Submission #288330

#	Time	Username	Problem	Language	Result	Execution time	Memory
288330		someone_aa	Discharging (NOI20_discharging)	C++17	100 / 100	968 ms	68144 KiB

Discharging

#include <bits/stdc++.h>
#define ll long long
#define pb push_back
#define mp make_pair
#define ld long double
#define pii pair<int,int>
#define pll pair<ll, ll>
#define sz(x) int(x.size())
using namespace std;
const int maxn = 1000100;
const ll inf = 1e18;
ll n, q, arr[maxn];

class node {
public:
	ll val;
	ll ind;
}tree[4*maxn];

node leaf_value(ll val, ll ind) {
	return {val, ind};
}

node merge_values(node a, node b) {
	node c;

	if(a.val > b.val)
		c = a;
	else if(a.val < b.val) 
		c = b;
	else {
		c.val = a.val;
		c.ind = min(a.ind, b.ind);
	}

	return c;
}

void build(int li=0, int ri=n-1, int index=1) {
	if(li == ri) {
		tree[index] = leaf_value(arr[li], li);
	}
	else {
		int mid = (li + ri) / 2;

		build(li, mid, 2*index);
		build(mid+1, ri, 2*index+1);

		tree[index] = merge_values(tree[2*index], tree[2*index+1]);
	}
}

node empty_node;
node query(int ql, int qr, int li=0, int ri=n-1, int index=1) {
	if(li > qr || ri < ql) return empty_node;
	else if(li >= ql && ri <= qr) return tree[index];
	else {
		int mid = (li + ri) / 2;

		return merge_values(query(ql, qr, li, mid, 2*index), query(ql, qr, mid+1, ri, 2*index+1));
	}
}

struct cht {
	struct line {
		ll k, b; ld x;
		ll val; bool isquery;

		line(ll _k = 0, ll _b = 0) :
			k(_k), b(_b), x(-inf), val(0), isquery(false) {}

		ll eval(ll x) const { return k * x + b; }
		bool parallel(const line& l) const {return k == l.k; }
		ld intersection(const line& l) const {
			if(parallel(l)) return inf;
			return (1.0*l.b - b) / (1.0 * k - l.k);
		}

		bool operator <(const line& l) const {
			if(l.isquery) return x < l.val;
			else return k < l.k;
		}
	};

	set<line> hull;
	typedef set<line>::iterator iter;

	bool cPrev(iter it) { return it != hull.begin(); }
	bool cNext(iter it) { return it != hull.end() && next(it) != hull.end(); }

	bool bad(const line &l1, const line &l2, const line &l3) {
		return l1.intersection(l3) <= l1.intersection(l2);
	}
	bool bad(iter it) {
		return cPrev(it) && cNext(it) && bad(*prev(it), *it, *next(it));
	}	

	iter update(iter it) {
		if(!cPrev(it)) return it;

		ld x = it -> intersection(*prev(it));
		line tmp(*it); tmp.x = x;

		it = hull.erase(it);
		return hull.insert(it, tmp);
	}

	void addLine(ll k, ll b) {
		line l(k, b);
		iter it = hull.lower_bound(l);
		if(it != hull.end() && l.parallel(*it)) {
			if(it->b < b) it = hull.erase(it);
			else return;
		}

		it = hull.insert(it, l);
		if(bad(it)) return (void) hull.erase(it);

		while(cPrev(it) && bad(prev(it))) hull.erase(prev(it));
		while(cNext(it) && bad(next(it))) hull.erase(next(it));

		it = update(it);
		if(cPrev(it)) update(prev(it));
		if(cNext(it)) update(next(it));
	}

	ll query(ll x) {
		if(hull.empty()) return -inf;

		line tmp;
		tmp.val = x; tmp.isquery = true;
		iter it = --hull.lower_bound(tmp);
		return it->eval(x);
	}

}ds;

ll pref[maxn];
ll dp[maxn];

int main() {
	cin>>n;

	empty_node = {INT_MIN, -1};

	for(int i=0;i<n;i++) {
		cin>>arr[i];
	}

	build();
	
	ll curr = n - 1;
	ll result = 0LL;

	vector<pll> values; 
	while(curr >= 0) {
		node curr_query = query(0, curr);
		values.pb(mp(curr_query.val, curr - curr_query.ind + 1));
		curr = curr_query.ind - 1;
	}

	values.pb(mp(0, 0));
	reverse(values.begin(), values.end());
	for(int i=1;i<sz(values);i++) {
		pref[i] = pref[i-1] + values[i].second;

		dp[i] = dp[i-1] + (n - pref[i-1]) * values[i].first;

	//	cout<<values[i].first<<" "<<values[i].second<<"\n";
		
		if(ds.hull.size() > 0) dp[i] = min(dp[i], values[i].first*(n) - ds.query(-values[i].first));
		ds.addLine(-pref[i-1], -dp[i-1]);
	}

	cout<<dp[sz(values) - 1]<<"\n";

	return 0;
}

Compilation message (stderr)

Discharging.cpp: In function 'int main()':
Discharging.cpp:153:5: warning: unused variable 'result' [-Wunused-variable]
  153 |  ll result = 0LL;
      |     ^~~~~~

• Subtask 1: 9 / 9
• Subtask 2: 13 / 13
• Subtask 3: 25 / 25
• Subtask 4: 11 / 11
• Subtask 5: 14 / 14
• Subtask 6: 28 / 28