This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
/*
ID: USACO_template
LANG: C++
PROG: 10542-005137
*/
#include <iostream> //cin , cout
#include <fstream> //fin, fout
#include <stdio.h> // scanf , pringf
#include <cstdio>
#include <algorithm> // sort , stuff
#include <stack> // stacks
#include <queue> // queues
#include <map>
#include <string>
#include <string.h>
#include <set>
using namespace std;
typedef pair<int, int> pii;
typedef vector<int> vi; /// adjlist without weight
typedef vector<pii> vii; /// adjlist with weight
typedef vector<pair<int,pii>> vpip; /// edge with weight
typedef long long ll;
#define mp make_pair
#define ff first
#define ss second
#define pb push_back
#define sz(x) (int)(x).size()
const int MOD = 1e9+7; // 998244353;
const int MX = 2e5+5; //
const ll INF = 1e18; //
#define MAXV 100007
#define MAXE 100007
bool debug;
int N, M, K;
vi adjlist[MAXV];
int d[MAXV], w[MAXV];
map<int, ll> dp[MAXV]; /// at each node, the extra fruit you can get at time t
void dfs(int v, int p=0) {
if(sz(adjlist[v])==0) {
if(d[v]!=0) dp[v][d[v]] = w[v];
return;
}
for(auto x : adjlist[v]) {
if(x == p) continue;
dfs(x, v);
// small to large merge, O(N log N)
if(sz(dp[v])<sz(dp[x])) dp[v].swap(dp[x]);
for(auto y : dp[x]) {
if(y.ss == 0) continue;
dp[v][y.ff] += y.ss;
}
}
if(debug) {
cout << v << " : before" << endl;
for(auto x : dp[v]) cout << " " << x.ff << " - " << x.ss << endl;
}
if(d[v]==0) return; // no fruit here
dp[v][d[v]] += w[v]; // now deal with insertion;
ll ps = 0LL;
for(auto it = dp[v].lower_bound(d[v]); it != dp[v].end() && ps < w[v]; it++) ps += it->ss;
if(ps <= w[v]) {
dp[v][d[v]] -= w[v];
} else {
auto it = dp[v].lower_bound(d[v]);
auto it2 = prev(dp[v].end());
while(it2 != it) dp[v].erase(it2--);
dp[v].erase(it);
}
if(debug) {
cout << v << " : after " << endl;
for(auto x : dp[v]) cout << " " << x.ff << " - " << x.ss << endl;
}
}
int main() {
debug = false;
ios_base::sync_with_stdio(false); cin.tie(0);
cin >> N >> M >> K;
for(int i=2; i<=N; i++) {
int a; cin >> a;
adjlist[a].pb(i);
}
for(int i=0;i<M;i++) {
int a, b, c; cin >> a >> b >> c;
d[a] = b; w[a] = c;
}
dfs(1);
ll ans = 0LL;
for(auto x : dp[1]) ans += x.ss;
cout << ans << endl;
if(debug) cout << endl << "EOL" << endl;
}
/**
6 4 10
1
2
1
4
4
3 4 5
4 7 2
5 4 1
6 9 3
4 3 3
1
2
2
2 2 5
3 3 10
4 4 10
*/
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