CF833D Red-Black Cobweb

题面

题解

点分治大火题。。。

设白边数量为$a$，黑边为$b$，则$2min(a,b)\geq max(a,b)$

即$2a\geq b\;\&\&2b\geq a$

考虑点分治时如何统计答案：

$2(a_1 +a_2) \geq b_1 + b_2$

$\therefore 2a_1-b_1\geq b_2-2a_2$

另外一边同理

于是我们可以愉快地用$sort+BIT$统计答案了

但是路径有可能重复计算，可以套一个$CDQ$分治什么的来搞一下

代码

#include<cstdio>
#include<cstring>
#include<algorithm>
#define RG register
#define clear(x, y) memset(x, y, sizeof(x));

namespace IO
{
	const int BUFSIZE = 1 << 20;
	char ibuf[BUFSIZE], *is = ibuf, *it = ibuf;
	inline char getchar() { if (is == it) it = (is = ibuf) + fread(ibuf, 1, BUFSIZE, stdin); return *is++; }
}

inline int read()
{
	int data = 0, w = 1;
	char ch = IO::getchar();
	while(ch != '-' && (ch < '0' || ch > '9')) ch = IO::getchar();
	if(ch == '-') w = -1, ch = IO::getchar();
	while(ch >= '0' && ch <= '9') data = data * 10 + (ch ^ 48), ch = IO::getchar();
	return data*w;
}

const int maxn(1e5 + 10), Mod(1e9 + 7);
inline int fastpow(int x, int y)
{
	int ans = 1;
	while(y)
	{
		if(y & 1) ans = 1ll * ans * x % Mod;
		x = 1ll * x * x % Mod, y >>= 1;
	}
	return ans;
}

struct edge { int next, to, val, col; } e[maxn << 1];
int n, head[maxn], e_num, size[maxn], Size, min, root;
struct qry { int r, b, v, o; } stk[maxn], q[maxn << 2];
int top, cntq, cntup, csum[maxn << 2], cmul[maxn << 2], vis[maxn];
inline bool cmpr(const qry &a, const qry &b)
	{ return a.r == b.r ? a.b < b.b : a.r < b.r; }

void clean(int x)
{
	while(x <= (n << 2 | 1)) csum[x] = 0, cmul[x] = 1, x += x & -x;
}

void add(int x, int v)
{
	while(x <= (n << 2 | 1))
		++csum[x], cmul[x] = 1ll * cmul[x] * v % Mod, x += x & -x;
}

int query_sum(int x)
{
	int ans = 0;
	while(x) ans += csum[x], x -= x & -x;
	return ans;
}

int query_mul(int x)
{
	int ans = 1;
	while(x) ans = 1ll * ans * cmul[x] % Mod, x -= x & -x;
	return ans;
}

inline void add_edge(int from, int to, int val, int col)
{
	e[++e_num] = (edge) {head[from], to, val, col};
	head[from] = e_num;
}

void getRoot(int x, int fa)
{
	size[x] = 1; int tot = 0;
	for(RG int i = head[x]; i; i = e[i].next)
	{
		int to = e[i].to; if(vis[to] || to == fa) continue;
		getRoot(to, x); tot = std::max(tot, size[to]);
		size[x] += size[to];
	}
	tot = std::max(tot, Size - size[x]);
	if(tot < min) min = tot, root = x;
}

void getVal(int x, int fa, int r, int b, int v)
{
	stk[++top] = (qry) {r, b, v, 0};
	for(RG int i = head[x]; i; i = e[i].next)
	{
		int to = e[i].to; if(vis[to] || to == fa) continue;
		getVal(to, x, r + (!e[i].col), b + e[i].col, 1ll * v * e[i].val % Mod);
	}
}

int ans = 1;
void CDQ(int l, int r)
{
	if(l >= r) return;
	int mid = (l + r) >> 1;
	CDQ(l, mid); CDQ(mid + 1, r);
	int j = l;
	for(RG int i = mid + 1; i <= r; i++)
	{
		if(!q[i].o) continue;
		while(q[j].r <= q[i].r && j <= mid)
		{
			if(!q[j].o) add(q[j].b, q[j].v);
			++j;
		}
		ans = 1ll * ans * query_mul(q[i].b) % Mod *
			fastpow(q[i].v, query_sum(q[i].b)) % Mod;
	}
	for(RG int i = l; i < j; i++) if(!q[i].o) clean(q[i].b);
	std::inplace_merge(q + l, q + mid + 1, q + r + 1, cmpr);
}

void calc(int x)
{
	int PLUS = n << 1 | 1;
	cntq = cntup = 0;
	for(RG int i = head[x]; i; i = e[i].next)
	{
		int to = e[i].to; if(vis[to]) continue;
		top = 0; getVal(to, x, !e[i].col, e[i].col, e[i].val);
		for(RG int j = 1; j <= top; j++)
		{
			int a = stk[j].r, b = stk[j].b, c = 2 * a - b, d = 2 * b - a;
			q[++cntq] = (qry) {c + PLUS, d + PLUS, stk[j].v, 1};
		}
		for(RG int j = 1; j <= top; j++)
		{
			int a = stk[j].r, b = stk[j].b, c = 2 * a - b, d = 2 * b - a;
			q[++cntq] = (qry) {-c + PLUS, -d + PLUS, stk[j].v, 0};
			if(2 * std::min(a, b) >= std::max(a, b))
				ans = 1ll * ans * stk[j].v % Mod;
		}
	}
	CDQ(1, cntq);
}

void dfs(int x)
{
	vis[x] = 1; calc(x);
	for(RG int i = head[x]; i; i = e[i].next)
	{
		int to = e[i].to; if(vis[to]) continue;
		Size = min = size[to]; getRoot(to, x); dfs(root);
	}
}

int main()
{
	Size = min = n = read();
	for(int i = 1, a, b, c, d; i < n; i++)
		a = read(), b = read(), c = read(), d = read(),
		add_edge(a, b, c, d), add_edge(b, a, c, d);
	for(RG int i = 1; i <= (n << 2 | 1); i++) csum[i] = 0, cmul[i] = 1;
	getRoot(1, 0); dfs(root);
	printf("%d\n", ans);
	return 0;
}