Codeforces Round 130 (Div. 2) E. Blood Cousins（LCA+DFS序+二分）【2100】

题目链接

https://codeforces.com/contest/208/problem/E

思路

此题有两个要点：第一，快速找到节点$u$的$p$级祖先。第二，在以节点$u$为根的子树中找到与节点$u$深度相同的节点的个数。

对于第一点，我们可以使用LCA算法在树上倍增，实现快速查询。

对于第二点，我们可以按照深度，将所有节点的DFS序全部存储到vector中，因为DFS序的单调性，直接二分查找即可。

时间复杂度：$O(nlo{g}_{2}n)$

代码

#include 

using namespace std;

#define int long long
#define double long double

typedef long long i64;
typedef unsigned long long u64;
typedef pair<int, int> pii;

const int N = 1e5 + 5, M = 1e2 + 5;
const int mod = 998244353;
const int inf = 0x3f3f3f3f3f3f3f3f;

std::mt19937 rnd(time(0));

int n, m;
int r[N];
struct LCA
{
	vector<vector<int>>mp;
	vector<int>depth;
	vector<int>L, R;
	vector<vector<int>>fa;
	vector<vector<int>>dep;
	int idx;

	LCA() {}
	LCA(int n) {init(n);}

	void init(int n)
	{
		mp.resize(n + 1);
		depth.resize(n + 1);
		L.resize(n + 1), R.resize(n + 1);
		fa.resize(n + 1, vector<int>(20));
		dep.resize(n + 1);
		idx = 0;
		fill(depth.begin(), depth.end(), inf);
	}

	void add_edge(int a, int b)
	{
		//建双向边
		mp[a].push_back(b);
		mp[b].push_back(a);
	}

	void dfs(int u, int fu)
	{
		L[u] = ++idx;
		dep[depth[u]].push_back(L[u]);
		for (int j : mp[u])
		{
			if (j == fu) continue;
			dfs(j, u);
		}
		R[u] = idx;
	}

	void bfs(int root)
	{
		depth[0] = 0, depth[root] = 1;
		queue<int>q;
		q.push(root);
		while (q.size())
		{
			int u = q.front();
			q.pop();
			for (int i = 0; i < mp[u].size(); i++)
			{
				int j = mp[u][i];
				if (depth[j] > depth[u] + 1)
				{
					depth[j] = depth[u] + 1;
					q.push(j);
					fa[j][0] = u;
					for (int k = 1; k <= 19; k++)
					{
						fa[j][k] = fa[fa[j][k - 1]][k - 1];
					}
				}
			}
		}
	}

	int lca(int a, int b)
	{
		if (depth[a] < depth[b]) swap(a, b);
		for (int k = 19; k >= 0; k -- )
			if (depth[fa[a][k]] >= depth[b])
				a = fa[a][k];
		if (a == b) return a;
		for (int k = 19; k >= 0; k -- )
			if (fa[a][k] != fa[b][k])
			{
				a = fa[a][k];
				b = fa[b][k];
			}
		return fa[a][0];
	}

	int find(int u, int len)
	{
		for (int k = 19; k >= 0; k--)
		{
			int res = 1ll << k;
			if (res <= len)
			{
				len -= res;
				u = fa[u][k];
			}
		}
		return u;
	}
};
void solve()
{
	cin >> n;
	LCA tree(n);
	for (int i = 1; i <= n; i++)
	{
		cin >> r[i];
		if (r[i]) tree.add_edge(i, r[i]);
	}
	for (int i = 1; i <= n; i++)
	{
		if (!r[i])
			tree.bfs(i);
	}
	for (int i = 1; i <= n; i++)
	{
		if (!r[i])
			tree.dfs(i, 0);
	}
	cin >> m;
	while (m--)
	{
		int u, p;
		cin >> u >> p;
		if (tree.depth[u] <= p)
		{
			cout << 0 << " ";
		}
		else
		{
			int zu = tree.find(u, p);
			int deep = tree.depth[u];
			int low = lower_bound(tree.dep[deep].begin(), tree.dep[deep].end(), tree.L[zu]) - tree.dep[deep].begin();
			int high = upper_bound(tree.dep[deep].begin(), tree.dep[deep].end(), tree.R[zu]) - tree.dep[deep].begin();
			high--;
			cout << high - low + 1 - 1 << " ";
		}
	}
	cout << endl;
}

signed main()
{
	ios::sync_with_stdio(false);
	cin.tie(0), cout.tie(0);
	int test = 1;
	// cin >> test;
	for (int i = 1; i <= test; i++)
	{
		solve();
	}
	return 0;
}