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Submission #943797

# Submission time Handle Problem Language Result Execution time Memory
943797 2024-03-12T00:50:48 Z vjudge1 Arboras (RMI20_arboras) C++17
100 / 100
 800 ms 57712 KB 
#include <bits/stdc++.h>
using namespace std;

#define int long long
#define pii pair <int, int>
#define fi first
#define se second
#define mp make_pair

const int NM = 1e5, LOG = 16, MOD = 1e9+7;

struct node{
	int sz, f, g;
};

struct tag{
	pii f, g;
	tag(){
		f = g = mp(1, 0);
	}
	tag(pii y, pii z){
		f = y, g = z;
	}
};

int n, q, p[NM+5], d[NM+5], dep[NM+5], sumd[NM+5], sz[NM+5], f[NM+5], g[NM+5], jump[NM+5][LOG+5], cur = 0;
vector <int> son[NM+5];
int head[NM+5], timer = 0, tin[NM+5], tour[NM+5], tout[NM+5];
node st[4*NM+5];
tag lazy[4*NM+5];

void dfs_sz(int u){
	dep[u] = (u == 1 ? 0 : dep[p[u]]+1);
	sumd[u] = sumd[p[u]]+d[u];
	sz[u] = 1;
	f[u] = g[u] = 0;
	for (int v : son[u]){
		dfs_sz(v);
		sz[u] += sz[v];
		if (f[v]+d[v] > f[u]){
			g[u] = f[u];
			f[u] = f[v]+d[v];
		}
		else if (f[v]+d[v] > g[u]){
			g[u] = f[v]+d[v];
		}
	}
	cur += 2*sumd[u];
}

void build_sparse(){
	for (int i = 1; i <= n; i++) jump[i][0] = p[i];
	for (int j = 1; j <= LOG; j++)
		for (int i = 1; i <= n; i++)
			jump[i][j] = jump[jump[i][j-1]][j-1];
}

void dfs_hld(int u){
	tin[u] = ++timer;
	tour[timer] = u;
	int mxVtx = -1;
	for (int v : son[u]){
		if (mxVtx == -1 || sz[v] > sz[mxVtx]) mxVtx = v;
	}
	if (mxVtx != -1){
		head[mxVtx] = head[u];
		dfs_hld(mxVtx);
	}
	for (int v : son[u]){
		if (v == mxVtx) continue;
		head[v] = v;
		dfs_hld(v);
	}
	tout[u] = timer;
}

node operator + (node a, node b){
	node c;
	c.sz = a.sz+b.sz;
	c.f = a.f+b.f;
	c.g = a.g+b.g;
	return c;
}

void build(int id, int l, int r){
	if (l == r){
		int u = tour[l];
		st[id].sz = 1;
		st[id].f = f[u]+sumd[u];
		st[id].g = g[u]+sumd[u];
		return;
	}
	int mid = (l+r)/2;
	build(2*id, l, mid);
	build(2*id+1, mid+1, r);
	st[id] = st[2*id]+st[2*id+1];
}

void apply(int id, tag T){
	if (T.f.fi == 1) st[id].f += T.f.se*st[id].sz; else st[id].f = T.f.se*st[id].sz;
	if (T.g.fi == 1) st[id].g += T.g.se*st[id].sz; else st[id].g = T.g.se*st[id].sz;
}

pii operator + (pii a, pii b){
	pii c;
	if (b.fi == 2) c = mp(2, b.se);
	else if (a.fi == 2) c = mp(2, a.se+b.se);
	else c = mp(1, a.se+b.se);
	return c;
}

tag operator + (tag a, tag b){
	tag c;
	c.f = a.f+b.f;
	c.g = a.g+b.g;
	return c;
}

void down(int id){
	apply(2*id, lazy[id]); apply(2*id+1, lazy[id]);
	lazy[2*id] = lazy[2*id]+lazy[id]; lazy[2*id+1] = lazy[2*id+1]+lazy[id];
	lazy[id] = tag();
}

void swap(int id, int l, int r, int i){
	if (i < l || i > r) return;
	if (l == r){
		swap(st[id].f, st[id].g);
		return;
	}
	down(id);
	int mid = (l+r)/2;
	swap(2*id, l, mid, i);
	swap(2*id+1, mid+1, r, i);
	st[id] = st[2*id]+st[2*id+1];
}

void cover(int id, int l, int r, int u, int v, pii P){
	if (v < l || u > r) return;
	if (l >= u && r <= v){
		pii x = mp(1, 0), y = mp(1, 0);
		if (P.fi != -1) x = mp(2, P.fi);
		if (P.se != -1) y = mp(2, P.se);
		tag T = tag(x, y);
		apply(id, T);
		lazy[id] = lazy[id]+T;
		return;
	}
	down(id);
	int mid = (l+r)/2;
	cover(2*id, l, mid, u, v, P);
	cover(2*id+1, mid+1, r, u, v, P);
	st[id] = st[2*id]+st[2*id+1];
}

void add(int id, int l, int r, int u, int v, pii P){
	if (v < l || u > r) return;
	if (l >= u && r <= v){
		tag T = tag(mp(1, P.fi), mp(1, P.se));
		apply(id, T);
		lazy[id] = lazy[id]+T;
		return;
	}
	down(id);
	int mid = (l+r)/2;
	add(2*id, l, mid, u, v, P);
	add(2*id+1, mid+1, r, u, v, P);
	st[id] = st[2*id]+st[2*id+1];
}

node get(int id, int l, int r, int i){
	if (l == r) return st[id];
	down(id);
	int mid = (l+r)/2;
	if (i <= mid) return get(2*id, l, mid, i);
	return get(2*id+1, mid+1, r, i);
}

void buff_f(int u, int a, int val){
	while (true){
		if (head[u] == head[a]){
			cover(1, 1, n, tin[a], tin[u], mp(val, -1));
			break;
		}
		cover(1, 1, n, tin[head[u]], tin[u], mp(val, -1));
		u = p[head[u]];
	}
}

void update(int u, int su, int a, int val){
	if (u == 0 || dep[u] < dep[a]) return;
	vector <int> arr = {};
	while (true){
		if (get(1, 1, n, tin[u]).f == get(1, 1, n, tin[su]).f){
			int v = u, tmp = get(1, 1, n, tin[su]).f;
			for (int i = LOG; i >= 0; i--){
				if (jump[v][i] == 0 || dep[jump[v][i]] < dep[a]) continue;
				if (get(1, 1, n, tin[jump[v][i]]).f == tmp) v = jump[v][i];
			}
			buff_f(u, v, val);
			u = p[v];
		}
		if (u == 0 || dep[u] < dep[a]) break;
		arr.push_back(u);
		su = u;
		u = p[u];
	}
	for (int u : arr){
		swap(1, 1, n, tin[u]);
		cover(1, 1, n, tin[u], tin[u], mp(val, -1));
	}
}

signed main(){
	ios_base::sync_with_stdio(0);
	cin.tie(0);
	cout.tie(0);
	
	cin >> n;
	for (int i = 2; i <= n; i++){
		cin >> p[i];
		p[i]++;
		son[p[i]].push_back(i);
	}
	for (int i = 2; i <= n; i++){
		cin >> d[i];
	}
	dfs_sz(1);
	build_sparse();
	head[1] = 1;
	dfs_hld(1);
	build(1, 1, n);
	
	cout << (st[1].f+st[1].g-cur)%MOD << '\n';
	cin >> q;
	while (q--){
		int x, y; cin >> x >> y;
		x++;
		cur += 2*sz[x]*y;
		int u = x, tmp = get(1, 1, n, tin[x]).f+y;
		for (int i = LOG; i >= 0; i--){
			if (jump[u][i] == 0) continue;
			if (tmp > get(1, 1, n, tin[jump[u][i]]).f) u = jump[u][i];
		}
		update(p[x], x, u, tmp);
		u = p[u];
		if (u > 0 && tmp > get(1, 1, n, tin[u]).g){
			cover(1, 1, n, tin[u], tin[u], mp(-1, tmp));
		}
		add(1, 1, n, tin[x], tout[x], mp(y, y));
		cout << (st[1].f+st[1].g-cur)%MOD << '\n';
	}
	return 0;
}

Subtask #1
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 7 ms 27480 KB Output is correct
2 Correct 8 ms 27228 KB Output is correct
3 Correct 6 ms 27228 KB Output is correct

Subtask #2
13.0 / 13.0

# Verdict Execution time Memory Grader output
1 Correct 545 ms 52496 KB Output is correct
2 Correct 348 ms 51452 KB Output is correct
3 Correct 313 ms 51740 KB Output is correct

Subtask #3
31.0 / 31.0

# Verdict Execution time Memory Grader output
1 Correct 787 ms 54168 KB Output is correct
2 Correct 670 ms 56672 KB Output is correct
3 Correct 583 ms 52840 KB Output is correct

Subtask #4
45.0 / 45.0

# Verdict Execution time Memory Grader output
1 Correct 7 ms 27480 KB Output is correct
2 Correct 8 ms 27228 KB Output is correct
3 Correct 6 ms 27228 KB Output is correct
4 Correct 545 ms 52496 KB Output is correct
5 Correct 348 ms 51452 KB Output is correct
6 Correct 313 ms 51740 KB Output is correct
7 Correct 787 ms 54168 KB Output is correct
8 Correct 670 ms 56672 KB Output is correct
9 Correct 583 ms 52840 KB Output is correct
10 Correct 800 ms 54356 KB Output is correct
11 Correct 699 ms 56948 KB Output is correct
12 Correct 575 ms 53040 KB Output is correct
13 Correct 767 ms 57276 KB Output is correct
14 Correct 713 ms 57712 KB Output is correct