Submission #783202

#	Time	Username	Problem	Language	Result	Execution time	Memory
783202		Charizard2021	Discharging (NOI20_discharging)	C++17	100 / 100	102 ms	33492 KiB

Discharging

#include<bits/stdc++.h>
using namespace std;
#define IOS ios::sync_with_stdio(false);; cin.tie(NULL)
void selfMax(long long& a, long long b){
    a = max(a, b);
}
void selfMin(long long& a, long long b){
    a = min(a, b);
}
template<typename T> istream& operator>>(istream& in, vector<T>& a) {for(auto &x : a) in >> x; return in;};
template<typename T1, typename T2> istream& operator>>(istream& in, pair<T1, T2>& x) {return in >> x.first >> x.second;}

template<typename T1, typename T2> ostream& operator<<(ostream& out, const pair<T1, T2>& x) {return out << x.first << ' ' << x.second;}
template<typename T> ostream& operator<<(ostream& out, vector<T>& a) {for(auto &x : a) out << x << ' '; return out;};
template<typename T> ostream& operator<<(ostream& out, vector<vector<T> >& a) {for(auto &x : a) out << x << '\n'; return out;};
template<typename T1, typename T2> ostream& operator<<(ostream& out, vector<pair<T1, T2> >& a) {for(auto &x : a) out << x << '\n'; return out;};

/*

Use DSU dsu(N);

*/
struct DSU {
	vector<long long> adj2;
	DSU(long long N) { adj2 = vector<long long>(N, -1); }

	// get representive component (uses path compression)
	long long get(long long x) { return adj2[x] < 0 ? x : adj2[x] = get(adj2[x]); }

	bool same_set(long long a, long long b) { return get(a) == get(b); }

	long long size(long long x) { return -adj2[get(x)]; }

	bool unite(long long x, long long y) {  // union by size
		x = get(x), y = get(y);
		if (x == y) return false;
		if (adj2[x] > adj2[y]) swap(x, y);
		adj2[x] += adj2[y]; adj2[y] = x;
		return true;
	}
};
/*

Run with Bit<long long> BIT

*/
template <class T> class BIT {
    private:
        long long size;
        vector<T> bit;
        vector<T> arr;
    public:
        BIT(long long size) : size(size), bit(size + 1), arr(size) {}
        void set(long long ind, long long val) { add(ind, val - arr[ind]); }
        void add(long long ind, long long val) {
            arr[ind] += val;
            ind++;
            for (; ind <= size; ind += ind & -ind) { bit[ind] += val; }
        }
        T pref_sum(long long ind) {
            ind++;
            T total = 0;
            for (; ind > 0; ind -= ind & -ind) { total += bit[ind]; }
            return total;
        }
};
/*

Change Comb for specific Seg tree probs, but run with Seg<long long> Seg;

*/
template<class T> struct Seg {
	const T ID = 1e18; T comb(T a, T b) { return min(a,b); }
	long long n; vector<T> seg;
	void init(long long _n) { n = _n; seg.assign(2*n,ID); }
	void pull(long long p) { seg[p] = comb(seg[2*p],seg[2*p+1]); }
	void upd(long long p, T val) {
		seg[p += n] = val; for (p /= 2; p; p /= 2) pull(p); }
	T query(long long l, long long r) {
		T ra = ID, rb = ID;
		for (l += n, r += n+1; l < r; l /= 2, r /= 2) {
			if (l&1) ra = comb(ra,seg[l++]);
			if (r&1) rb = comb(seg[--r],rb);
		}
		return comb(ra,rb);
	}
};
struct ConvexHull {
	deque<pair<long long, long long> > dq;
	long long yVal(pair<long long, long long> line,long long x){
		return line.first * x + line.second;
	}
	long long query(long long x){
		while(dq.size() > 1){
			if(yVal(dq[0], x) < yVal(dq[1], x)){
				dq.pop_front();
			}
            else{
				break;
			}
		}
		return yVal(dq[0], x);
	}
	long double Intersect(long long a,long long b,long long c,long long d){
		return (long double)(d - b)/(a - c);
	}
	long double intersect(pair<long long, long long> val1, pair<long long, long long> val2){
		return Intersect(val1.first, val1.second, val2.first, val2.second);
	}
	void insertLine(long long m, long long b){
		pair<long long,long long> line = make_pair(m, b);
		while(dq.size() > 1){
			long long s = dq.size();
			if(intersect(dq[s - 1], line) <= intersect(dq[s - 2], line)){
				dq.pop_back();
			}
            else{
				break;
			}
		}
		dq.push_back(line);
	}
} convexHullDynamic;
int main(){
    IOS;
    long long n;
    cin >> n;
    vector<long long> t(n + 1);
    for(long long i = 1; i <= n; i++){
        cin >> t[i];
    }
    long long prefMax[n];
    prefMax[0] = 0;
    for(long long i = 1; i <= n; i++){
        prefMax[i] = max(prefMax[i - 1], t[i]);
    }
    long long dp[n + 1];
	convexHullDynamic.dq.clear();
	convexHullDynamic.insertLine(-n, 0);
	for(long long i = 1; i <= n; i++){
		if(prefMax[i - 1] < t[i]){
			dp[i] = -convexHullDynamic.query(t[i]);
			long long cur = i;
			while(cur < n && t[cur] <= t[i]){
				cur++;
			}
			convexHullDynamic.insertLine(cur - n - 1, -dp[i]);
		}else{
			dp[i] = dp[i - 1];
		}
	}
    cout << dp[n] << "\n";
}

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