa *UnionFindArray) String() string {
	sb := []string{"UnionFindArray:"}
	for root, member := range ufa.GetGroups() {
		cur := fmt.Sprintf("%d: %v", root, member)
		sb = append(sb, cur)
	}
	sb = append(sb, fmt.Sprintf("Part: %d", ufa.Part))
	return strings.Join(sb, "\n")
}

yukicoder

結果

テストケース

ソースコード