Submission #131455

#	Time	Username	Problem	Language	Result	Execution time	Memory
131455		someone_aa	Split the sequence (APIO14_sequence)	C++17	50 / 100	288 ms	131072 KiB

sequence

#include <bits/stdc++.h>
#define ll long long 
#define pb push_back
#define mp make_pair
#define x real()
#define y imag()
#define pll pair<ll, ll>
using namespace std;
typedef long long ftype;
typedef complex<ftype> point;
const int maxn = 10100;
ll arr[maxn], n, k;
ll prefix[maxn], suffix[maxn];

ll dot(point a, point b) {
	return (a*conj(b)).x;
}

ll fx(point a, ll d) {
	return dot(a, {d, 1});
}

ll dp[2][maxn];
int dppntr[210][maxn];

class node {
public:
	point f;
	ll lb, rb;
	node *lchild, *rchild;
	int ind;

	node(ll _lb, ll _rb) {
		lb = _lb;
		rb = _rb;
		lchild = rchild = NULL;
		f = {0, INT_MIN};
		ind = 0;
	}
	void update(point nw, int _ind) {
		ll mid = (lb + rb) / 2;

		// SOMETHING NOT OKAY HERE
		bool lft = fx(nw, lb) > fx(f, lb);
		bool md = fx(nw, mid) > fx(f, mid);

		if(md) {
			swap(nw, f);
			swap(ind, _ind);
		}

		if(lb == rb) return;

		if(lft == md) {
			// they don't intersect in left, they might intersect in right part
			if(rchild == NULL) rchild = new node(mid+1, rb);
			rchild -> update(nw, _ind);
		}
		else {
			// they intersect in left part, continue searching in left
			if(lchild == NULL) lchild = new node(lb, mid);
			lchild -> update(nw, _ind);
		}
	}
	pll query(ll p) {
		ll mid = (lb + rb) / 2;

		if(lb == rb) return {fx(f, p), ind};
		else {
			if(p <= mid) {
				pll val = {INT_MIN, INT_MIN};
				if(lchild != NULL) val = lchild -> query(p);
				
				if(fx(f, p) > val.first) return {fx(f, p), ind};
				else return val;
			}
			else {
				pll val = {INT_MIN, INT_MIN};
				if(rchild != NULL) val = rchild -> query(p);
				
				if(fx(f, p) > val.first) return mp(fx(f, p), ind);
				else return val;
			}
		}
	}
};

int main() {
	cin>>n>>k;
	for(int i=1;i<=n;i++) {
		cin>>arr[i];
		prefix[i] = prefix[i-1] + arr[i];
	}

	for(int i=n;i>=1;i--) {
		suffix[i] = suffix[i+1] + arr[i];
	}

	for(int i=1;i<=n;i++) {
		dp[1][i] = prefix[i] * suffix[i+1];
	}

 	for(int p=2;p<=k;p++) {
 		node *root = new node(0, (1LL << 37));
 		for(int i=1;i<=n;i++) {
 			root -> update({-prefix[i-1], dp[(p-1)%2][i-1]}, i-1);

 			if(i < p) {
 				dp[p%2][i] = INT_MIN;
 				continue;
 			} 

 			pll qr = root -> query(suffix[i+1]);

 			dp[p%2][i] = qr.first + prefix[i] * suffix[i+1];
 			dppntr[p][i] = qr.second;
 		
 			//root -> update({-prefix[i-1], dp[p-1][i-1]}, i-1);
 		}

 		/*for(int i=1;i<=n;i++) {
 			for(int lst=i;lst>=1;lst--) {
 				if(dp[p-1][lst-1] + (prefix[i] - prefix[lst-1]) * suffix[i+1] > dp[p][i]) {
 					dp[p][i] = dp[p-1][lst-1] + (prefix[i] - prefix[lst-1]) * suffix[i+1];
 					dppntr[p][i] = lst-1;
 				}
 			}
 		}*/
 	}
 	
 	ll result = LLONG_MIN;
 	ll lst = 0;
 	for(int i=1;i<n;i++) {
 		if(dp[k%2][i] >= result) {
 			result = dp[k%2][i];
 			lst = i;
 		}
 	}

 	/*for(int p=1;p<=k;p++) {
 		cout<<p<<": ";
 		for(int i=1;i<=n;i++) {
 			cout<<dp[p][i]<<" ";
 		} cout<<"\n";
 	}*/

 	//lst++;
 	//cout<<lst<<"\n";

 	vector<int>v;
 	int p = k;
 	while(lst > 0) {
 		v.pb(lst);
 		lst = dppntr[p][lst];
 		p--;
 	}

 	//reverse(v.begin(), v.end());

 	cout<<result<<"\n";
 	for(int i:v) {
 		cout<<i<<" ";
 	} cout<<"\n";

 	//cout<<"KRAJ: "<<v.size()<<"\n";
}

• Subtask 1: 11 / 11
• Subtask 2: 11 / 11
• Subtask 3: 11 / 11
• Subtask 4: 17 / 17
• Subtask 5: 0 / 21
• Subtask 6: 0 / 29