package main import ( "bufio" "fmt" "math/bits" "os" "sort" "strings" ) // No.1170 Never Want to Walk // https://yukicoder.me/problems/no/1170 // 数轴上有n个车站,第i个位置在xi // 如果两个车站之间的距离di与dj满足 A<=|di-dj|<=B,则这两个车站可以相互到达,否则不能相互到达 // 对每个车站,求出从该车站出发,可以到达的车站的数量 // 1<=n<=2e5 0<=A<=B<=1e9 0<=x1<=x2<...<=xn<=1e9 // // !将序列搬到线段树上加速区间操作(线段树优化建图). func main() { in := bufio.NewReader(os.Stdin) out := bufio.NewWriter(os.Stdout) defer out.Flush() var n int32 var A, B int fmt.Fscan(in, &n, &A, &B) positions := make([]int, n) for i := int32(0); i < n; i++ { fmt.Fscan(in, &positions[i]) } D := NewDivideInterval(n) uf := NewUnionFindArray(D.Size()) weights := make([]int, D.Size()) for i := int32(0); i < n; i++ { weights[D.Id(i)] = 1 } f := func(big, small int32) { weights[big] += weights[small] } var dfs func(int32) // 线段树上dfs dfs = func(cur int32) { if D.IsLeaf(cur) { return } for k := int32(0); k < 2; k++ { child := cur<<1 | k if !uf.IsConnected(cur, child) { uf.UnionWithCallback(cur, child, f) dfs(child) } } } for i := int32(0); i < n; i++ { start := int32(sort.SearchInts(positions, positions[i]+A)) end := int32(sort.SearchInts(positions, positions[i]+B+1)) D.EnumerateSegment(start, end, func(segmentId int32) { uf.UnionWithCallback(D.Id(i), segmentId, f) dfs(segmentId) }) } for i := int32(0); i < n; i++ { fmt.Fprintln(out, weights[uf.Find(D.Id(i))]) } } type DivideInterval struct { Offset int32 // 线段树中一共offset+n个节点,offset+i对应原来的第i个节点. n int32 } // 线段树分割区间. // 将长度为n的序列搬到长度为offset+n的线段树上, 以实现快速的区间操作. func NewDivideInterval(n int32) *DivideInterval { offset := int32(1) for offset < n { offset <<= 1 } return &DivideInterval{Offset: offset, n: n} } // 获取原下标为i的元素在树中的(叶子)编号. func (d *DivideInterval) Id(rawIndex int32) int32 { return rawIndex + d.Offset } // O(logn) 顺序遍历`[start,end)`区间对应的线段树节点. func (d *DivideInterval) EnumerateSegment(start, end int32, f func(segmentId int32)) { if !(0 <= start && start <= end && end <= d.n) { panic("invalid range") } for _, i := range d.getSegmentIds(start, end) { f(i) } } func (d *DivideInterval) EnumeratePoint(index int32, f func(segmentId int32)) { if index < 0 || index >= d.n { return } index += d.Offset for index > 0 { f(index) index >>= 1 } } // O(n) 从根向叶子方向push. func (d *DivideInterval) PushDown(f func(parent, child int32)) { for p := int32(1); p < d.Offset; p++ { f(p, p<<1) f(p, p<<1|1) } } // O(n) 从叶子向根方向update. func (d *DivideInterval) PushUp(f func(parent, child1, child2 int32)) { for p := d.Offset - 1; p > 0; p-- { f(p, p<<1, p<<1|1) } } // 线段树的节点个数. func (d *DivideInterval) Size() int32 { return d.Offset + d.n } func (d *DivideInterval) IsLeaf(segmentId int32) bool { return segmentId >= d.Offset } func (d *DivideInterval) Depth(u int32) int32 { if u == 0 { return 0 } return int32(bits.LeadingZeros32(uint32(u))) - 1 } // 线段树(完全二叉树)中两个节点的最近公共祖先(两个二进制数字的最长公共前缀). func (d *DivideInterval) Lca(u, v int32) int32 { if u == v { return u } if u > v { u, v = v, u } depth1 := d.Depth(u) depth2 := d.Depth(v) diff := u ^ (v >> (depth2 - depth1)) if diff == 0 { return u } len := bits.Len32(uint32(diff)) return u >> len } func (d *DivideInterval) getSegmentIds(start, end int32) []int32 { if !(0 <= start && start <= end && end <= d.n) { panic("invalid range") } var leftRes, rightRes []int32 for start, end = start+d.Offset, end+d.Offset; start < end; start, end = start>>1, end>>1 { if start&1 == 1 { leftRes = append(leftRes, start) start++ } if end&1 == 1 { end-- rightRes = append(rightRes, end) } } for i := len(rightRes) - 1; i >= 0; i-- { leftRes = append(leftRes, rightRes[i]) } return leftRes } // // // NewUnionFindWithCallback ... func NewUnionFindArray(n int32) *_UnionFindArray { parent, rank := make([]int32, n), make([]int32, n) for i := int32(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 int32 rank []int32 n int32 parent []int32 } func (ufa *_UnionFindArray) Union(key1, key2 int32) 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) UnionWithCallback(key1, key2 int32, cb func(big, small int32)) 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-- cb(root2, root1) return true } func (ufa *_UnionFindArray) Find(key int32) int32 { 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 int32) bool { return ufa.Find(key1) == ufa.Find(key2) } func (ufa *_UnionFindArray) GetGroups() map[int32][]int32 { groups := make(map[int32][]int32) for i := int32(0); i < ufa.n; i++ { root := ufa.Find(i) groups[root] = append(groups[root], i) } return groups } func (ufa *_UnionFindArray) Size(key int32) int32 { 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") }