题目链接

https://codeforces.com/problemset/problem/191/C

思路

一道比较板的LCA和树上差分的题。

先预处理出这棵树的LCA，之后对于每一对$a_i,b_i$，在树上做差分，最后用$dfs$处理差分数组即可。

树上差分记得从叶子向根节点，不要弄反。

代码

#include <bits/stdc++.h>
using namespace std;
#define int long long
const int N = 1e5 + 5;
const int inf = 0x3f3f3f3f3f3f3f3f;
int n, k;
int u[N], v[N];
int d[N];//差分数组
struct LCA
{
	vector<vector<int>>mp;
	vector<int>depth;
	vector<vector<int>>fa;

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

	void init(int n)
	{
		mp.resize(n + 1);
		depth.resize(n + 1);
		fa.resize(n + 1, vector<int>(20));
	}

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

	void bfs(int root)
	{
		fill(depth.begin(), depth.end(), inf);
		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];
	}
};
void solve()
{
	cin >> n;
	LCA tree(n);
	map<int, int>st;
	for (int i = 1; i < n; i++)
	{
		cin >> u[i] >> v[i];
		tree.add_edge(u[i], v[i]);
		st[u[i] * n + v[i]] = i;
		st[v[i] * n + u[i]] = i;
	}
	tree.bfs(1);
	cin >> k;
	for (int i = 1, a, b; i <= k; i++)
	{
		cin >> a >> b;
		int zu = tree.lca(a, b);
		if (zu != a && zu != b)
		{
			d[a]++, d[b]++, d[zu] -= 2;
		}
		else
		{
			if (zu == a) d[b]++, d[a]--;
			else d[a]++, d[b]--;
		}
	}
	auto dfs1 = [&](auto dfs1, int u, int fu)->void {
		for (int j : tree.mp[u])
		{
			if (j == fu) continue;
			dfs1(dfs1, j, u);
			d[u] += d[j];
		}
	};

	dfs1(dfs1, 1, -1);//树上差分->前缀和

	vector<int>ans(n);

	auto dfs2 = [&](auto dfs2, int u, int fu)-> void {
		for (int j : tree.mp[u])
		{
			if (j == fu) continue;
			int idx = st[u * n + j];
			ans[idx] = d[j];
			dfs2(dfs2, j, u);
		}
	};
	dfs2(dfs2, 1, -1);
	for (int i = 1; i < n; i++)
	{
		cout << ans[i] << " ";
	}
	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;
}