-
Notifications
You must be signed in to change notification settings - Fork 1
/
LinkCutTreeLca.java
185 lines (171 loc) · 4.64 KB
/
LinkCutTreeLca.java
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
package Data_Structures;
import java.util.*;
// Based on Daniel Sleator's implementation http://www.codeforces.com/contest/117/submission/860934
public class LinkCutTreeLca {
public static class Node {
Node left;
Node right;
Node parent;
// tests whether x is a root of a splay tree
boolean isRoot() {
return parent == null || (parent.left != this && parent.right != this);
}
}
static void connect(Node ch, Node p, Boolean isLeftChild) {
if (ch != null)
ch.parent = p;
if (isLeftChild != null) {
if (isLeftChild)
p.left = ch;
else
p.right = ch;
}
}
// rotates edge (x, x.parent)
// g g
// / /
// p x
// / \ --> / \
// x p.r x.l p
// / \ / \
// x.l x.r x.r p.r
static void rotate(Node x) {
Node p = x.parent;
Node g = p.parent;
boolean isRootP = p.isRoot();
boolean leftChildX = (x == p.left);
// create 3 edges: (x.r(l),p), (p,x), (x,g)
connect(leftChildX ? x.right : x.left, p, leftChildX);
connect(p, x, !leftChildX);
connect(x, g, !isRootP ? p == g.left : null);
}
// brings x to the root, balancing tree
//
// zig-zig case
// g x
// / \ p / \
// p g.r rot(p) / \ rot(x) x.l p
// / \ --> x g --> / \
// x p.r / \ / \ x.r g
// / \ x.l x.r p.r g.r / \
// x.l x.r p.r g.r
//
// zig-zag case
// g g
// / \ / \ x
// p g.r rot(x) x g.r rot(x) / \
// / \ --> / \ --> p g
// p.l x p x.r / \ / \
// / \ / \ p.l x.l x.r g.r
// x.l x.r p.l x.l
static void splay(Node x) {
while (!x.isRoot()) {
Node p = x.parent;
Node g = p.parent;
if (!p.isRoot())
rotate((x == p.left) == (p == g.left) ? p/*zig-zig*/ : x/*zig-zag*/);
rotate(x);
}
}
// makes node x the root of the virtual tree, and also x becomes the leftmost node in its splay tree
static Node expose(Node x) {
Node last = null;
for (Node y = x; y != null; y = y.parent) {
splay(y);
y.left = last;
last = y;
}
splay(x);
return last;
}
public static Node findRoot(Node x) {
expose(x);
while (x.right != null)
x = x.right;
splay(x);
return x;
}
public static void link(Node x, Node y) {
if (findRoot(x) == findRoot(y))
throw new RuntimeException("error: x and y are already connected");
expose(x);
if (x.right != null)
throw new RuntimeException("error: x is not a root node");
x.parent = y;
}
public static void cut(Node x) {
expose(x);
if (x.right == null)
throw new RuntimeException("error: x is a root node");
x.right.parent = null;
x.right = null;
}
public static Node lca(Node x, Node y) {
if (findRoot(x) != findRoot(y))
throw new RuntimeException("error: x and y are not connected");
expose(x);
return expose(y);
}
// random test
public static void main(String[] args) {
Random rnd = new Random(1);
for (int step = 0; step < 1000; step++) {
int n = rnd.nextInt(50) + 1;
int[] p = new int[n];
Arrays.fill(p, -1);
Node[] nodes = new Node[n];
for (int i = 0; i < n; i++)
nodes[i] = new Node();
for (int query = 0; query < 10_000; query++) {
int cmd = rnd.nextInt(10);
int u = rnd.nextInt(n);
Node x = nodes[u];
if (cmd == 0) {
expose(x);
if ((x.right != null) != (p[u] != -1))
throw new RuntimeException();
if (x.right != null) {
cut(x);
p[u] = -1;
}
} else if (cmd == 1) {
int v = rnd.nextInt(n);
Node y = nodes[v];
if ((findRoot(x) == findRoot(y)) != (root(p, u) == root(p, v)))
throw new RuntimeException();
if (findRoot(x) == findRoot(y)) {
Node lca = lca(x, y);
int cur = u;
Set<Integer> path = new HashSet<>();
for (; cur != -1; cur = p[cur])
path.add(cur);
cur = v;
for (; cur != -1 && !path.contains(cur); cur = p[cur]);
if (lca != nodes[cur])
throw new RuntimeException();
}
} else {
expose(x);
if ((x.right == null) != (p[u] == -1))
throw new RuntimeException();
if (x.right == null) {
int v = rnd.nextInt(n);
Node y = nodes[v];
if ((findRoot(x) != findRoot(y)) != (root(p, u) != root(p, v)))
throw new RuntimeException();
if (findRoot(x) != findRoot(y)) {
link(x, y);
p[u] = v;
}
}
}
}
}
}
static int root(int[] p, int u) {
int root = u;
while (p[root] != -1)
root = p[root];
return root;
}
}