洛谷P4719 【模板】动态dp(ddp LCT)

题意

题目链接

Sol

动态dp板子题。有些细节还没搞懂，待我研究明白后再补题解。。。

#include<bits/stdc++.h>
#define LL long long
using namespace std;
const int MAXN = 1e5 + 10, INF = INT_MAX;
template<typename A, typename B> inline bool chmax(A &x, B y) {
	return x < y ? x = y, 1 : 0;
}
inline int read() {
	char c = getchar(); int x = 0, f = 1;
	while(c < '0' || c > '9') {if(c == '-') f = -1; c = getchar();}
	while(c >= '0' && c <= '9') x = x * 10 + c - '0', c = getchar();
	return x * f;
}
int N, M, a[MAXN], f[MAXN][2];
struct Ma {
	LL m[3][3];
	Ma() {
		memset(m, -0x3f, sizeof(m));
	}
	Ma operator * (const Ma &rhs) const {
		Ma ans;
		for(int i = 1; i <= 2; i++)
			for(int j = 1; j <= 2; j++)
				for(int k = 1; k <= 2; k++)
					chmax(ans.m[i][j], m[i][k] + rhs.m[k][j]);
		return ans;
	}
}val[MAXN], sum[MAXN];
vector<int> v[MAXN];
int ch[MAXN][2], fa[MAXN];
#define ls(x) ch[x][0]
#define rs(x) ch[x][1]
void update(int k) {
	sum[k] = val[k];
	if(rs(k)) sum[k] = sum[k] * sum[rs(k)];
	if(ls(k)) sum[k] = sum[ls(k)] * sum[k];
}
bool ident(int x) {
	return rs(fa[x]) == x;
}
bool isroot(int x) {
	return ls(fa[x]) != x && rs(fa[x]) != x;
}
void connect(int x, int _fa, int tag) {
	fa[x] = _fa;
	ch[_fa][tag] = x;
}
void rotate(int x) {
	int y = fa[x], r = fa[y], yson = ident(x), rson = ident(y);
	int b = ch[x][yson ^ 1];
	fa[x] = r;
	if(!isroot(y)) connect(x, r, rson);
	connect(b, y, yson);
	connect(y, x, yson ^ 1);
	update(y); update(x);
}
void splay(int x) {
	for(int y = fa[x]; !isroot(x); rotate(x), y = fa[x])
		if(!isroot(y))
			rotate(ident(y) == ident(x) ? y : x);
}
void access(int x) {
	for(int y = 0; x; x = fa[y = x]) {
		splay(x);
		if(rs(x)) {
			val[x].m[1][1] += max(sum[rs(x)].m[1][1], sum[rs(x)].m[2][1]);
			val[x].m[2][1] += sum[rs(x)].m[1][1];
		}
		if(y) {
			val[x].m[1][1] -= max(sum[y].m[1][1], sum[y].m[2][1]);
			val[x].m[2][1] -= sum[y].m[1][1];
		}
		val[x].m[1][2] = val[x].m[1][1];
		rs(x) = y;
		update(x);
	}
}
int Modify(int p, int v) {
	access(p); splay(p);
	val[p].m[2][1] -= a[p] - v;
	update(p);
	a[p] = v;
	splay(1);
	return max(sum[1].m[1][1], sum[1].m[2][1]);
}
void dfs(int x, int _fa) {
	fa[x] = _fa;
	f[x][1] = a[x];
	for(auto &to : v[x]) {
		if(to == _fa) continue;
		dfs(to, x);
		f[x][0] += max(f[to][0], f[to][1]);
		f[x][1] += f[to][0];
	}
	val[x].m[1][1] = f[x][0]; val[x].m[1][2] = f[x][0];
	val[x].m[2][1] = f[x][1]; val[x].m[2][2] = -INF;
	update(x);
//	sum[x] = val[x];
}
int main() {
	//freopen("a.in", "r", stdin);
	N = read(); M = read();
	for(int i = 1; i <= N; i++) a[i] = read();
	for(int i = 1; i < N; i++) {
		int x = read(), y = read();
		v[x].push_back(y);
		v[y].push_back(x);
	}
	dfs(1, 0);
	while(M--) {
		int x = read(), y = read();
		printf("%d\n", Modify(x, y));
	}
	return 0;
}