[POI2014]HOT-Hotels 加强版

长链剖分优化 \(dp\) 模板

不过这 \(dp\) 真毒

\(\text{Code}\)

#include <cstdio>
#define RE register
#define IN inline
using namespace std;
typedef long long LL;

const int N = 1e5 + 5;
int n, h[N], tot, len[N], son[N];
struct edge{int to, nxt;}e[N << 1];
IN void add(int x, int y){e[++tot] = (edge){y, h[x]}, h[x] = tot;}
void dfs(int x, int fa)
{
	for(RE int i = h[x]; i; i = e[i].nxt)
	{
		int v = e[i].to;
		if (v == fa) continue;
		dfs(v, x), son[x] = (len[v] > len[son[x]] ? v : son[x]);
	}
	len[x] = len[son[x]] + 1;
}

LL tmp[N << 2], *id = tmp, *f[N], *g[N], ans;
void DP(int x, int fa)
{
	if (son[x]) f[son[x]] = f[x] + 1, g[son[x]] = g[x] - 1, DP(son[x], x);
	f[x][0] = 1, ans += g[x][0];
	for(RE int i = h[x]; i; i = e[i].nxt)
	{
		int v = e[i].to;
		if (v == fa || v == son[x]) continue;
		f[v] = id, id += len[v] << 1, g[v] = id, id += len[v] << 1, DP(v, x);
		for(RE int j = 0; j < len[v]; j++)
		{
			if (j) ans += f[x][j - 1] * g[v][j];
			ans += g[x][j + 1] * f[v][j];
		}
		for(RE int j = 0; j < len[v]; j++)
		{
			g[x][j + 1] += f[x][j + 1] * f[v][j];
			if (j) g[x][j - 1] += g[v][j];
			f[x][j + 1] += f[v][j];
		}
	}
}

int main()
{
	scanf("%d", &n);
	for(RE int i = 1, x, y; i < n; i++) scanf("%d%d", &x, &y), add(x, y), add(y, x);
	dfs(1, 0), f[1] = id, id += len[1] << 1, g[1] = id, id += len[1] << 1, DP(1, 0);
	printf("%lld\n", ans);
}