Submission #265535

#	Time	Username	Problem	Language	Result	Execution time	Memory
265535		square1001	Split the sequence (APIO14_sequence)	C++14	100 / 100	684 ms	83168 KiB

sequence

// APIO 2014 Problem 2 - Split the Sequence

#include <vector>
#include <iostream>
#include <algorithm>
using namespace std;
const long long inf = 1LL << 62;
int main() {
	// step #1. read input
	cin.tie(0);
	ios_base::sync_with_stdio(false);
	int N, K;
	cin >> N >> K; ++K;
	vector<int> A(N);
	for(int i = 0; i < N; ++i) {
		cin >> A[i];
	}
	// step #2. preparation for calculating the answer
	vector<int> S(N + 1);
	for(int i = 0; i < N; ++i) {
		S[i + 1] = S[i] + A[i];
	}
	// step #3. calculate the answer with dynamic programming
	vector<long long> dp(N + 1, inf);
	vector<vector<int> > pre(K + 1, vector<int>(N + 1, -1));
	dp[0] = 0;
	for(int i = 1; i <= K; ++i) {
		vector<int> st;
		for(int j = 0; j <= N; ++j) {
			while(st.size() >= 2) {
				int sz = st.size();
				__int128_t lc = __int128_t(dp[j] - dp[st[sz - 1]]) * (S[j] - S[st[sz - 2]]);
				__int128_t rc = __int128_t(dp[j] - dp[st[sz - 2]]) * (S[j] - S[st[sz - 1]]);
				if(lc <= rc) st.pop_back();
				else break;
			}
			st.push_back(j);
		}
		vector<long long> ndp(N + 1, inf);
		int pos = 0;
		for(int j = 1; j <= N; ++j) {
			while(pos + 1 != st.size()) {
				long long la = dp[st[pos]] - 1LL * S[st[pos]] * S[j];
				long long lb = dp[st[pos + 1]] - 1LL * S[st[pos + 1]] * S[j];
				if(la > lb) ++pos;
				else break;
			}
			long long x = dp[st[pos]] - 1LL * S[st[pos]] * S[j];
			if(ndp[j] > x) {
				ndp[j] = x;
				pre[i][j] = st[pos];
			}
			ndp[j] += 1LL * S[j] * S[j];
		}
		dp = ndp;
	}
	// step #4. print the answer
	cout << 1LL * S[N] * S[N] - dp[N] << endl;
	int pos = N;
	vector<bool> sol(N + 1, false);
	int cnt = 0;
	for(int i = K; i >= 2; --i) {
		pos = pre[i][pos];
		if(!sol[pos]) {
			sol[pos] = true;
			++cnt;
		}
	}
	for(int i = 1; i < N; ++i) {
		if(cnt < K - 1 && !sol[i]) {
			sol[i] = true;
			++cnt;
		}
	}
	for(int i = 1; i < N; ++i) {
		if(sol[i]) {
			cout << i << (--cnt ? ' ' : '\n');
		}
	}
	return 0;
}

Compilation message (stderr)

sequence.cpp: In function 'int main()':
sequence.cpp:42:18: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   42 |    while(pos + 1 != st.size()) {
      |          ~~~~~~~~^~~~~~~~~~~~

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