static void Main()
{
Console.SetOut(new System.IO.StreamWriter(Console.OpenStandardOutput())
{
AutoFlush = false
});
var h = Read();
int n = h[0], qc = h[1];
var qs = Array.ConvertAll(new bool[qc], _ => Read());
var uf = new UF(n);
foreach (var q in qs)
{
if (q[0] == 0)
{
uf.Unite(q[1], q[2]);
}
else
{
Console.WriteLine(uf.AreUnited(q[1], q[2]) ? 1 : 0);
}
}
Console.Out.Flush();
}
static void Main()
{
var h = Read();
var n = h[0];
var ab = new int[h[1]].Select(_ => Read()).ToArray();
var cd = new int[h[2]].Select(_ => Read()).ToArray();
var uf = new UF(n + 1);
foreach (var x in ab)
{
uf.Unite(x[0], x[1]);
}
var roots = Enumerable.Range(0, n + 1).GroupBy(uf.GetRoot).ToDictionary(g => g.Key, g => g.Count());
var c = Enumerable.Range(0, n + 1).Select(uf.GetRoot).Select(x => roots[x] - 1).ToArray();
foreach (var x in ab)
{
c[x[0]]--;
c[x[1]]--;
}
foreach (var x in cd)
{
if (!uf.AreUnited(x[0], x[1]))
{
continue;
}
c[x[0]]--;
c[x[1]]--;
}
Console.WriteLine(string.Join(" ", c.Skip(1)));
}
static object Solve()
{
var(n, m) = Read2();
var es = Array.ConvertAll(new bool[m], _ => Read2());
var uf = new UF(n + 1);
var vs = new List <int>();
foreach (var e in es)
{
if (uf.AreUnited(e.u, e.v))
{
vs.Add(e.u);
}
else
{
uf.Unite(e.u, e.v);
}
}
if (vs.Select(uf.GetRoot).Distinct().Count() != vs.Count)
{
return(0);
}
if (uf.GroupsCount - 1 != vs.Count)
{
return(0);
}
return(MPow(2, vs.Count));
}
static void Main()
{
var n = int.Parse(Console.ReadLine());
var qc = int.Parse(Console.ReadLine());
var qs = Array.ConvertAll(new bool[qc], _ => Read4());
var roots = new int[n + 1];
var d = new long[n + 1];
foreach (var(_, x, y, v) in qs.Where(q => q.t == 0).OrderBy(q => q.x))
{
if (roots[x] == -1)
{
roots[x] = x;
}
roots[y] = roots[x];
d[y] = v - d[x];
}
var uf = new UF(n + 1);
Console.SetOut(new System.IO.StreamWriter(Console.OpenStandardOutput())
{
AutoFlush = false
});
foreach (var(t, x, y, v) in qs)
{
if (t == 0)
{
uf.Unite(x, y);
}
else
{
if (uf.AreUnited(x, y))
{
var v0 = (x - roots[x]) % 2 == 0 ? v - d[x] : d[x] - v;
var vy = (y - roots[y]) % 2 == 0 ? d[y] + v0 : d[y] - v0;
Console.WriteLine(vy);
}
else
{
Console.WriteLine("Ambiguous");
}
}
}
Console.Out.Flush();
}
// 連結な無向グラフから無向木を取り出します。
static int[][] GetUndirectedTree(int n, int[][] ues)
{
var uf = new UF(n);
var res = new List <int[]>();
foreach (var e in ues)
{
if (uf.AreUnited(e[0], e[1]))
{
continue;
}
uf.Unite(e[0], e[1]);
res.Add(e);
}
return(res.ToArray());
}
static Edge[] Kruskal(int n, Edge[] ues)
{
var uf = new UF(n);
var mes = new List <Edge>();
foreach (var e in ues.OrderBy(e => e.cost))
{
if (uf.AreUnited(e.i, e.j))
{
continue;
}
uf.Unite(e.i, e.j);
mes.Add(e);
}
return(mes.ToArray());
}
static int[][] Kruskal(int n, int[][] ues)
{
var uf = new UF(n);
var mes = new List <int[]>();
foreach (var e in ues.OrderBy(e => e[2]))
{
if (uf.AreUnited(e[0], e[1]))
{
continue;
}
uf.Unite(e[0], e[1]);
mes.Add(e);
}
return(mes.ToArray());
}
static void Main()
{
var(h, w) = Read2();
var qc = int.Parse(Console.ReadLine());
h += 2;
w += 2;
int ToId(int i, int j) => i * w + j;
int[] Nexts(int id) => new[] { id + 1, id - 1, id + w, id - w };
var u = new bool[h * w];
var uf = new UF(h * w);
Console.SetOut(new System.IO.StreamWriter(Console.OpenStandardOutput())
{
AutoFlush = false
});
for (int k = 0; k < qc; k++)
{
var q = Read();
if (q[0] == 1)
{
var(i, j) = (q[1], q[2]);
var p = ToId(i, j);
u[p] = true;
foreach (var np in Nexts(p))
{
if (u[np])
{
uf.Unite(p, np);
}
}
}
else
{
var(ai, aj, bi, bj) = (q[1], q[2], q[3], q[4]);
var a = ToId(ai, aj);
var b = ToId(bi, bj);
Console.WriteLine(u[a] && u[b] && uf.AreUnited(a, b) ? "Yes" : "No");
}
}
Console.Out.Flush();
}
public static int[][] Kruskal(int n, int[][] ues)
{
var uf = new UF(n);
var mes = new List <int[]>();
foreach (var e in ues.OrderBy(e => e[2]))
{
if (uf.AreUnited(e[0], e[1]))
{
continue;
}
uf.Unite(e[0], e[1]);
mes.Add(e);
// 実際の頂点数に注意。
// あまり実行速度に影響しないようです。
//if (mes.Count == n - 1) break;
}
return(mes.ToArray());
}
// Partitioning
static (int[][], int[][]) GetUndirectedTree(int n, int[][] ues)
{
var uf = new UF(n);
var res = new List <int[]>();
var res2 = new List <int[]>();
foreach (var e in ues)
{
if (uf.AreUnited(e[0], e[1]))
{
res2.Add(e);
}
else
{
uf.Unite(e[0], e[1]);
res.Add(e);
}
}
return(res.ToArray(), res2.ToArray());
}
static void Main()
{
Func <int[]> read = () => Console.ReadLine().Split().Select(int.Parse).ToArray();
var h = read();
var uf = new UF(h[0]);
var l = new List <string>();
foreach (var q in new int[h[1]].Select(_ => read()))
{
if (q[0] == 0)
{
uf.Unite(q[1], q[2]);
}
else
{
l.Add(uf.AreUnited(q[1], q[2]) ? "Yes" : "No");
}
}
Console.WriteLine(string.Join("\n", l));
}
static void Main()
{
var r = new List <int>();
var h = Read();
var n = h[0];
var uf = new UF(n);
for (int i = 0; i < h[1]; i++)
{
var q = Read();
if (q[0] == 0)
{
uf.Unite(q[1], q[2]);
}
else
{
r.Add(uf.AreUnited(q[1], q[2]) ? 1 : 0);
}
}
Console.WriteLine(string.Join("\n", r));
}
static void Main()
{
var(n, m) = Read2();
var uf = new UF(n);
foreach (var r in new int[m].Select(_ => Read()))
{
uf.Unite(r[0], r[1]);
}
var q = int.Parse(Console.ReadLine());
Console.WriteLine(string.Join("\n", new int[q].Select(_ => Read()).Select(r => uf.AreUnited(r[0], r[1]) ? "yes" : "no")));
}
static void Main()
{
var h = Read();
var n = h[0];
var es = new int[h[1]].Select(_ => Read()).ToArray();
var qs = new int[int.Parse(Console.ReadLine())].Select(_ => Read()).ToArray();
var map = Array.ConvertAll(new int[n], _ => new List <int>());
var map_r = Array.ConvertAll(new int[n], _ => new List <int>());
foreach (var e in es)
{
map[e[0]].Add(e[1]);
map_r[e[1]].Add(e[0]);
}
var uf = new UF(n);
var u = new bool[n];
var order = new List <int>();
Action <int> Dfs = null;
Dfs = v =>
{
u[v] = true;
foreach (var nv in map[v])
{
if (u[nv])
{
continue;
}
Dfs(nv);
}
order.Add(v);
};
for (int v = 0; v < n; v++)
{
if (!u[v])
{
Dfs(v);
}
}
Action <int> Dfs_r = null;
Dfs_r = v =>
{
u[v] = true;
foreach (var nv in map_r[v])
{
if (u[nv])
{
continue;
}
uf.Unite(v, nv);
Dfs_r(nv);
}
};
Array.Clear(u, 0, n);
order.Reverse();
foreach (var v in order)
{
if (!u[v])
{
Dfs_r(v);
}
}
Console.WriteLine(string.Join("\n", qs.Select(v => uf.AreUnited(v[0], v[1]) ? 1 : 0)));
}
static void Main()
{
var(h, w) = Read2();
// 1-indexed に注意
var sv = Read2();
var ev = Read2();
var s = GridHelper.ReadEnclosedGrid(ref h, ref w);
sv = (sv.i + 1, sv.j + 1);
ev = (ev.i + 1, ev.j + 1);
GridHelper.EncloseGrid(ref h, ref w, ref s);
const char Wall = '#';
var idMap = new int[h, w];
for (int i = 0; i < h; i++)
{
for (int j = 0; j < w; j++)
{
idMap[i, j] = i * w + j;
}
}
var uf = new UF(h * w);
for (int i = 2; i < h - 2; i++)
{
for (int j = 2; j < w - 2; j++)
{
if (s[i][j] == Wall)
{
continue;
}
if (s[i - 1][j] != Wall)
{
uf.Unite(idMap[i, j], idMap[i - 1, j]);
}
if (s[i][j - 1] != Wall)
{
uf.Unite(idMap[i, j], idMap[i, j - 1]);
}
}
}
var es = new List <(int v1, int v2)>();
var sv2 = uf.GetRoot(idMap[sv.i, sv.j]);
var ev2 = uf.GetRoot(idMap[ev.i, ev.j]);
for (int i = 2; i < h - 2; i++)
{
for (int j = 2; j < w - 2; j++)
{
if (s[i][j] == Wall)
{
continue;
}
var id = idMap[i, j];
for (int di = -2; di <= 0; di++)
{
for (int dj = -2; dj <= 2; dj++)
{
if (s[i + di][j + dj] == Wall)
{
continue;
}
var did = idMap[i + di, j + dj];
if (uf.AreUnited(id, did))
{
continue;
}
var(v1, v2) = (uf.GetRoot(id), uf.GetRoot(did));
if (v1 > v2)
{
(v1, v2) = (v2, v1);
}
es.Add((v1, v2));
}
}
}
}
var r = ShortestPath.Bfs(h * w, es.Distinct().Select(e => new[] { e.v1, e.v2 }).ToArray(), false, sv2, ev2);
Console.WriteLine(r.IsConnected(ev2) ? r[ev2] : -1);
}
static void Main()
{
var h = Read();
int n = h[0], m = h[1];
var rs = new int[m].Select(_ => Read()).Select((x, id) => (id, a: x[0], b: x[1], c: (long)x[2])).ToArray();
var n2 = Enumerable.Range(0, 20).Select(i => 1 << i).First(x => x >= n - 1);
var uf = new UF(n + 1);
var minEdges = new List <int>();
var extraEdges = new int[n2].Select(_ => new List <int>()).ToArray();
var maxCost = new long[m];
foreach (var r in rs.OrderBy(r => r.c))
{
if (!uf.AreUnited(r.a, r.b))
{
uf.Unite(r.a, r.b);
minEdges.Add(r.id);
}
else
{
extraEdges[n2 >> 1].Add(r.id);
}
}
var minCost = minEdges.Sum(id => rs[id].c);
// 並列二分探索。
for (int f = n2 >> 1; f > 0; f >>= 1)
{
var uf2 = new UF(n + 1);
for (int i = 0; i < n2; i++)
{
// unite する前に判定します。
if (i % f == 0 && i / f % 2 == 1)
{
foreach (var id in extraEdges[i])
{
var(_, a, b, _) = rs[id];
if (f > 1)
{
if (uf2.AreUnited(a, b))
{
extraEdges[i - (f >> 1)].Add(id);
}
else
{
extraEdges[i + (f >> 1)].Add(id);
}
}
else
{
var maxIndex = uf2.AreUnited(a, b) ? i - 1 : i;
maxCost[id] = rs[minEdges[maxIndex]].c;
}
}
extraEdges[i].Clear();
}
if (i < n - 1)
{
var r = rs[minEdges[i]];
uf2.Unite(r.a, r.b);
}
}
}
Console.WriteLine(string.Join("\n", maxCost.Select((x, id) => x == 0 ? minCost : minCost + rs[id].c - x)));
}
static int MinCostArborescence(int n, int sv, List <int[]>[] map, UF uf)
{
// 入る辺のうち最小のもの。
var minEdges = new int[n][];
for (int v = 0; v < n; v++)
{
if (v == sv || map[v]?.Any() != true)
{
continue;
}
var min = map[v].Min(e => e[2]);
minEdges[v] = map[v].First(e => e[2] == min);
uf.Unite(v, minEdges[v][0]);
}
var rn = Enumerable.Range(0, n).ToArray();
if (rn.All(v => uf.AreUnited(v, sv)))
{
return(minEdges.Sum(e => e?[2] ?? 0));
}
// 根と非連結になっているパスのうち、サイクルとなっている部分を縮約します。
// 0 型と 6 型のいずれか。
var sum = 0;
var u = new bool[n];
var reductMap = new int[n];
for (int v = 0; v < n; v++)
{
if (uf.AreUnited(v, sv))
{
map[v].Clear();
sum += minEdges[v]?[2] ?? 0;
reductMap[v] = sv;
continue;
}
if (u[v])
{
continue;
}
var cycle = Array.FindAll(rn, i => uf.AreUnited(v, i));
foreach (var i in cycle)
{
u[i] = true;
}
// vc0 に縮約します。
var vc0 = cycle[0];
var gs2 = cycle.Where(i => minEdges[i] != null).Select(i => minEdges[i][0]).GroupBy(i => i).Where(g => g.Count() == 2).ToArray();
if (gs2.Any())
{
// 6 型の場合。
vc0 = gs2[0].Key;
var path = new List <int> {
vc0
};
for (var t = vc0; (t = minEdges[t][0]) != vc0;)
{
path.Add(t);
}
cycle = path.ToArray();
}
var cycleSum = cycle.Sum(i => minEdges[i]?[2] ?? 0);
foreach (var i in cycle)
{
reductMap[i] = vc0;
map[i].RemoveAll(e => uf.AreUnited(e[0], e[1]));
if (i == vc0)
{
foreach (var e in map[i])
{
e[2] += cycleSum - minEdges[i][2];
}
}
else
{
foreach (var e in map[i])
{
e[2] += cycleSum - minEdges[i][2];
map[vc0].Add(e);
}
map[i].Clear();
}
}
}
foreach (var es in map)
{
foreach (var e in es)
{
e[0] = reductMap[e[0]];
e[1] = reductMap[e[1]];
}
}
return(MinCostArborescence(n, sv, map, uf) + sum);
}