Submission #25210

#	Time	Username	Problem	Language	Result	Execution time	Memory
25210		RezwanArefin01	Split the sequence (APIO14_sequence)	C++14	100 / 100	753 ms	86556 KiB

sequence

//Bismillahir Rahmanir Rahim
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const int N = 100001, K = 201; 
ll dp[2][N], p[N];
int par[K][N];
     
struct CHT{
	vector<ll> m, b, id;
	int ptr = 0; 
	bool bad(int l1, int l2, int l3) {
		return (b[l3] - b[l1]) * (m[l1] - m[l2]) <= (b[l2] - b[l1]) * (m[l1] - m[l3]);
	} 
	void clear() {
		ptr = 0;
		m.clear(); 
		b.clear();
		id.clear();
	}
	void add(ll _m, ll _b, ll idx) { 
		m.push_back(_m);
		b.push_back(_b);  
		id.push_back(idx); 
		int s = m.size(); 
		while(s >= 3 && bad(s-3, s-2, s-1)) {
			s--; 
			m.erase(m.end()-2);
			b.erase(b.end()-2); 
			id.erase(id.end()-2);
		}
	}  
	ll f(int i, ll x) { return m[i]*x + b[i]; }
 
	pair<ll,ll>  query(ll x) {    
		if(ptr >= m.size()) ptr = m.size()-1;
		while(ptr < m.size()-1 && 
			f(ptr+1, x) >= f(ptr, x)) ptr++; 
		return {id[ptr], f(ptr, x)};
	}
}; 
 
 
void recon(int k, int n) {
	if(!k) return; 
	recon(k-1, par[k][n]); 
	cout<<par[k][n]<<" ";
}

int main(int argc, char const *argv[]) {
#ifdef LOCAL_TESTING
	freopen("in", "r", stdin);
#endif
	int n, kk; cin>>n>>kk;
	for(int i=1; i <= n; i++) {
		cin>>p[i];
		p[i] += p[i-1];
	} 
	for(int i=0; i<=1; i++) 
		for(int j=0; j<=n; j++) 
			dp[i][j] = -1e18; 
	for(int i=0; i<=n; i++) 
		dp[0][i] = 0; 
	CHT ds; 
 
	for(int _k=1; _k <= kk; _k++) {
		ds.clear();
		ds.add(0, 0, 0);
		int k = _k & 1;
		for(int i=_k; i<=n; i++) {  
			auto it = ds.query(p[i]); 
			dp[k][i] = it.second; 
			ds.add(p[i], dp[k ^ 1][i] - p[i] * p[i], i);
			par[_k][i] = it.first;
		}
	}  
	cout<<dp[kk & 1][n]<<endl; 	
	recon(kk, n);
}

Compilation message (stderr)

sequence.cpp: In member function 'std::pair<long long int, long long int> CHT::query(ll)':
sequence.cpp:36:10: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
   if(ptr >= m.size()) ptr = m.size()-1;
          ^
sequence.cpp:37:13: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
   while(ptr < m.size()-1 && 
             ^

• Subtask 1: 11 / 11
• Subtask 2: 11 / 11
• Subtask 3: 11 / 11
• Subtask 4: 17 / 17
• Subtask 5: 21 / 21
• Subtask 6: 29 / 29