Luogu P1505.[国家集训队]旅游

题解

真真正正是个码农题，不过很套路，熟练就打得很快，不过要用点维护边的信息在 \(\text{LCA}\) 出要注意，不能处理此点的信息

\(Code\)

#include<cstdio>
#include<iostream>
#include<cstring>
using namespace std;

const int N = 2e5 + 5;
int n, m, h[N];

struct edge{int to, nxt, w, id;}e[N << 1];
inline void add(int u, int v, int w, int id)
{
	static int tot = 0;
	e[++tot] = edge{v, h[u], w, id}, h[u] = tot;
}

int top[N], fa[N], dfn[N], dep[N], siz[N], son[N], ver[N], edg[N];
void dfs1(int x)
{
	siz[x] = 1;
	for(register int i = h[x]; i; i = e[i].nxt)
	{
		int v = e[i].to;
		if (v == fa[x]) continue;
		edg[v] = e[i].w, ver[e[i].id] = v, fa[v] = x, dep[v] = dep[x] + 1, dfs1(v), siz[x] += siz[v];
		if (siz[v] > siz[son[x]]) son[x] = v;
	}
}
void dfs2(int x)
{
	static int dfc = 0;
	dfn[x] = ++dfc;
	if (son[x]) top[son[x]] = top[x], dfs2(son[x]);
	for(register int i = h[x]; i; i = e[i].nxt)
	{
		int v = e[i].to;
		if (v == fa[x] || v == son[x]) continue;
		top[v] = v, dfs2(v);
	}
}

struct Tree{
	#define ls (p << 1)
	#define rs (ls | 1)
	const int INF = 0x3f3f3f3f;
	int sum[N << 2], mn[N << 2], mx[N << 2], tag[N << 2];

	inline Tree(){memset(mn, 0x3f3f3f3f, sizeof mn), memset(mx, -0x3f3f3f3f, sizeof mx);}
	void change(int p){sum[p] *= -1, mx[p] *= -1, mn[p] *= -1, swap(mx[p], mn[p]), tag[p] ^= 1;}
	void pushup(int p){sum[p] = sum[ls] + sum[rs], mn[p] = min(mn[ls], mn[rs]), mx[p] = max(mx[ls], mx[rs]);}
	void pushdown(int p)
	{
		if (!tag[p]) return;
		change(ls), change(rs), tag[p] ^= 1;
	}

	void update_node(int p, int l, int r, int x, int v)
	{
		if (l == r)
		{
			sum[p] = mn[p] = mx[p] = v;
			if (l == 1) mn[p] = INF, mx[p] = -INF;
			return;
		}
		pushdown(p);
		int mid = (l + r) >> 1;
		if (x <= mid) update_node(ls, l, mid, x, v);
		else update_node(rs, mid + 1, r, x, v);
		pushup(p);
	}

	void update_rev(int p, int l, int r, int x, int y)
	{
		if (x <= l && r <= y) return void(change(p));
		pushdown(p);
		int mid = (l + r) >> 1;
		if (x <= mid) update_rev(ls, l, mid, x, y);
		if (y > mid) update_rev(rs, mid + 1, r, x, y);
		pushup(p);
	}
	inline void tree_rev(int x, int y)
	{
		int fx = top[x], fy = top[y];
		while (fx ^ fy)
		{
			if (dep[fx] > dep[fy]) update_rev(1, 1, n, dfn[fx], dfn[x]), x = fa[fx], fx = top[x];
			else update_rev(1, 1, n, dfn[fy], dfn[y]), y = fa[fy], fy = top[y];
		}
		if (dep[x] > dep[y]) swap(x, y);
		if (x == y) return;
		update_rev(1, 1, n, dfn[x] + 1, dfn[y]);
	}

	int query_sum(int p, int l, int r, int x, int y)
	{
		if (x <= l && r <= y) return sum[p];
		pushdown(p);
		int mid = (l + r) >> 1, ret = 0;
		if (x <= mid) ret += query_sum(ls, l, mid, x, y);
		if (y > mid) ret += query_sum(rs, mid + 1, r, x, y);
		return ret;
	}
	inline int tree_sum(int x, int y)
	{
		int fx = top[x], fy = top[y], ret = 0;
		while (fx ^ fy)
		{
			if (dep[fx] > dep[fy]) ret += query_sum(1, 1, n, dfn[fx], dfn[x]), x = fa[fx], fx = top[x];
			else ret += query_sum(1, 1, n, dfn[fy], dfn[y]), y = fa[fy], fy = top[y];
		}
		if (dep[x] > dep[y]) swap(x, y);
		if (x == y) return ret;
		return ret + query_sum(1, 1, n, dfn[x] + 1, dfn[y]);
	}

	int query_max(int p, int l, int r, int x, int y)
	{
		if (x <= l && r <= y) return mx[p];
		pushdown(p);
		int mid = (l + r) >> 1, ret = -INF;
		if (x <= mid) ret = max(ret, query_max(ls, l, mid, x, y));
		if (y > mid) ret = max(ret, query_max(rs, mid + 1, r, x, y));
		return ret;
	}
	inline int tree_max(int x, int y)
	{
		int fx = top[x], fy = top[y], ret = -INF;
		while (fx ^ fy)
		{
			if (dep[fx] > dep[fy]) ret = max(ret, query_max(1, 1, n, dfn[fx], dfn[x])), x = fa[fx], fx = top[x];
			else ret = max(ret, query_max(1, 1, n, dfn[fy], dfn[y])), y = fa[fy], fy = top[y];
		}
		if (dep[x] > dep[y]) swap(x, y);
		if (x == y) return ret;
		return max(ret, query_max(1, 1, n, dfn[x] + 1, dfn[y]));
	}

	int query_min(int p, int l, int r, int x, int y)
	{
		if (x <= l && r <= y) return mn[p];
		pushdown(p);
		int mid = (l + r) >> 1, ret = INF;
		if (x <= mid) ret = min(ret, query_min(ls, l, mid, x, y));
		if (y > mid) ret = min(ret, query_min(rs, mid + 1, r, x, y));
		return ret;
	}
	inline int tree_min(int x, int y)
	{
		int fx = top[x], fy = top[y], ret = INF;
		while (fx ^ fy)
		{
			if (dep[fx] > dep[fy]) ret = min(ret, query_min(1, 1, n, dfn[fx], dfn[x])), x = fa[fx], fx = top[x];
			else ret = min(ret, query_min(1, 1, n, dfn[fy], dfn[y])), y = fa[fy], fy = top[y];
		}
		if (dep[x] > dep[y]) swap(x, y);
		if (x == y) return ret;
		return min(ret, query_min(1, 1, n, dfn[x] + 1, dfn[y]));
	}
}seg;

int main()
{
	scanf("%d", &n);
	for(register int i = 1, u, v, w; i < n; i++)
		scanf("%d%d%d", &u, &v, &w), ++u, ++v, add(u, v, w, i), add(v, u, w, i);
	dfs1(1), top[1] = 1, dfs2(1);
	for(register int i = 1; i <= n; i++) seg.update_node(1, 1, n, dfn[i], edg[i]);
	scanf("%d", &m);
	char op[5];
	for(int u, v; m; --m)
	{
		scanf("%s%d%d", op, &u, &v), ++u, ++v;
		if (op[0] == 'C') seg.update_node(1, 1, n, dfn[ver[u - 1]], v - 1);
		else if (op[0] == 'N') seg.tree_rev(u, v);
		else if (op[0] == 'S') printf("%d\n", seg.tree_sum(u, v));
		else if (op[1] == 'A') printf("%d\n", seg.tree_max(u, v));
		else printf("%d\n", seg.tree_min(u, v));
	}
}